THE UNIVERSITY OF ADELAIDE
School of Electrical and Electronic Engineering
Phase Advance Modulation of
Low-Cost Power Electronic Converters
for SPM Wind Turbine Generators
Mehanathan Pathmanathan
A thesis presented for the degree of Doctor of Philosophy
April 2012
i
Dedicated to my parents
ii
Table of Contents
Table of Contents ............................................................................................................ iii
List of Figures ................................................................................................................. vii
Abstract ........................................................................................................................ xiv
Statement of Originality ................................................................................................ xvi
Acknowledgements ...................................................................................................... xvii
Nomenclature ................................................................................................................ xx
Acronyms ..................................................................................................................... xxii
Chapter 1:
Introduction .................................................................................................................. 1
1.1
Background .............................................................................................................1
1.2
Fundamentals of Wind Power .................................................................................2
1.3
Wind Turbine Generators........................................................................................4
1.3.1
Squirrel-Cage Induction Generator ..................................................................5
1.3.2
Doubly-Fed Induction Generator .....................................................................6
1.3.3
Surface Permanent Magnet Generator ............................................................6
1.4
AC/DC Power Electronic Converters ........................................................................7
1.4.1
Rectifier ..........................................................................................................7
1.4.2
Switched Mode Rectifier (SMR) .......................................................................9
1.4.3
Inverter ......................................................................................................... 11
iii
1.5
Thesis Overview .................................................................................................... 12
1.5.1
Research Gap ................................................................................................ 12
1.5.2
Original Contributions ................................................................................... 13
1.5.3
Thesis Outline ............................................................................................... 14
Chapter 2:
2.1
Surface Permanent Magnet Generator Models ..................................................... 17
2.1.1
Single-Phase Equivalent Circuit...................................................................... 18
2.1.2
Normalisation of Generator Parameters ........................................................ 23
2.2
Single Phase Power Electronic Converter Models .................................................. 24
2.2.1
Rectifier ........................................................................................................ 24
2.2.2
SMR .............................................................................................................. 27
2.2.3
Inverter ......................................................................................................... 29
2.2.4
Performance Predictions ............................................................................... 30
2.3
Conclusion ............................................................................................................ 32
Chapter 3:
AC/DC Power Electronic Converter Simulation Models .................................................35
3.1
Analytical Conversion between AC/DC Quantities ................................................. 36
3.2
Three Phase PWM Inclusive Simulation Models .................................................... 38
3.2.1
Rectifier ........................................................................................................ 39
3.2.2
SMR .............................................................................................................. 44
3.2.3
Inverter ......................................................................................................... 50
3.3
Simplified Simulation Model ................................................................................. 53
3.3.1
Simplified Model for Single-switch SMR ........................................................ 54
3.3.2
Simplified Semi-bridge SMR Model ............................................................... 55
3.3.3
Simplified Inverter Model .............................................................................. 56
3.4
Simplified and PWM inclusive Model Comparison ................................................. 57
3.4.1
Ideal Single-Switch and Semi-Bridge Comparison .......................................... 57
3.4.2
Comparison of Ideal Inverter Simulation Results ........................................... 59
3.5
Conclusion ............................................................................................................ 62
Chapter 4:
4.1
iv
Analytical Modelling of Surface PM Generator Drives ...................................................17
Generator Modelling ....................................................................................................63
Parameter Testing ................................................................................................ 64
4.1.1
Open-Circuit Test .......................................................................................... 65
4.1.2
Resistance Test ............................................................................................. 68
4.1.3
Short-Circuit Test .......................................................................................... 69
4.1.4
4.2
Summary of Parameters ................................................................................ 70
Performance Testing ............................................................................................. 71
4.2.1
Power Electronic Converter Properties .......................................................... 72
4.2.2
Rectifier Tests................................................................................................ 75
4.2.3
SMR Tests ..................................................................................................... 80
4.3
Conclusion ............................................................................................................ 83
Chapter 5:
Power Capability and Limits of Phase Advance Modulation ......................................... 85
5.1
Fundamental Analysis ........................................................................................... 85
5.2
Conventional Phase Advance Modulation ............................................................. 90
5.2.1
5.3
Zero-epsilon Modulation ............................................................................... 93
Variable Speed Performance ................................................................................. 96
5.3.1
Optimisation of Parameters........................................................................... 99
5.3.2
Comparison Betweeen Analysis and Simulations ......................................... 102
5.4
Implementation of the Control System................................................................ 104
5.4.1
Zero-Crossing Detection Circuit ................................................................... 104
5.4.2
Control Circuitry .......................................................................................... 105
5.4.3
Software Design .......................................................................................... 107
5.5
Experimental Results........................................................................................... 108
5.5.1
Rated Speed Performance ........................................................................... 109
5.5.2
Variable Speed Performance ....................................................................... 111
5.6
Conclusion .......................................................................................................... 114
Chapter 6:
6.1
Maximum Torque per Ampere Control of Phase Advance Modulation ....................... 117
Analytical Methods ............................................................................................. 118
6.1.1
Inverter Modulation .................................................................................... 118
6.1.2
Phase Advance Modulation ......................................................................... 122
6.1.3
Comparison of Inverter and Phase Advance Modulation.............................. 123
6.2
Simulation Results............................................................................................... 128
6.3
Implementation of Control Algorithms ................................................................ 131
6.3.1
Open-Loop Control Algorithm ..................................................................... 132
6.3.2
Closed-Loop Control Algorithms .................................................................. 133
6.3.3
Simulation Results ....................................................................................... 136
6.4
Experimental Results........................................................................................... 136
6.4.1
Control Algorithm Implementation .............................................................. 138
v
6.4.2
Preliminary Results...................................................................................... 138
6.4.3
Results of Open-Loop Control Scheme......................................................... 141
6.4.4
Closed-Loop Current Feedback Results ........................................................ 145
6.5
Conclusion .......................................................................................................... 147
Chapter 7:
Conclusion .................................................................................................................149
7.1
Summary ............................................................................................................ 149
7.2
Key Results and Original Contributions................................................................ 151
7.3
Suggestions for Further Research ........................................................................ 153
Appendix A: Microcontroller Code ............................................................................... 155
Appendix B: dSPACE Simulink Programs ....................................................................... 160
Appendix C: Code Used to Generate Simulation .DLL File ............................................. 165
Appendix D: Relevant Publications ............................................................................... 169
References ................................................................................................................... 172
vi
List of Figures
1-1: Definition of pitch angle of a wind turbine blade ....................................................... 2
1-2: Comparison of cp as a function of tip speed ratio  for wind turbines with varying
blade types. ....................................................................................................................... 3
1-3: Comparison of wind turbine output power and torque as a function of turbine speed .. 4
1-4: Comparison of wind turbine topologies. ..................................................................... 5
1-5: Comparison of wind turbine power electronic converters ........................................... 8
1-6: Comparison of waveforms obtained with different power electronic converters. ......... 9
1-7: Thesis structure showing chapter breakdown ............................................................ 15
2-1: Single-phase models of SPM generators. .................................................................. 18
2-2: Phasor diagram of SPM generator and definition of d and q-axes ............................. 20
2-3: VI Loci for low and high inductance SPM generators ............................................... 21
2-4: Comparison of current limiting and voltage limiting circles on the dq axis plane ...... 22
2-5: Analytical models and phasor diagrams of SPM generators operating with different
power electronic converters ............................................................................................. 25
2-6: SPM generator phase current and output power versus output voltage ...................... 26
vii
2-7: Comparison of the dq axis current loci for a SPM generator operating with a rectifier,
SMR and inverter .............................................................................................................27
2-8: SMR and rectifier output power as a function of speed ..............................................28
2-9: Phase voltage, current, power factor and output power as a function of speed for a
SPM generator using a rectifier, SMR and inverter as the power converter. ......................31
3-1: Illustration of the conversion process in order convert the AC quantities calculated by
the single-phase equivalent circuit model into DC values. ................................................36
3-2: Comparison of AC/DC voltage conversion factors. ...................................................37
3-3: Non-sinusoidal simulation model for SPM generator with rectifier ...........................39
3-4: Comparison of analytical and simulated SPM generator phase voltage and current as
a function of speed.. .........................................................................................................40
3-5: Waveforms of simulated phase voltage and current for an SPM generator operating
into a rectifier ...................................................................................................................42
3-6: Analytical and simulated phase voltage, current and output power as a function of DC
link voltage for a SPM generator operating into a rectifier. ...............................................43
3-7: Three-phase non-sinusoidal simulation model of a semi-bridge SMR operating with a
SPM generator .................................................................................................................44
3-8: Comparison of analytical and simulated SPM generator phase voltage, current and
output power as a function of duty cycle when operating into an SMR .............................46
3-9: Simulated phase voltage and current waveforms for SPM generator operating with an
SMR at different duty cycles ............................................................................................47
3-10: Analytical and simulated P vs I loci and Id vs. Iq loci for an ideal SPM generator
operating into a SMR. ......................................................................................................48
3-11: Analytical and simulated phase voltage, current and output power as a function of
generator speed for a SPM generator operating into a SMR or a rectifier ..........................49
3-12: Three-phase non-sinusoidal simulation model of a SPM generator operating into an
inverter with a constant voltage load. ...............................................................................51
3-13: Analytical and simulated phase voltage, current, power factor and output power as a
function of generator speed for an ideal SPM generator operating into an inverter. ...........52
3-14: Simulated phase voltage and current waveforms for an SPM generator operating into
a inverter ..........................................................................................................................53
3-15: Simplified PSIM simulation model for single-switch SMR .....................................55
viii
3-16: Simplified simulation model of a semi-bridge SMR ............................................... 55
3-17: Simplified simulation model of an inverter ............................................................. 57
3-18: Phase voltage, current and output power as a function of duty cycle for the singleswitch and semi-bridge SMRs for PWM inclusive and simplified models ........................ 58
3-19: Inverter voltage, current, power factor angle and output power using simplified and
complete simulation models. ........................................................................................... 60
3-20: Phase voltage and current waveforms obtained using the simplified and complete
inverter models. ............................................................................................................... 61
4-1: SPM generator used to obtain experimental results ................................................... 64
4-2: Experimental setup used for parameter and variable load testing of the generator ..... 65
4-3: Experimental setup for the open-circuit test, and the measured generator back-EMF
voltage as a function of generator electrical angular frequency. ....................................... 65
4-4: Experimental open-circuit line to line back-EMF voltages and short-circuit line to line
current waveforms. .......................................................................................................... 66
4-5: Shaft torque obtained when the open-circuited generator was spun in the clockwise
direction and the counter clockwise direction .................................................................. 67
4-6: Corrected measured CW and CCW torque values as a function of speed, and the
measured open-circuit power loss as a function of speed. ................................................ 67
4-7: Experimental setup for the resistance test, and measured SPM generator phase
resistance as a function of DC input current. .................................................................... 68
4-8: Experimental setup used for the short-circuit test and comparison of SPM generator
current as a function of speed. ......................................................................................... 69
4-9: Calculated efficiency map for the SPM generator. .................................................... 71
4-10: Photograph of the power electronic converter utilized ............................................ 74
4-11: Circuit diagram of the power electronic converter utilized ...................................... 74
4-12: Diode and IGBT voltage drop as a function of line current ..................................... 75
4-13: Experimental arrangement for testing of SPM generator with diode rectifier .......... 76
4-14: Phasor diagram used to analyse SPM generator when I and V are in phase. ............ 77
4-15: Analytical, simulated and experimental results of a SPM generator operating with
speed from 0-1000 rpm with a 42 V DC load. .................................................................. 79
4-16:Phase leg voltage and line current waveforms obtained from the SPM generator
operating into a rectifier with a 42 V DC load.................................................................. 80
ix
4-17: Experimental arrangement for testing of SPM generator with semi-bridge switchedmode rectifier and fixed voltage load ...............................................................................81
4-18: Analytical, simulated and experimental SPM generator phase voltage, current and
output power as a function of SMR duty cycle. ................................................................82
4-19: Simulated and experimental phase leg voltage and current waveforms obtained for a
SPM generator operating under SMR modulation. ...........................................................83
5-1: Phase leg voltage and phase current waveforms for inverter, conventional SMR,
conventional phase advance and zero-epsilon modulation ................................................87
5-2: Achievable values of V and  for inverter, conventional SMR, conventional phase
advance and zero-epsilon modulation. ..............................................................................88
5-3: Analytical and simulated contour plots of output power and phase current for
conventional phase advance modulation. ..........................................................................91
5-4:Simulated and analytical waveforms of phase current and voltage with conventional
phase advance modulation. ...............................................................................................92
5-5: Analytical and simulated zero epsilon phase current, phase leg voltage and
fundamental phase voltage waveforms .............................................................................93
5-6: Analytical and simulated phase voltage, , current and output power as a function of
phase advance angle. ........................................................................................................95
5-7: Analytical and simulated phase voltage versus power-factor angle trajectories. .........96
5-8: Single-phase equivalent circuit and phasor diagrams for an SPM generator operating
under inverter, SMR and phase advance modulation. .......................................................97
5-9: Phase voltage, current, , power factor and output power corresponding to maximum
output power for SMR, phase advance and inverter modulation .......................................98
5-10: Low speed phasor diagrams for inverter and phase advance modulation ................ 100
5-11: High speed phasor diagrams for inverter and phase advance modulation ............... 100
5-12: Analytical and simulated optimal VOV and . ......................................................... 102
5-13: Analytical and simulated phase current waveforms for optimized zero-epsilon
modulation ..................................................................................................................... 103
5-14: Analytical and simulated output power versus speed for SMR, phase advance and
inverter modulation ........................................................................................................104
5-15: Circuit diagram for a comparator with hysteresis................................................... 105
5-16: Simplified circuit diagram for control electronics system ......................................106
x
5-17: Flow chart for software used to implement phase advance modulation ................. 108
5-18: Measured SMR and phase-advance modulation waveforms. ................................. 109
5-19: Simulated and experimental generator phase voltage, current and output power as a
function of δ .................................................................................................................. 111
5-20: Simulated and experimental optimal VOV and , output power and efficiency as a
function of speed obtained using zero-epsilon modulation.. ........................................... 112
5-21: Comparison of simulated and experimental V- loci. ............................................ 113
6-1: Comparison of V as a function of Id ........................................................................ 120
6-2: Comparison of d-q axis current for inverter and phase advance modulation ............ 124
6-3 : SPM generator Id and Iq as a function of generator torque. ..................................... 125
6-4: I, V and  obtained using inverter and phase advance modulation as a function of
generator torque. The required phase advance modulation parameters are also shown. .. 126
6-5: Contour plots of torque and current as functions of V and  at 0.5 pu speed ............ 127
6-6: Contour plots of torque and current as functions of V and  at 1 pu speed............... 127
6-7: Simulated and analytical generator voltage and current as a function of torque a SPM
generator using phase advance modulation .................................................................... 129
6-8: Simulated and analytical phase current and simulated and analytical fundamental
phase voltage along with simulated phase leg voltage waveforms .................................. 130
6-9: Analytical and simulated generator torque as a function of torque command, T*and
generator current as a function of torque ........................................................................ 131
6-10: Block diagram of the control system used............................................................. 132
6-11: Comparison of the effects of symmetrical and non-symetrical phase current
waveforms on phase advance modulation. ..................................................................... 134
6-12: Hardware block diagram for experimental setup ................................................... 137
6-13: Open-circuit loss torque and power loss as a function of speed. ............................ 139
6-14: Analytical, simulated and experimental phase current and efficiency as a function of
torque for SMR, phase advance and inverter modulation. .............................................. 140
6-15: Simulated and experimental  and VOV computed by the open-loop controller as a
function of command torque. ......................................................................................... 141
6-16: Experimental and simulated phase leg voltage and line current waveforms for
command torques of 5 Nm and 10 Nm at 240 rpm ......................................................... 142
xi
6-17: Experimental and simulated phase leg voltage and line current waveforms for
command torques of 5 Nm and 10 Nm at 490 rpm ......................................................... 143
6-18: Analytical, simulated and experimental generator torque as a function of command
torque using open-loop and closed-loop control at 245 rpm ............................................ 144
6-19: Analytical, simulated and experimental generator torque as a function of command
torque using open-loop and closed-loop control at 490 rpm ............................................ 144
6-20: Values of  obtained with open-loop and closed-loop controllers at speeds of 245 and
490 rpm ......................................................................................................................... 145
6-21:Efficiency as a function of generator torque obtained by varying the control
parameters manually and using the closed-loop controller .............................................. 147
xii
List of Tables
3-1: Calculated VDC/VL .......................................................................................... 38
3-2 Voltage and current for single-switch and semi-bridge SMR. ........................... 59
4-1: Summary of SPM generator parameters .......................................................... 70
4-2: Parameters of power electronic converter ........................................................ 73
5-1: Analytical results for inverter, phase advance and SMR modulation .............. 101
5-2: Summary of the performance results for the case shown in Figure 5-18 ......... 110
6-1: Maximum torque error under open-loop and closed-loop control................... 146
xiii
Abstract
This research investigates the control of low-cost power electronic converters for
small-scale wind turbines under standalone applications. The system utilizes a surface
permanent magnet (SPM) generator operating with a semi-bridge switched-mode rectifier
(SMR) into a DC voltage load.
Conventional control of a semi-bridge SMR results in lower output power than an
inverter (i.e. fully-controlled voltage source rectifier) due to the SMR’s inability to control
its input power factor. Phase-advance modulation was introduced by Rivas et al. as a
method of generating increased output power from a semi-bridge SMR by modulating the
leg voltage of each phase at three different levels during the phase current positive half
cycle. This method produced a controllable leading phase shift on the phase current
waveform with respect to the phase voltage.
Previous studies focussed on using phase advance modulation to extract maximum
power from Lundell alternator and interior permanent magnet (IPM) generators at a fixed
speed (1,800 rpm). No research had been conducted on the performance of SPM generators
under phase advance modulation techniques. This study examines how the voltage and
power factor angle of a SPM generator can be controlled to ensure that the generator
produces maximum output power at a given speed. A simplified version of phase advance
xiv
modulation, called zero-epsilon modulation, is used to implement voltage-power factor
angle control and hence extract the maximum value of power at a given SPM generator
speed.
Wind turbine generators are required to have controllable values of torque in order to
perform maximum power point tracking. It is desirable therefore to be able to control a
SPM generator used in wind turbines to a commanded value of torque while maintaining a
high value of efficiency. This study will present the techniques required to use zero-epsilon
modulation to control a SPM generator under maximum torque per ampere conditions,
thereby minimizing generator copper losses. The voltage and power factor required by an
inverter operating under maximum torque per ampere control for a given generator speed
and commanded torque is used to calculate the required zero-epsilon control parameters. A
closed-loop current controller was used to minimize the error between the commanded and
actual values of generator torque. Simulation and experimental results are used to validate
the proposed approach.
The above research has demonstrated the feasibility of phase advance modulation as
a low-cost alternative to inverter modulation for controlling a SPM generator to produce
maximum output power at a given speed. In addition, phase advance modulation has been
shown to be capable of controlling a SPM generator to produce a commanded value of
torque under maximum torque per ampere conditions at a given speed. These results make
a significant contribution towards the development of low-cost, high performance smallscale wind turbine generators.
xv
Statement of Originality
I, Mehanathan Pathmanathan certify that this work contains no material which has
been accepted for the award of any other degree or diploma in any university or other
tertiary institution and, to the best of my knowledge and belief, contains no material
previously published or written by another person, except where due reference has been
made in the text.
I give consent to this copy of my thesis when deposited in the University Library,
being made available for loan and photocopying, subject to the provisions of the Copyright
Act 1968.
I also give permission for the digital version of my thesis to be made available on the
web, via the University’s digital research repository, the Library catalogue and also
through web search engines, unless permission has been granted by the University to
restrict access for a period of time.
Signed: ___________________________________________________
Date: _____________________________________________________
xvi
Acknowledgements
Firstly I would like to thank my supervisor, Associate Professor Wen L. Soong for
his excellent guidance and assistance throughout the course of my research. I am also
grateful for the help provided by my co-supervisor, Associate Professor Nesimi Ertugrul. I
express gratitude towards the University of Adelaide and the Australian Research Council
for supporting my studies through the Australian Research Council Discovery Grant,
DP0878530.
I would sincerely like to thank the staff of the Electrical Engineering Workshop for
all the time they invested in aiding my projects. In addition, I am appreciative of the aid
provided by Danny Di Giacomo and Pavel Simcik in the field of hardware design. I also
express gratitude to Chong-Zhi Liaw for his assistance in microcontroller programming.
I am particularly grateful for the aid and companionship of the members of the
“Power Electronics and Control Systems” group, in particular Dr David Whaley, Dr
Gurhan Ertasgin and Chun Tang. Finally, I would like to thank my family for the
invaluable support they provided throughout the course of this project.
xvii
List of Publications
[1] M. Pathmanathan, C. Tang, W.L. Soong and N. Ertugrul, “Detailed Investigation of
Semi-Bridge Switched-Mode Rectifier for Small-Scale Wind Turbine Applications”, IEEE
International Conference on Sustainable Energy Technologies, Nov. 2008, Singapore, pp.
950-955.
[2] M. Pathmanathan, C. Tang, W.L. Soong and N. Ertugrul, “Comparison of Power
Converters for Small-Scale Wind Turbine Operation”, Australasian Universities Power
Engineering Conference (AUPEC), Dec. 2008, Sydney, Australia, pp. 1-6.
[3] C. Tang, M. Pathmanathan, W.L. Soong and N. Ertugrul, “Effects of Inertia on
Dynamic Performance of Wind Turbines”, Australasian Universities Power Engineering
Conference (AUPEC) Dec. 2008, Sydney, Australia, pp. 1-6.
[4] M. Pathmanathan, W.L. Soong and N. Ertugrul, “Investigation of Phase Advance
Modulation with Surface Permanent Magnet Generators”, Australasian Universities Power
Engineering Conference (AUPEC) Sep. 2009, Adelaide, Australia, pp. 1-6.
xviii
[5] M. Pathmanathan, W.L. Soong and N. Ertugrul, “Output Power Capability of Surface
PM Generators with Switched-Mode Rectifiers”, IEEE International Conference on
Sustainable Energy Technologies, Dec. 2010, Kandy, Sri Lanka, pp. 1-6.
[6] M. Pathmanathan, W.L. Soong and N. Ertugrul, “Maximum Torque per Ampere
Control of Phase Advance Modulation of a SPM Wind Generator”, IEEE Energy
Conversion Congress and Exposition, Sep. 2011, Phoenix, USA, pp. 1676-1683.
Pending Publication
[1] M.Pathmanathan, W.L. Soong and N.Ertugrul, “Maximum Torque per Ampere
Control of Phase Advance Modulation of a SPM Wind Generator”, accepted by IEEE
Transactions on Industry Applications, Apr. 2012.
[2] C. Tang, M. Pathmanathan, W.L. Soong , N. Ertugrul, and P. Freere “Dynamic Wind
Turbine Output Power Reduction Under Varying Speed Conditions Due to Inertia”,
submitted to Wind Energy, Feb. 2012.
xix
Nomenclature

Phase advance interval 1
deg
ε
Phase advance interval 2
deg

Phase advance interval 3
deg

Generator phase current angle
deg
ΨM
Magnet flux linkage
Wb

Angle between phase current and voltage
deg

Electrical frequency
c/s
M
Generator speed
c/s
O
Generator rated angular speed
c/s
d
Duty cycle
%
d
Duty cycle during interval 
%
dε
Duty cycle during interval ε
%
d
Duty cycle during interval 
%
E
Generator back EMF voltage
Vrms
I
Generator phase current
Arms
Id
Generator d-axis phase current
Arms
xx
Iq
Generator q-axis phase current
Arms
IX
Generator characteristic current
Arms
ISC
Generator short circuit current
Arms
IDC
Generator DC link current
A
IO
Generator limiting current
Arms
IOUT
Generator load current
A
k
Generator back EMF constant
Vrms/cs-1
LS
Generator synchronous inductance
H
Ld
Generator d-axis inductance
H
Lq
Generator q-axis inductance
H
m
Number of generator phases
n
Generator speed
p
Number of generator pole pairs
P
Generator output power
W
PM
Generator mechanical power
W
PO
Generator base power
W
RS
Generator stator resistance

RO
Generator base stator resistance

RL
Generator load resistance

RL’
Adjusted SMR load resistance

T
Generator input torque
Nm
V
Generator phase voltage
Vrms
Vd
Generator d-axis phase voltage
Vrms
Vq
Generator q-axis phase voltage
Vrms
VO
Generator limiting voltage
Vrms
VOUT
Generator load voltage
V
Vd
Generator d-axis voltage
V
Vq
Generator q-axis voltage
V
VD
Power electronic converter voltage drop
V
VDC
Generator DC link voltage
V
VL
Generator line to line voltage
Vrms
XS
Generator stator reactance

rpm, pu
xxi
Acronyms
SPM
Surface Permanent Magnet
IPM
Interior Permanent Magnet
SMR
Switched-mode rectifier
PWM
Pulse width modulation
PA
Phase advance
ZE
Zero-epsilon
xxii
Chapter 1: Introduction
1.1 Background
The use of fossil fuels to generate electricity has a number of unwanted side effects
such as an increase in greenhouse gases, acid rain and oil pollution. Nuclear power has
been touted as an alternative energy source, but concerns exist over the environmental
impact of radioactive wastes and the potential for nuclear meltdowns.
The world’s supply of fossil fuels is limited, which gives rise to concerns over the
impact of the collapse of fuel supplies. In addition, the distribution of fossil fuel reserves is
also uneven, with the Middle East holding the majority of the world’s oil supplies, and
former Soviet Union nations holding the bulk of the gas reserves [1]. These concentrated
reserves can be source of political and economic conflict.
Renewable energy sources present an attractive alternative to fossil fuels, largely due
to the lack of pollution and their unlimited supply. Examples of renewable energy sources
are solar, wind, biomass, hydroelectric and geothermal [2]. Wind turbines are capable of
harnessing wind power and converting it to electrical energy [3], [4]. This thesis aims to
improve the cost-effectiveness of small-scale wind turbines by introducing low-cost, high
performance control strategies for their power electronics systems.
1
CHAPTER 1: INTRODUCTION
1.2 Fundamentals of Wind Power
The mechanical power which can be converted from wind power by a wind turbine is
given by the following equation.
(1-1)
In this equation, cp and r represent the coefficient of performance and blade radius of
the wind turbine respectively,  is the air density and v is the wind speed. cp is a function of
the generator tip-speed ratio (TSR) , and the blade pitch angle .  can be calculated by:
(1-2)
where m is the rotational speed of the wind turbine.
The blade pitch angle is defined as the angle between the rotor plane and the chord of
the blade [5]. This angle is illustrated in Figure 1-1. If a fixed value of blade pitch is
assumed, cp is solely dependent on the characteristics of the wind turbines blades. Figure
1-2 shows the typical wind turbine cp curves as a function of  for different wind turbine
blade types. The dashed line on Figure 1-2 represents the maximum theoretical cp which
was defined as 59.3 % by Betz’s Law [7].
A
NOTE:
This figure/table/image has been removed
to comply with copyright regulations.
It is included in the print copy of the thesis
held by the University of Adelaide Library.
Figure 1-1: Definition of pitch angle of a wind turbine blade [6]
2
1.2. FUNDAMENTALS OF WIND POWER
Figure 1-2: Comparison of cp as a function of tip speed ratio  for wind turbines with varying blade
types. The maximum cp derived from Betz’s law is shown as a dashed line. [7]
It can be seen that three-bladed horizontal axis rotors offer the highest maximum
values for cp. Disadvantages with horizontal axis wind turbines are that the generator must
be placed at the top of the tower, the requirement of a yaw control system to maximize
output power. [7-9]. Vertical axis wind turbines have an advantage in that no yaw system
is required, and their simple design allows electrical components to be housed at ground
level [7-9]. However, vertical axis wind turbines exhibit high values of starting torque at
low wind speeds, and may require external excitation for the blades to begin moving [8],
[9] .
Equation (1-2) shows that  is proportional to m. This indicates that the value of 
resulting in maximum cp can be obtained by controlling m to the appropriate value. This
optimum value of m changes as a function of wind speed v. An example of this
phenomenon is displayed in the left side Figure 1-3, which shows that the required turbine
speed to extract maximum power is linearly proportional to wind speed.
Equations (1-1) and (1-2) can be used to calculate the turbine torque as shown below:
3
CHAPTER 1: INTRODUCTION
(1-3)
Using this relationship, the turbine torque for a given wind speed and generator
rotational speed can be calculated. This allows the value of turbine torque giving rise to
maximum turbine power to be calculated. An example of turbine torque as a function of
rotational and wind speed is shown on the right hand side of Figure 1-3. It is apparent that
the value of turbine torque can be controlled as a function of turbine speed in order to
maintain maximum turbine power.
The mechanical energy produced by a wind turbine must be converted into electrical
energy before it can be stored or transmitted to the electrical grid. This process is achieved
by an electrical generator. The next section will cover the types of generators which are
commonly used in wind turbines.
Figure 1-3: Comparison of wind turbine output power (left) and torque (right) as a function of
turbine speed for wind speeds in the range 5 m/s to 12 m/s. [6]
1.3 Wind Turbine Generators
Important considerations of wind turbine generators are the power rating of the
turbine, cost, efficiency and availability [10]. Availability is defined as the proportion of
time in which a generator is able to produce power divided by the total amount of time in a
given period. Another factor is whether the generator is designed for constant speed or
variable speed operation. The mechanical connection of the generator to the turbine can be
achieved either through a direct drive system or a gearbox.
4
1.3. WIND TURBINE GENERATORS
1.3.1 Squirrel-Cage Induction Generator
The “Danish Concept” of wind turbines used a squirrel-cage induction generator
directly coupled to the electrical grid [11] (Figure 1-4a). This family of wind turbines made
use of a fixed-ratio gearbox to couple the wind turbines rotor to the generator shaft.
Capacitor banks are generally used to provide reactive power compensation for the
induction generator’s magnetizing current, and are often rated at 30% of wind farm
capacity [12], [13].
An advantage of this design is that no power electronics are required, which reduces
the cost of the system. The induction generator must however be controlled to operate at a
nearly constant speed, in order to ensure that the electrical power produced is compatible
with the grid frequency. Fixed speed operation means that the wind turbine would not be
able to adjust its tip speed ratio for a given speed in order to achieve the optimal cp and
hence will produce a lower output power. Pole adjustable winding configurations have
been used to provide some degree of speed control [7], [8]. The gearbox used in these
turbines requires maintenance and can be a source of noise pollution, and can cause power
losses due to tooth-flank friction and oil flow splash losses [7].
Grid
Connection
vwind
Gearbox
IG
AC/AC
vwind
m (fixed speed)
Grid
Connection
DFIG
m
a)
Capacitor
bank
b)
Grid
Connection
vwind
SPM
AC/DC
m
DC/AC
SPM
vwind
AC/DC
Load
Battery
m
c)
d)
Figure 1-4: Comparison of “Danish concept” wind turbine (a), variable-speed wind turbine with a
DFIG (b), grid-connected wind turbine using a SPM generator (c) and stand-alone wind turbine
using a SPM generator (d).
5
CHAPTER 1: INTRODUCTION
1.3.2 Doubly-Fed Induction Generator
A doubly-fed induction generator (DFIG) has a rotor with a frequency converter
connected via slip rings [14] (Figure 1-4b). This frequency converter can be used be used
to inject an AC current into the rotor windings, which allows the stator electrical frequency
to be controlled independently of the shaft speed [15]. Such a control system allows for
variable-speed operation of the wind turbine, which would result in higher efficiency due
to the ability to control  in order to obtain the maximum cp. An additional advantage of
variable speed operation is that wind turbines with this capability are more stable under
grid fluctuations than fixed-speed induction generators [13].
The power electronic converter connected to the rotor of the DFIG is not required to
be rated at the total system power. For a speed range of
, the power electronics is
typically only required to be approximately 25% of the total system power [11]. This can
result in a substantial reduction in cost, since the cost of power electronics systems is
proportional to their power rating.
The primary disadvantages of the DFIG wind turbine generator are that the
construction of a wound rotor is more complex and costly than a squirrel-cage or
permanent magnet rotor, and that slip rings are required [16]. The addition of slip rings
adds to the maintenance costs of the system [8].
1.3.3 Surface Permanent Magnet Generator
The surface permanent magnet (SPM) generator is an attractive choice for wind
turbines due to its property of self-excitation, which allows for operation at high power
factor and efficiency [12]. Additionally, they are capable at operating at variable turbine
speeds, which allows the generator speed to be controlled to the optimal speed which gives
rise to the peak value of cp.
A disadvantage of SPM generators is that they have a larger variation in terminal
voltage than induction generators [17]. Additionally, the power electronic converter and
inverter output filters must be rated at the full power capability of the generator [11]. This
means that the power electronic converter in a SPM generator system would cost more
than the converter utilized in a similarly rated DFIG system, since the power electronic
converter in the latter case would not be rated at full power capability. However, unlike the
6
1.4. AC/DC POWER ELECTRONIC CONVERTERS
DFIG, the SPM generator does not use slip rings, which reduces the amount of
maintenance required.
While most large wind turbines are connected to the electrical grid (Figure 1-4c),
stand-alone turbines are often used in applications such as battery charging in rural areas
[18] (Figure 1-4d). In such a system, the DC/AC converter is not required since the load is
DC. The lower power ratings required for stand-alone applications makes SPM generators
an attractive choice. Stand-alone wind turbines usually operate with a fixed blade pitch,
which means that some form of variable speed generator, such as the SPM generator, is
required [10].
This thesis will focus on small-scale wind turbines with SPM generators due to the
high efficiency and low cost of this approach. The following section will outline the
AC/DC power electronic converters commonly used in small-scale wind turbines with
SPM generators.
1.4 AC/DC Power Electronic Converters
The primary concerns in the AC/DC power electronic converters used in small-scale
wind turbines are their output power performance, efficiency, cost, and control complexity.
1.4.1 Rectifier
The simplest AC/DC converter used is the uncontrolled rectifier (Figure 1-5a). This
converter requires no control [19], and has the lowest cost of the power electronics systems
examined in this section. This low cost is due to the lack of controllable power electronic
switches, sensors and control circuitry [20]. If an ideal three-phase SPM generator is
assumed as the input to the rectifier, a three-phase back-emf voltage E and inductance LS
will be connected to the AC side of the rectifier. The magnitude of E will increase as a
function of generator speed.
The greatest disadvantage of this topology is that the rectifier is unable to produce
output power when the magnitude of E is smaller than VDC [21], which only occurs at low
generator speeds. This is caused by the inability of the rectifier to control the phase shift
between the generator phase voltage V and phase current I for fixed values of E and VDC.
7
CHAPTER 1: INTRODUCTION
IDC
IDC
E
LS I
E
LS
I
+
VDC
-
+
VDC
VLeg
VLeg
a)
LS
E
b)
IDC
E
I
LS
I
IDC
+
+
VDC
-
-
VDC
VLeg
VLeg
c)
d)
Figure 1-5: Comparison of rectifier (a), single-switch SMR (b), semi-bridge SMR (c) and inverter
(d)
The displacement power factor of a rectifier is approximately unity [19] (Figure
1-6a), and cannot be controlled. The displacement factor is the power factor calculated
between the fundamental waveforms of V and I. This means that it is impossible to shift
the phase current waveform I to be in phase with the back-emf voltage, E. A lower output
power would therefore be generated than if E and I were in phase. The theoretical
explanations for these phenomena will be examined in Chapter 2.
8
1.4. AC/DC POWER ELECTRONIC CONVERTERS
E
VLeg
VLeg
Vo
I
E
I
VB
t
t
V(fund)
V(fund)
a)
E
I
VOV
E
b)
I
VLeg
VLeg
VINV
VB
t


t

V(fund)
c)
V(fund)
d)
Figure 1-6: Comparison of supply voltage (E), phase current (I), phase leg to negative rail voltage
(VLeg) and fundamental phase to neutral voltage V(fund) for rectifier (a), conventional SMR (b),
phase advance SMR (c) and inverter (d) modulation.
1.4.2 Switched Mode Rectifier (SMR)
The switched-mode rectifier (SMR) consists of a diode rectifier with a boost switch
placed between the rectifier output and the DC voltage load (Figure 1-5b) [26]. For a
constant DC link voltage, modifying the duty cycle of the boost converter stage allows the
rectifier output voltage to be changed. This will in turn allow output power to be produced
in cases where E has a smaller magnitude than VDC [20].
These benefits come at price of increased cost and control complexity. Sensors are
required in order to determine the optimal duty cycle for a given operating condition.
These sensors, along with the additional power electronic switch and diode are the reason
for the increase in cost when compared to a rectifier.
The total number of device voltage drops can be reduced by incorporating the boost
stage of the single-switch SMR into the lower half of the rectifier bridge [21] (Figure
1-5c). This topology is called the semi-bridge SMR, and behaves identically to the circuit
9
CHAPTER 1: INTRODUCTION
in Figure 1-5b if all three switches are driven at the same duty cycle [21]. An alternative
method of semi-bridge SMR control was proposed by [55], which reduced switching and
conduction losses by only applying PWM modulation to one leg of the converter bridge at
a time. The advantage of this topology is that an additional power electronic converter drop
is removed from the circuit. In the remainder of this thesis, the topology illustrated in
Figure 1-5b will be referred to as the single-switch SMR, while the one shown in Figure
1-5c will be called the semi-bridge SMR.
Both the single-switch and semi-bridge SMR are only capable of controlling the
phase leg to negative rail voltage, VLeg when the phase current I is positive. A singleswitch SMR would therefore only be capable of unity power factor operation, since it
would not be able to create a phase shift between V and I [22] (Figure 1-6b). The semibridge SMR encounters the same issue if all three of the switches in the bottom half of the
converter bridge are driven at the same duty cycle. This modulation technique will
henceforth be referred to as conventional SMR or load matching modulation. Chapter 2
will examine how the generator phase voltage V can be controlled using the SMR topology
to maximize output power for a given generator speed and hence value of E.
A method of obtaining non-unity power factor in a semi-bridge SMR was introduced
by [23] (Figure 1-6c). In this technique, three separate duty cycles were used during the
positive half-cycle of the current waveform in order to control the effective phase leg
voltage of the semi-bridge SMR. During period , the duty cycle was set to unity, whilst in
 it was set to the value used for conventional SMR modulation. Finally, the duty cycle
was set to zero during period . The combination of these three periods caused a leading
phase shift on I with respect to V, while also increasing the magnitude of I. It will be
shown in Chapter 2 that producing such a phase shift could produce up to two times the
output power obtained using conventional SMR modulation at low speeds. Previous
studies [56], [57] showed that a lagging phase current command could be used to reduce
the phase current total harmonic distortion (THD).
The modulation strategy used by [23] will be henceforth referred to as conventional
phase advance modulation in this thesis. Conventional phase advance modulation was
introduced in order to improve the output power of automotive Lundell alternators at their
idle speed (1,800 rpm). Power improvements of 15% compared to conventional SMR
modulation were found whilst increasing current by 10%. Reference [24] applied the same
10
1.4. AC/DC POWER ELECTRONIC CONVERTERS
modulation strategy to an interior permanent magnet generator, resulting in a 67% power
increase while maintaining generator current below the rated value.
The analysis, simulations and experiments conducted by [23] and [24] were
conducted at fixed values of generator speed as in the automotive alternator application the
authors were concerned about performance at the engine idle speed. As a result, no
analysis was presented on the control parameters required to obtain maximum output
power at a over a range of generator speeds. In addition, no analysis was presented on how
to control the torque produced by the generator at a fixed value of generator speed while
maximizing generator efficiency. Generator torque control is essential in wind turbine
applications for maximizing the turbine’s mechanical power, as was seen in Figure 1-3.
The cost of using conventional phase advance modulation is greater than that of
conventional SMR modulation due to the requirement of current sensors. However [23]
has indicated that lower cost voltage sensors monitoring the freewheeling diodes in each
phase could be utilized as only the current zero-crossings need to be detected.
An issue with conventional phase advance modulation was that using a stepped
phase leg voltage waveform VLeg to generate the leading phase shift on I (Figure 1-6c)
resulted in a smaller fundamental phase voltage compared to the voltage waveform which
would be generated with 180o conduction. This was caused by the semi-bridge SMR only
being able to control a given phase leg voltage while the corresponding generator phase
current was positive. As a result, larger values of phase shift would result in smaller
magnitudes of the fundamental voltage. It is only possible to maintain this conduction
period whilst producing a phase shift on the current and voltage waveforms by using a
power electronic converter with controllable switches in the top half of its bridge, such as
the inverter.
1.4.3 Inverter
The final AC/DC converter which will be examined is the inverter, or fully
controlled voltage source rectifier, shown in Figure 1-5d. This topology is similar to the
semi-bridge SMR, with the main difference being that the top half of the bridge contains
controllable switches instead of diodes. The presence of controllable switches in the top
half allows a positive phase leg voltage VLeg to be generated while the corresponding phase
current I is negative (Figure 1-6d) [25]. This flexibility avoids the trade-off between the
11
CHAPTER 1: INTRODUCTION
magnitude of the fundamental voltage and the phase shift between V and I which is
observed with phase advance modulation of the semi-bridge SMR.
The primary benefit of controlling power factor during the AC/DC conversion
process is that the output power can be maximized by keeping Vs and I in phase [22].
Chapter 2 will show that an inverter can produce two times the output power of
conventional SMR modulation at low speeds. An additional feature of an inverter is that
unlike a SMR, it can be used to control the SPM machine to act as a motor or a generator.
This ability can be used with automotive alternators to act as an integrated starter/alternator
(ISA) [25].
A key drawback to the implementation of an inverter is its high cost. The inverter’s
cost is increased compared to the semi-bridge SMR due to the higher number of
controllable power electronic switches present in the inverter. Additionally, the control of
an inverter used with SPM generators is more complex than an SMR, and generally
requires rotor position information compared to the current or voltage sensors required by
conventional phase advance modulation [25].
1.5 Thesis Overview
1.5.1 Research Gap
Small-scale wind turbines usually use surface permanent magnet (SPM) generators
due to their high efficiency and ability to operate under variable speeds. The electrical
power produced by a variable-speed SPM generator will be of variable frequency and
magnitude as the wind speed changes. An AC/DC power electronic converter is therefore
required to convert this power to DC.
Power electronics present a greater proportional cost for small-scale wind turbines
than their larger counterparts [12]. The inverter topology is capable of producing a larger
value of output power or torque when compared to the conventional SMR modulation of a
semi-bridge SMR at low speeds. The inverter has a higher cost due to the higher number of
controllable power electronic switches and the rotor position information requirement.
Conventional phase advance modulation has been used in automotive applications to
increase the output power produced by alternators. This modulation strategy was used with
Lundell [23] and interior permanent magnet (IPM) [24] alternators. These studies focussed
12
1.5. THESIS OVERVIEW
on power improvement at the engine idle speed only (1,800 rpm). A novel area of research
would thus be to investigate the application of phase advance modulation strategies to
SPM generators intended for wind turbine use. Given that SPM generators in wind turbines
operate at variable speeds, the control parameters required to generate maximum power or
a commanded value of torque with maximum efficiency at a particular speed are required.
1.5.2 Original Contributions
The aim of this research was to conduct a detailed investigation of the use of phase
advance modulation in controlling an SPM generator. There were a number of novel
aspects to this research, which included:
1. The construction of simplified simulation models which were used to model the
performance of the SMR and inverter topologies. These models made use of
phase leg averaging to describe the operation of the PWM controlled switches in
each of these topologies, which allowed for a larger simulation time step to be
used. These simplified simulation models were verified by comparing their
results with analytical and experimental data.
2. The development of a new modulation strategy for the semi-bridge SMR called
zero-epsilon modulation. This modulation method was based on a simplified
version of the technique specified by [23] with a reduced number of controlled
parameters, and was found to have similar performance capability.
3. The voltage power-factor angle plane was used to describe the operation of
different AC/DC power electronic converters with a SPM generator operating at
variable speeds. This plane was also used to compare the performance of zeroepsilon modulation to that of an inverter, and to show the trade-off between
voltage magnitude and achievable phase shift observed for zero-epsilon
modulation.
4. The implementation of maximum torque per ampere control of a SPM generator
using zero-epsilon modulation of a semi-bridge SMR. The required zero-epsilon
control parameters for maximum torque per ampere control at a given SPM
generator speed were derived by calculating the required generator voltage and
power-factor angle for the generation of a required torque with the minimum
13
CHAPTER 1: INTRODUCTION
phase current magnitude. Simulated and experimental results were also obtained,
proving the accuracy of the maximum torque per ampere control of the SPM
generator.
5. Construction of a closed loop control system designed to implement maximum
torque per ampere control with zero-epsilon modulation. The generator current
magnitude was used as a feedback parameter. The viability of the length of the
generator phase current’s positive half cycle as an alternative feedback parameter
was also investigated.
1.5.3 Thesis Outline
Figure 1-7 provides a graphical summary of the thesis structure. Chapters 2 to 4 are used to
describe the analytical and simulation models used in this thesis, and to obtain models of
the experimental apparatus which will be utilized. Chapters 5 and 6 utilize these models to
investigate the implementation of phase advance modulation. A brief summary of the
chapters in this thesis is provided below.
Chapter 2: Describes the analytical models used to describe SPM generators, as well
as the AC/DC power electronic converters used with them.
Chapter 3: Introduces the simulation models used to describe the power electronic
converters presented in this thesis.
Chapter 4: Characterises the SPM generator and power electronic converter used to
obtain experimental results in this thesis, and presents some preliminary results.
Chapter 5: Determines the output power capability of SPM generators operating
with phase advance modulation of a semi-bridge SMR. This chapter formed the basis of
the conference paper “Output Power Capability of Surface PM Generators with SwitchedMode Rectifiers” the abstract of which is listed in Appendix D.
Chapter 6: Investigates maximum torque per ampere control of a SPM generator
operating with phase advance modulation of a semi-bridge SMR. This chapter formed the
basis of the conference paper “Maximum Torque per Ampere Control of Phase Advance
Modulation of a SPM Wind Generator” the abstract of which is listed in Appendix D.
Chapter 7: Summarises the results presented in this thesis, and highlights the
original contributions made throughout.
14
1.5. THESIS OVERVIEW
Ch 1: Introduction
Ch 2: Analytical Modelling of
SPM Generator Drives
Ch 3: AC/DC Power Electronic
Converter Simulation Models
System
Modelling
Ch 4: Experimental
Verification of Models
Ch 5: Power Capability of PA
Modulation
Ch 6: Max. Torque/Amp
Control of PA Modulation
Implementation
of Phase
Advance
Modulation
Ch 7: Conclusion
Figure 1-7: Thesis structure showing chapter breakdown
15
CHAPTER 1: INTRODUCTION
16
Chapter 2: Analytical Modelling of Surface
PM Generator Drives
Small-scale stand-alone wind turbines commonly make use of a permanent magnet
generator, and an AC-DC power electronic converter [26]. This chapter will detail and
compare the methods used to model the generator and power electronic converter of a
small-scale wind turbine.
Firstly, the single-phase equivalent circuit used to model a surface permanent magnet
(SPM) generator will be examined. This circuit will then be used along with the singlephase equivalent representation of the power electronic converters, in order to predict their
performance. The information provided by these models will then be used to discover how
the performance of each power electronic converter varies as the generator’s parameters
change.
2.1 Surface Permanent Magnet Generator Models
Surface permanent magnet (SPM) generators are often utilised in small-scale wind
turbines due to their high efficiency, ability to operate at variable speeds [27], and low
maintenance [28]. A simple analytical model is required in order to predict the
17
CHAPTER 2: ANALYTICAL MODELLING OF SURFACE PM GENERATOR DRIVES
performance of such a machine. The single-phase equivalent circuit model, presented
below, fulfils these requirements.
2.1.1 Single-Phase Equivalent Circuit
Figure 2-1(a) shows the single-phase equivalent circuit of a surface permanent
magnet (SPM) generator. The back EMF produced by the generator is represented by the
voltage E, while the reactance of the generator’s stator winding is given by ωLS, where LS
is the generator stator inductance and ω is its electrical frequency. The magnitude of the
back EMF voltage, E, can be calculated using the following relationship, where m is the
magnet flux linkage of the SPM generator.
(2-1)
The equivalent circuit model represents an ideal SPM generator which converts all
the input mechanical energy into electrical energy. A more realistic model can be obtained
by including a series resistance R S representing the generator’s stator winding resistance,
as shown in Figure 2-1(b). The ideal model is representative of a SPM generator with a
much higher value of reactance than resistance, or any SPM generator at high speeds.
I
LS
E
I
V
a)
LS
RS
E
V
b)
Figure 2-1: Single-phase models of SPM generators, a) ideal, b) with stator resistance.
18
2.1. SURFACE PERMANENT MAGNET GENERATOR MODELS
Kirchhoff’s voltage law (KVL) can be used to relate the voltages present in the SPM
generator’s non-ideal single-phase equivalent circuit. This equation is given below:
(2-2)
V and I were defined in Figure 2-1 as the SPM generator’s phase output voltage and
current respectively. This equation can then be represented in the form of a phasor
diagram, which is shown in Figure 2-2(a). The d-axis is defined as being aligned with the
permanent magnet rotor flux. The q-axis is defined as being perpendicular to the d-axis
[29]. As a result, the induced back EMF voltage E will be in the q-axis. The waveforms V
and I can be separated into d-q components based on their magnitude and phase. The qaxis values of V and I represent the components of these quantities which are in phase with
the back EMF waveform.
The d and q axis components of the phase current waveform can be calculated using
the magnitude of this waveform and , the phase angle between the stator current and the
q-axis. The equations used to calculate these quantities are given below.
(2-3)
(2-4)
The d and q-axis voltage components can be calculated using the d and q current
components, shown below [30, 31].
(2-5)
(2-6)
19
CHAPTER 2: ANALYTICAL MODELLING OF SURFACE PM GENERATOR DRIVES
q
Iq
q - axis
Vq
jωLSI
E
S
 I

Id
V
Iq
Vd
N
d
IRS
Id
Vq
Vd
d - axis
a)
b)
Figure 2-2: Phasor diagram of non-ideal SPM generator (a) and definition of d and q-axes
These expressions are derived for a SPM generator: if a motor was used, the signs
of the d and q-axis current terms would be reversed. The d and q-axis inductances Ld and
Lq can be explained as shown in Figure 2-2(b) as the inductance seen by the d-axis and qaxis flux respectively. For a SPM generator, Ld = Lq.
The mechanical input power for an ideal (RS = 0) SPM generator is given by (2-7)
where m represents the number of phases of the machine in question. This relationship can
then be used to calculate the torque produced by such a generator, which is given in (2-8).
In this equation, p is the number of pole pairs of the generator.
(2-7)
(2-8)
For a non-ideal SPM generator (RS  0), the electrical output power is given by:
20
2.1. SURFACE PERMANENT MAGNET GENERATOR MODELS
(2-9)
SPM generators and their associated power electronics systems have maximum or
rated values of operating voltage (VO) and current (IO). The high speed short-circuit current
is referred to as IX, the characteristic current, given by (2-10).
(2-10)
SPM generators can be divided into high and low inductance categories [20]. Low
inductance generators typically operate at rated values of voltage which are close to EO, the
generator open-circuit voltage at rated speed, but values of current which are significantly
smaller than IX. In contrast, high inductance generators operate at values of voltage which
are considerably less than EO, but at values of current which are close to IX. At rated speed,
a high inductance SPM generator can be viewed as a constant current source, while a low
inductance generator can be represented as a constant voltage source. These concepts are
illustrated by Figure 2-3, which shows the VI loci obtained for high and low-inductance
SPM generators. The VI loci are the curves of I vs V obtained when a SPM generator is
operated into a resistive load. The analysis in this thesis will be for high-inductance
generator models where the generator rated current Io to equal the characteristic current, IX,
which results in good field-weakening performance and low short-circuit fault currents.
I
Low-inductance
Rated Operation
High-inductance
V
Figure 2-3: VI Loci for low and high inductance SPM generators
21
CHAPTER 2: ANALYTICAL MODELLING OF SURFACE PM GENERATOR DRIVES
The voltage and current constraints of a SPM generator can be expressed as a
function of their dq transformed current. The voltage limit is given by equation (2-11)
below:
(2-11)
Where VO is the rated value of phase voltage waveform’s magnitude. If an ideal
generator model (RS = 0) is used with equations (2-5) and (2-6), this relationship can be
expressed in the form of the equation of a circle in the dq current plane (see Figure 2-4),
given below:
(2-12)
2
1.5
1
I Lim
1 pu
I q (pu)
0.5
2 pu
0
-0.5
-1
VLim
-1.5
(n = 0.5 pu)
-2
-1
0
1
I d (pu)
2
3
Figure 2-4: Comparison of current limiting circle and voltage limiting circle at speeds of 0.5, 1 and
1.5 pu on the dq axis plane for a high-inductance generator
22
2.1. SURFACE PERMANENT MAGNET GENERATOR MODELS
It should be noted that the radius of this circle decreases as the electrical frequency of
the generator increases. This indicates that as generator speed increases, a smaller range of
Id and Iq will result in a magnitude of phase voltage which is lesser than the rated voltage.
The relationship between the d and q-axis currents and the rated value of phase
current magnitude is shown in (2-13). This equation can again be expressed as the equation
of a circle with a unity per-unit radius. It should be noted that radius of this limiting circle
is not affected by generator speed.
(2-13)
Figure 2-4 illustrates the voltage and current limits of a SPM generator on the dq
axis current plane. The current limit circle is unchanged by generator speed, is centred
about the origin and has a radius of 1 pu. The voltage limiting circle on the other hand is
centred about unity on the d-axis and zero on the q-axis. This is because the value of V at a
given speed is minimized by setting Id = 1pu. This circle is shown to contract as the
generator’s speed increases [32]. At low generator speeds, the achievable values of Id and
Iq will be limited by the current limit circle, while at higher speeds they will be constrained
by the voltage limit circle.
2.1.2 Normalisation of Generator Parameters
The analysis presented in this chapter will use parameters which have been
normalised in such a fashion that they provide valid results for all SPM generators where
the rated current equals the characteristic current. These parameters can be divided into
input and output categories. The input parameters of interest are the SPM generator speed
n, and the stator resistance RS.
The base or rated generator speed was defined as the speed where the back EMF
voltage equals the rated output voltage, Vo.
(2-14)
23
CHAPTER 2: ANALYTICAL MODELLING OF SURFACE PM GENERATOR DRIVES
The stator resistance of a SPM generator can be normalised with respect to the
generator’s reactance at rated speed. This base value of stator resistance is given by:
(2-15)
It was also important to normalise the output voltage and current of each simulation.
The rated output voltage and characteristic current were chosen as the base values. Finally,
the value of power used to normalise the simulated values of power is given by:
(2-16)
2.2 Single Phase Power Electronic Converter Models
As stated in Chapter 1, three of the most common AC/DC power electronic
converters utilised in small-scale wind turbines are the rectifier, SMR and inverter [20].
These converters can be analysed mathematically by representing them as a load to the
single-phase equivalent circuit of a SPM generator. The single phase sinusoidal model
makes a key assumption of presuming that all AC waveforms present in the circuit will be
perfect sinusoids.
Figure 2-5 shows a comparison of the circuit diagram, single-phase equivalent
circuit, and low and high-speed phasor diagrams for each of these three topologies. The
rectifier is presented on the first row, followed by the SMR on the second row, and the
inverter on the third row. The remainder of this chapter will investigate the usage of the
single-phase equivalent model to predict SPM generator performance with the three
different power electronic converters.
2.2.1 Rectifier
A rectifier is an AC/DC converter which operates by converting a single-phase or
three-phase AC input voltage into a fixed DC output voltage. A three-phase example of
this circuit is shown in Figure 2-5. The output phase voltage and current of the rectifier are
assumed to be in phase [33], which gives rise to a unity power factor. The single phase
model of the rectifier for the case where E > VO is shown on the centre of the top row in
24
2.2. SINGLE PHASE POWER ELECTRONIC CONVERTER MODELS
Phasor Diagrams
Circuit Diagram
Single-Phase Equivalent
RS
I
Rectifier
a)
+
VDC
-
Low Speed
ωLS
n < 1 pu
High Speed
n > 1 pu
E
jωLSI
V
E
E
RL
V
 I
E< V
I
RS
ωLS
n < 1.41 pu
E
E> V
n > 1.41 pu
E
jωLSI
+
VDC
E
-
SMR
b)
RL
V
45o
V
jωLSI
I

I
V
I RS
ωLS
I= 0.71 pu
V =1pu
n < 0.71 pu
n > 0.71 pu
jωLSI
Inverter
c)
+
VDC
-
RL
E

1
j C
I
V
E
I
E
45o
I = 1 pu
 
V
I,V = 1 pu
Figure 2-5: Three-phase (left column), and single-phase equivalent (centre column) models, and
phasor diagrams at low and high speeds (right column) for SPM generators operating with a
rectifier (first row), SMR (second row), and inverter (third row)
Figure 2-5. The rectifier is represented by a variable load resistance RL in order to indicate
that the phase voltage and current are ideally in phase. If a constant value of DC link
voltage is assumed, as in Figure 2-5a, RL is modified in order to control V to a constant
value of voltage which is defined by VDC. The analytical relationship between V and VDC
will be examined in section 3.1.
The phasor diagrams of generator back EMF, output voltage and phase current for
the rectifier are shown on Figure 2-5. The two phasor diagrams displayed describe the
rectifier operation at low speeds (n < 1pu) and high speeds (n > 1pu). At low speeds, the
back EMF E is smaller in magnitude than the fixed value of phase voltage V, and as a
result no current will flow in the circuit and no output power will be produced. As a result,
the single-phase equivalent circuit load in this speed range would be an open circuit. At
speeds above 1 pu, E will be greater than V, causing a phase current to flow from the
generator to the DC load voltage. The single-phase equivalent load in this range would be a
value of resistance, which is varied in order to maintain V at a constant value. This value of
25
CHAPTER 2: ANALYTICAL MODELLING OF SURFACE PM GENERATOR DRIVES
resistance RL can be evaluated by (2-17), if RS is neglected. RL can then be used to calculate
the value of phase current, and output power.
(2-17)
Figure 2-6 shows the phase current and output power as functions of the phase
voltage for an ideal (RS = 0) SPM generator with a resistive load. These simulations were
conducted at rated generator speed, as well as speeds of half and 1.5 times this value. It is
clear from the topmost graph that the generator’s open-circuit voltage changes
proportionally with speed, while the short-circuit current remains constant. This is because
the inductive reactance and back-EMF in a SPM generator are both proportional to speed
[27]. The lower graph shows that the maximum value of power and the phase voltage
which results in this point are proportional to the generator’s speed.
I (pu)
1
0.5
 = 0.5 pu
1 pu
1.5 pu
1 pu
n = 1.5 pu
P (pu)
0
1
0.5
0
0
0.5 pu
0.5
1
1.5
V (pu)
Figure 2-6: Plots of SPM generator phase current and output power as a function of output voltage
for generator speeds of 0.5, 1, and 1.5 pu
26
2.2. SINGLE PHASE POWER ELECTRONIC CONVERTER MODELS
1
Inverter
0.8
Iq
0.6
Rectifier, SMR
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
Id
Figure 2-7: Comparison of the dq axis current loci for a SPM generator operating with a rectifier,
SMR and inverter with a fixed voltage load
Figure 2-7 shows a comparison of the dq current axis loci obtained when a SPM
generator was operated into a rectifier, SMR and inverter. The locus obtained for the
rectifier was resembled a semi-circle centred about 0.5 pu on the Id axis and 0 pu on the Iq
axis. It should be noted that this curve was in the positive side of the d-axis because the
SPM machine was being operated as a generator.
The main weakness of the rectifier is its inability to produce output power at low
speeds (n < 1pu). This will be highlighted in the next section. The next topology which
will be investigated, the SMR, seeks to address this problem.
2.2.2 SMR
The circuit diagram of a single-switch SMR was given in Figure 2-5b. Figure 2-8
shows the output power versus speed characteristic of rectifiers with different values of DC
voltage. It is clear that a rectifier with a higher value of DC link voltage will produce a
greater value of maximum output power than one with a lower value of DC link voltage
[34]. However, a lower value of DC link voltage will allow power generation to occur at
lower speeds. It is apparent that there is a trade-off between power generation at low
speeds, and maximum power generation.
The SMR eliminates this conundrum by reducing the rectifier output voltage at low
speeds [21]. This causes the phase voltage of the SPM generator to be a controllable
27
CHAPTER 2: ANALYTICAL MODELLING OF SURFACE PM GENERATOR DRIVES
1
P (pu)
0.8
0.6
SMR (VDC)
Rectifier (VDC)
0.4
Rectifier (VDC/2)
0.2
Rectifier (VDC/4)
0
0
0.5
1
1.5
2
2.5
3
n (pu)
Figure 2-8: Comparison of SMR and rectifier output power P as a function of speed n for rectifiers
with output voltages equal to, half and a quarter of the SMR output voltage. Output power is
normalised as a function of high speed SMR power, while speed is normalised to that at which the
induced voltage equals rated voltage [20]
variable value, unlike the rectifier. The generator output voltage is essentially decoupled
from the DC output voltage. This varying voltage allows the SMR to produce output power
at low speeds for a fixed value of DC link voltage, which is illustrated by Figure 2-8.
A similarity between the SMR and rectifier is that both topologies are incapable of
performing a phase shift between the output voltage and current waveforms, and hence
must operate at unity power factor. As a result, the SMR also be modelled as a resistive
load in the single-phase equivalent circuit model of a SPM generator, as shown in the
central diagram in the second row of Figure 2-5 [35]. Despite the similarities in equivalent
circuit model, the generator output voltage V for the rectifier case is a constant value
defined by the DC link voltage, while in the SMR case V can be controlled to a value
which is smaller than the rectifier output voltage.
This circuit can be analysed using the assumption that for maximum power
transfer, the magnitude of the source and load impedances of a system must be equal. The
load resistance used in the single-phase equivalent model of the SMR is then calculated by:
(2-18)
28
2.2. SINGLE PHASE POWER ELECTRONIC CONVERTER MODELS
The phasor diagrams for a SPM generator operating into an SMR at low (n < 1.41
pu) and high (n > 1.41 pu) are shown in Figure 2-5. If an ideal (RS = 0) SPM generator
model is used, (2-18) shows the phase current waveform will have a magnitude of 0.71 pu,
and a phase angle of 45 o [20]. This is expected since RL will be equal to the magnitude of
XS in this case.
At higher speeds (n>1.41 pu), the magnitude of V required for maximum power
generation will increase past VO. In order to limit V to VO, the effective value of load
resistance RL’ at high speeds must be adjusted by:
(2-19)
Once this value has been determined, the phase current, voltage and output power of
the system can be calculated again using the previous equations.
The dq axis current plot of the SMR is identical to that of the rectifier, shown in
Figure 2-7. This is because like the rectifier, the SMR always keeps V and I in phase.
2.2.3 Inverter
The last topology which will be analysed is the inverter. The circuit diagram of this
topology is shown on the left-hand side of the bottom row of Figure 2-5. This device
operates by generating a leading phase shift, which keeps the generator back-EMF and
current waveforms in phase at speeds where the voltage is below the rated voltage [20]. As
a result of this phase shift, the inverter can be represented as an RC load in the single-phase
equivalent circuit model, shown in the central diagram of the bottom row of Figure 2-5.
At phase voltages below the SPM generator’s rated voltage VO (n < 0.71pu), the
inverter operates by producing its rated value of current [36]. At low speeds, the SPM
generator was controlled such that I was in phase with E. This indicated that the d-axis
component of the phase current waveform would be zero. Equations (2-5) and (2-6) were
then used to calculate the d and q-axis voltage components, before (2-11) was used to
calculate the magnitude of the phase voltage, V. The phasor diagram for this speed range is
shown on the right-hand side of the bottom row of Figure 2-5. A 45o phase shift exists
between V and I.
29
CHAPTER 2: ANALYTICAL MODELLING OF SURFACE PM GENERATOR DRIVES
Once the SPM generator’s speed was increased such that V > VO (n > 0.71pu), the
inverter controls V to be equal to VO by reducing the leading phase shift on I, such that I
was no longer in phase with E. This technique is known as field or flux-weakening, and
operates by increasing the value of Id in order to reduce V at the cost of a higher current
magnitude and hence copper losses [37].
This required generator parameters for field-weakening control were found
numerically by varying , the angle between E and I from 0o to 90o for a given value of
speed. The values of Vd and Vq were then be calculated by (2-5) and (2-6). The value of V
was once again be determined by (2-11). The angle  was swept until V = VO, at which
point it was be used to calculate the value of . The output power produced by the inverter
could then be calculated by (2-9).
As in the previous cases, the magnitude and phase of the current waveform could be
used to calculate the values of Id and Iq. These simulated results were compared with those
obtained for the rectifier and SMR in Figure 2-7. The inverter was capable of producing an
Iq value of unity when Id was zero, which was twice than the maximum value of Iq
produced by the rectifier or SMR (0.5 pu). This indicates that at low speeds, the inverter is
capable of producing twice the output power when compared to the SMR or rectifier. At
higher speeds the power produced by an inverter is comparable to that of a rectifier or
SMR, since field-weakening is used to limit the value of V to VO.
2.2.4 Performance Predictions
Figure 2-9 shows a comparison of the phase voltage, current, power factor and output
power for a SPM generator using a rectifier, SMR or inverter as its load. The top most
graph of Figure 2-9 shows the phase voltage versus generator speed curve. In this graph,
the voltages are normalised with respect to the generator and power electronics rated
voltage, VO. It can be seen that the voltage rises linearly at low speeds, but is eventually
clamped to its rated value, VO. The rate of change of the voltage characteristic prior to the
rated value depends on the power converter used. The inverter’s voltage increases fastest
with speed, followed by the rectifier, and finally by the SMR.
The second graph in Figure 2-9 shows the phase current versus generator speed plot
for an SPM generator, when operating with each of the three power electronic converters.
The rectifier does not produce current below its rated speed, which is shown as 1 pu on this
30
2.2. SINGLE PHASE POWER ELECTRONIC CONVERTER MODELS
V (pu)
1.5
1
Inverter
SMR
0.5
0
Rectifier
0
I (pu)
1.5
SMR
0.5
2
1.5
2
1.5
2
1.5
2
Rectifier
0
1.5
pf
1.5
Inverter
1
0
0.5
0.5
SMR, Rectifier
1
Inverter
0.5
0
0
0.5
P (pu)
1
Inverter
0.5
SMR
Rectifier
0
0
0.5
1
n (pu)
Figure 2-9: Summary of phase voltage, current, power factor and output power for a SPM
generator with RS = 0 pu using a rectifier, SMR and inverter as the power converter.
graph. In contrast, the SMR produces current at a magnitude of 0.71 pu at speeds below
1.41 pu, after which the current begins to rise towards 1 pu. Lastly, the inverter produces a
current of magnitude 1 pu at all speeds.
The third graph in Figure 2-9 shows the graph of generator output power factor with
respect to generator speed. For the rectifier and SMR, this value is always unity, and is not
affected by generator speed. The inverter, in contrast, has a power factor of 0.71 below
speeds of 0.71 pu. The value of power factor rises towards unity at higher speeds.
The output power versus speed plot of the SPM generator with rectifier load is
presented in the bottom graph of Figure 2-9. The values of power in this graph are
normalised with respect to the rated power, PO. This graph is identical to the phase current
versus speed plot for the rectifier, since the rectifier voltage and power factor are equal to 1
pu at this point. The inverter produces the largest value of output power, and produces
twice the output power of the SMR at low speeds. At high speeds the values of power
asymptote towards one per-unit for all three power converters.
31
CHAPTER 2: ANALYTICAL MODELLING OF SURFACE PM GENERATOR DRIVES
The single phase sinusoidal model makes a key assumption of presuming that all AC
waveforms present in the circuit will be perfect sinusoids. In reality the line-side current
waveforms are highly distorted at low generator speeds [38], while the output voltage
waveforms resemble a six-step waveform at higher speeds [33]. A simulation model which
takes these non-ideal characteristics of the AC waveforms is clearly required. The three
phase SPM generator model is used, along with a three phase model of the power
electronic converters.
2.3 Conclusion
This chapter has investigated the analytical models used to describe surface
permanent magnet (SPM) generators and their AC/DC power electronic converters. The dq
current plane was introduced as a tool to visualize the rated voltages and currents of a
generator and their variation with speed.
The power electronic converters examined were the rectifier, semi-bridge switched
mode rectifier (SMR) and inverter. The rectifier operated with unity power factor and a
fixed output voltage, and could be represented as a resistive load to the single-phase
equivalent circuit of a SPM generator as a result. The semi-bridge SMR was capable of
modifying the output voltage of the generator, but was also limited to unity power factor.
As a result, the SMR could be represented as a resistive load with a controllable voltage.
Lastly, the inverter was able to modify the generator’s voltage magnitude V as well as . It
could therefore be represented as a RC load to the single-phase analytical model of the
generator.
The SMR possessed a significant advantage over the rectifier in that it was capable
of producing output power at low speeds, due to its ability to modify the value of V as a
function of generator speed. It was shown, however, that for an ideal (RS  0) SPM
generator model, maximum output power could be obtained when a leading phase shift of
45o was applied to the generator’s phase current at low speeds. Such a phase shift could
only produced by an inverter, and resulted in the inverter being able to produce two times
the output power of a SMR at low generator speeds.
The analysis presented in this chapter was based on sinusoidal assumptions for the
generator’s voltage and current waveforms. In practice this is not true when AC/DC
converters are used to load the generator. The next chapter will present time stepping
32
2.3. CONCLUSION
simulation results which will examine the effects of non-sinusoidal waveforms in the
converter’s operation.
33
CHAPTER 2: ANALYTICAL MODELLING OF SURFACE PM GENERATOR DRIVES
34
Chapter 3: AC/DC Power Electronic
Converter Simulation Models
The strength of the single-phase analytical model is the small amount of time required
to conduct performance predictions over a large range of parameters. This model assumes
that all of the AC waveforms described are sinusoids. This assumption is not always valid
and could cause discrepancies when compared to experimental findings. Non-sinusoidal
AC waveforms also cause the analytically derived constants used to convert between AC
and DC voltages and current to be inaccurate.
More accurate simulated results could be attained by utilising a time-stepping
simulation model. The main disadvantage of a time-stepping simulation model which
includes PWM is the increased time of simulation when compared to analytical
calculations. A simplified model using phase leg averaging is introduced with the intention
of modelling the effects of non-sinusoidal generator waveforms while requiring a smaller
simulation time than the PWM inclusive model.
35
CHAPTER 3: AC/DC POWER ELECTRONIC CONVERTER SIMULATION MODELS
3.1 Analytical Conversion between AC/DC Quantities
The single-phase equivalent circuit models shown in Figure 2-5 were utilized to
obtain analytical representations for the AC quantities of a SPM generator. A method of
converting these AC values into a DC representation is therefore required to analytically
model an AC/DC power electronic converter (see Figure 3-1).
Three methods of modelling the conversion process between AC and DC values will be
investigated. If the current I entering an AC/DC power electronic converter is
discontinuous, [19] stated that the DC voltage would be related to the line to line RMS
voltage VL by the following equation.
(3-1)
E
IDC
I
VL
AC/DC
VDC
Analytical
Representation
I
E
IDC
V
Conversion
Ratio
VDC
Figure 3-1: Illustration of the requirement for a conversion process in order convert the AC
quantities calculated by the single-phase equivalent circuit model into DC values.
36
3.1. ANALYTICAL CONVERSION BETWEEN AC/DC QUANTITIES
a)
2/3 VDC
V
b)
c)
t
t
VL
-2/3 VDC
V (fund)
Figure 3-2: Comparison of AC/DC voltage conversion factors obtained for sinusoidal line voltage
VL with discontinuous line current (a), continuous line current (b), and six-step phase voltage V (c).
which states that the DC voltage in such a system would be equal to the peak of the line to
line voltage. The DC voltage obtained using this conversion ratio is illustrated as line a) in
Figure 3-2. Another case investigated by [19] was the one where I was continuous. In such
a scenario, the relationship between the line and DC voltages was given by the following
equation. The DC voltage obtained using this technique is illustrated by line b) in Figure
3-2.
(3-2)
It was noted by [33] that the phase voltage V in a rectifier operating into a fixed
voltage load resembled a six-step waveform for the cases where the supply voltage E was
greater than VDC. The relationship between the peak phase voltage V and the DC voltage
was found by this study to be:
(3-3)
The DC voltage obtained using this technique is shown as line c) in Figure 3-2. The
relationship between the RMS line to line voltage and the DC voltage could then be found
to be:
37
CHAPTER 3: AC/DC POWER ELECTRONIC CONVERTER SIMULATION MODELS
(3-4)
It is useful to describe the conditions under which each of the conversion ratios are
suitable by the shape of the generator output voltage and phase current waveforms.
Equation (3-1) is valid for the case where the generator output voltage is sinusoidal, and
the phase current is discontinuous. This condition corresponds to generator speeds where
the generator back-emf voltage is slightly lower than rectifier DC output voltage. Equation
(3-2) is valid when both the voltage and current are sinusoidal. Equation (3-4) is valid for
the case where the current is sinusoidal and the voltage resembles a six-step waveform.
This scenario corresponds to high speeds where the generator back-emf voltage is much
larger than the rectifier load voltage.
A summary of the calculated ratio between line and DC voltages using the
relationships specified by (3-1), (3-2) and (3-4) are shown in Table 3-1 below.
Table 3-1: VDC/VL calculated using the equations presented in (3-1), (3-2), and (3-4).
Equation Used
VDC/VL
(3-1)
1.41
(3-2)
1.35
(3-4)
1.283
If we then make the assumption that the rectifier input power is equal to its output
power (which means that there are no losses in the conversion process) we can then find
the relationship between the AC and DC current waveforms. If the VDC/VL conversion ratio
of 1.283 is used, the following conversion ratio for IDC/IL can be calculated to be 1.35.
A comparison between the analytical results obtained using these three techniques and
simulated data is shown in the following section.
3.2 Three Phase PWM Inclusive Simulation Models
The three power electronic converters analysed in the previous chapter were the
rectifier, semi-bridge SMR and inverter. As stated previously, a time stepping simulation
model was required in order to determine the effects of non-sinusoidal waveforms. The
38
3.2. THREE PHASE PWM INCLUSIVE SIMULATION MODELS
PSIM® software was used to implement these models. In addition to modelling the effects
of non-sinusoidal waveforms, this model also investigated the effects of PWM voltage and
current signals.
3.2.1 Rectifier
Figure 3-3 shows the simulation model used to describe a three phase bridge
rectifier. The back EMF sources E, the stator resistances RS and reactance XS were assumed
to be balanced. This model can be used for ideal or non-ideal SPM generator models,
where RS = 0 for ideal models. The diodes in this model were assumed to be ideal in this
section, which meant that their forward voltage drop was 0 V.
Generator Model
Rectifier
I
VL
E
Constant
Voltage Load
VDC
RS XS
Figure 3-3: Circuit used for non-sinusoidal simulations for non-ideal SPM generator with rectifier
The graph on the upper left hand side of Figure 3-4 shows the SPM generator phase
voltage as a function of per unit speed, where the SPM generator is connected to a diode
rectifier with a constant DC voltage load, as in Figure 3-3. An ideal simulation model was
used, where the voltage drop across each diode and stator resistance RS were set to zero.
This graph shows the voltage obtained through simulations, as well as those obtained
analytically using each of the three VDC/VL conversion factors in Table 3-1. It is apparent
that for generator speeds above 1 pu, the simulated curve follows the analytical curve
obtained using the VDC/VL = 1.283 conversion ratio. This is to be expected, since the
voltage waveforms at high speeds are found to resemble six-step waveforms [33]. This is
confirmed by examining the voltage waveform for point d) in Figure 3-5, which shows a
six-step voltage.
A closer examination of the behaviour of the simulated voltage as a function of generator
speed can be obtained by viewing a zoomed in version of the graph examined previously.
39
CHAPTER 3: AC/DC POWER ELECTRONIC CONVERTER SIMULATION MODELS
This is shown on the top right hand side of Figure 3-4, where the speed range is limited
from 0.8 to 1.1 pu. It is clear that the simulated curve begins to deviate away from the
analytical curves when n was approximately 0.9 pu. The analytical curve obtained for
VDC/VL = 1.41 reaches its limiting value for a similar generator speed. This finding
indicates that the conversion ratio of 1.41 predicts the conduction point of the rectifier
more accurately. This is understandable since this conversion ratio was derived for
sinusoidal voltage waveforms, and the simulated voltage found at this speed (point (a) on
Figure 3-5) was found to be sinusoidal.
1.1
1
1.283
0.6
V (pu)
V (pu)
0.8
0.4
1
sim
0.9
1.41 1.35
0.2
0
0
1
0.8
0.8
2
1
0.9
1
1.1
0.3
d)
0.6
0.4
0.2
0.1
0.2
0
0
c)
I (pu)
I (pu)
0.8
b)
a)
1
n (pu)
2
0
0.8
0.9
1
n (pu)
1.1
Figure 3-4: Comparison of analytical (solid lines) and simulated (broken lines) SPM generator
phase voltage (top row) and current (bottom row) as a function of speed. Analytical graphs are
shown for VDC/VL conversion factors of 1.283, 1.41 and 1.35. The left hand column shows the
voltage and current for speeds between 0 and 2 pu, while the right hand column shows these
quantities for speeds limited between 0.8 and 1.1 pu.
40
3.2. THREE PHASE PWM INCLUSIVE SIMULATION MODELS
The bottom left graph of Figure 3-4 shows the SPM generator phase current as a
function of generator speed. Similarly, analytical curves obtained with each of the three
conversion ratios presented in Table 3-1 are compared with simulated values. It is clear
that for high generator speeds, the analytical current which matches the simulated results
most closely is that obtained for the VDC/VL ratio of 1.283. If we examine the same graph
for speeds in the range 0.8 to 1.1 pu (bottom right hand side of Figure 3-4) it is apparent
that the simulated current becomes non-zero for a speed of approximately to 0.9 pu, which
is similar to the speed predicted by the analytical curve obtained using the VDC/VL curve of
1.41. These findings validate the earlier inference made from the voltage results, which
was that the VDC/VL ratio of 1.41 was more suitable for calculating analytical results at
speeds near the rectifier conduction point, while the VDC/VL ratio of 1.283 was more valid
for higher generator speeds.
Generator speeds of 0.9 (a), 1 (b), 1.1 (c) and 2 (d) pu were highlighted on Figure 3-4
as points of interest. The phase voltage and current waveforms obtained at each of these
speeds are presented in Figure 3-5. It has been previously stated that the voltage waveform
at point (a) resembled a sinusoid, while the voltage at point (d) resembled a six-step
waveform. The voltages at points (b) and (c) show how the voltage waveform becomes
less sinusoidal and more like a six-step waveform as generator speed is increased. The
phase current produced at (a) is close to zero, but increases with generator speed. The
shape of the phase current waveform is highly distorted at points (b) and (c), but becomes
sinusoidal at the higher speed of point (d).
The analysis and simulations presented up to this point have shown that the VDC/VL
ratio of 1.41 provides analytical results which match simulations closely for generator
speeds close to the rectifier conduction point, where the magnitude of the phase current is
small. At higher speeds, the ratio of 1.283 provides accurate analytical results due to its
derivation from the six-step voltage waveform model. The ratio of 1.35 provides analytical
results which fall in between the other two ratios. It is apparent that a highly accurate
analytical model would require the use of a variable VDC/VL conversion ratio, which
changes as a function of generator speed. It was decided however to simplify the analysis
presented in this thesis by only using the VDC/VL conversion ratio of 1.283. The reasoning
behind this choice was that the ratios of 1.41 and 1.35 were only valid for generator speeds
very close to the rectifier conduction point. For higher speed values, the ratio of 1.283
41
CHAPTER 3: AC/DC POWER ELECTRONIC CONVERTER SIMULATION MODELS
V = 0.91 pu
I (pu)
V (pu)
a)
0
-1
0
0.01
V = 0.97 pu
I (pu)
V (pu)
0
0.01
c)
0
0.01
0.02
I = 0.26 pu
c)
I (pu)
V (pu)
I = 0.087 pu
1
0
-1
0.01
0
I (pu)
0
-1
0.02
0.01
0.02
I = 0.84 pu
1
d)
0.01
t (s)
0
-1
0.02
V = 1 pu
V (pu)
0.02
0
-1
0.02
V = 0.99 pu
0
0.01
b)
-1
1
0
1
0
0
0
-1
0.02
1 b)
1
I = 0 pu
1
1 a)
d)
0
-1
0
0.01
t (s)
0.02
Figure 3-5: Waveforms of simulated phase voltage and current for an SPM generator with R S = 0
pu operating into a rectifier at speeds of 0.9 (a), 1 (b), 1.1 (c) and 2 (d) pu
resulted in a smaller error between experimental and simulated curves.
Another method of examining the correspondence between simulated and analytical
values for a SPM generator operating into a diode rectifier with a DC voltage load was to
operate at a constant generator speed, and vary the DC voltage. Graphs of the simulated
and analytical phase voltage, current and DC output power curves obtained where the DC
voltage was varied between 0 to 1 pu for generator speeds of 0.5, 1 and 1.5 pu are shown in
Figure 3-6. In should be noted that the analytical curves presented in this figure were
calculated using a VDC/VL ratio of 1.283.
42
3.2. THREE PHASE PWM INCLUSIVE SIMULATION MODELS
The discrepancy between the analytical and simulated phase voltages was found to
be minor for all three generator speeds. It should be noted, however, that the discrepancy
between analytical and simulated phase currents increases as the DC voltage was
increased. This increase in error as DC voltage was increased is also observed between the
analytical and simulated output power values. An increasing value of DC output voltage
for a fixed generator speed reduces the generator current, thereby causing the rectifier to
operate closer to its conduction point. This in turn resulted in greater errors between the
analytical and simulated values, since the conversion ratio of 1.283 used to calculate the
analytical results was only valid for six-step voltage waveforms, which occurred when the
magnitude of the phase current was large.
This section has showed that the time-stepping simulation model of a rectifier
constructed through PSIM® was able to accurately model the effects of non-sinusoidal
voltage and current waveforms. This simulation model will be extended to the SMR in the
following section.
V (pu)
1
1, 1.5 pu
0.5
0
0
n = 0.5 pu
0.2
0.4
0.6
0.8
I (pu)
1
0.5
0
0
1.5 pu
n = 0.5 pu
0.2
0.4
1 pu
0.6
0.8
1
PDC (pu)
1
1
1.5 pu
0.5
0
0
n = 0.5 pu
0.2
0.4
0.6
VDC (pu)
1 pu
0.8
1
Figure 3-6: Comparison of analytical and simulated values of phase voltage, current and DC output
power as a function of DC link voltage for a SPM generator operating into a rectifier with DC
voltage load at speeds of 0.5, 1 and 1.5 pu. The analytical results were obtained using the VDC/VL
conversion ratio of 1.283.
43
CHAPTER 3: AC/DC POWER ELECTRONIC CONVERTER SIMULATION MODELS
3.2.2 SMR
A semi-bridge SMR is capable of modifying the line voltage VL by changing the duty
cycle of the three switches in the bottom half of the power electronic converter bridge
shown in Figure 3-7. A comparator is used to generate a PWM signal with constant duty
cycle based on a reference voltage level. This signal is then fed into the gates of the IGBTs
used in the lower half of the power converter bridge. Reference [21] stated that the number
of semiconductor devices in this topology could be reduced by integrating the switch on
the output of the diode rectifier into the bottom half of the bridge, assuming that these three
switches were all driven at the same duty cycle. This would add an additional two
transistors, but remove three diodes. This topology is known as the semi-bridge SMR
(Figure 3-7), and is used as the basis for the non-sinusoidal simulations given in this
section.
Semi-bridge SMR
Generator Model
I
VL
VDC
Constant
Voltage Load
PWM Signal Generator
d
Figure 3-7: Three-phase non-sinusoidal simulation model of a semi-bridge SMR operating with a
SPM generator
44
3.2. THREE PHASE PWM INCLUSIVE SIMULATION MODELS
The analysis presented in (2-18) showed that there is particular value of load
resistance in the single-phase sinusoidal model of the SMR which corresponds to
maximum output power at a given speed. In the three-phase simulation model, this
optimum load value corresponds to a transistor PWM drive duty cycle which causes an
optimum line voltage, VL to be generated. Figure 3-8 plots the analytical and simulated
SPM generator fundamental phase voltage, current and DC output power as a function of
transistor duty cycle at generator speeds of 0.5, 1 and 1.5 pu. It should be noted that the
VDC/VL ratio of 1.283 was utilized to calculate the analytical results in this case. The diode
and IGBT voltage drops were set to zero in this case.
These diagrams clearly show that the generator output voltage V is proportional to
(1 - d), while I increases as a function of d. It is apparent from the power versus duty cycle
plots that the optimum value of duty cycle decreases as generator speed increases. There is
little difference between the simulated and analytical values of voltage. The plot of phase
current as a function of duty cycle, however, shows errors between the simulated and
analytical values for low values of current. This error is also noted between the analytical
and simulated values of output power at the corresponding duty cycles. It should be noted
that the graphs presented in Figure 3-8 closely resemble the graphs shown in Figure 3-6
which have been mirrored about the x-axis.
45
CHAPTER 3: AC/DC POWER ELECTRONIC CONVERTER SIMULATION MODELS
V (pu)
1
n = 1.5, 1 pu
A
0.5
0.5 pu
C
B
0
0
20
40
60
80
100
I (pu)
1 n = 1.5 pu
C
0.5
0
1 pu
(pu)
0.5 pu
A
0
1
20
40
60
80
100
n = 1.5 pu
B
0.5
P
DC
B
0
A
1 pu
C
0.5 pu
0
20
40
60
80
100
d (%)
Figure 3-8: Comparison of analytical (solid lines) and simulated (dashed lines) ideal SPM
generator phase voltage, current and output power as a function of duty cycle when operating into a
SMR with fixed output voltage at speeds of 0.5, 1 and 1.5 pu
The phase voltage and current waveforms at points A (d = 0%), B (maximum output
power, obtained at d = 39%) and C (d = 100%) are shown in Figure 3-9 below for a SPM
generator speed of 1 pu. This image shows that the phase voltage waveform changes from
a sinusoid at the open circuit point to a PWM value at the maximum power point, before
becoming zero at the short-circuit point. In contrast, the phase current waveform is small at
point A, slightly distorted at the maximum power point and a perfect sinusoid at point C.
5
1.5
5,
pu
pu
1p
46
3.2. THREE PHASE PWM INCLUSIVE SIMULATION MODELS
1
A
I (pu)
V (pu)
1
0
-1
0
0.01
1
0
0.01
0
0.01
0.02
0
0.01
0.02
0
0.01
t (s)
0.02
1
Fund
0
-1
-1
0.02
I (pu)
V (pu)
B
0
0
-1
0.02
1
1
I (pu)
V (pu)
C
0
-1
0
0.01
t (s)
0.02
0
-1
Figure 3-9: Simulated phase voltage and current waveforms obtained when an ideal SPM
generator is operated into a fixed voltage load at 1pu speed with duty cycles of 0% (A), 39% (B)
and 100% (C)
These phenomena can be explained by examining the circuit diagram of the semibridge SMR, shown in Figure 3-7. Driving the three transistors in the bottom half of the
power converter’s bridge with a duty cycle of 0% will cause these switches to form open
circuits, meaning that the free-wheeling diodes in parallel to the transistors would be the
only component in this section of the bridge. It is clear that this new topology would be the
same as a rectifier. Thus it can be concluded that the semi-bridge SMR has the same
performance as a rectifier with an output voltage of VDC when its three transistors have a
duty cycle of 0%. This explains why the current and power produced by the SMR are zero
at a speed of 0.5 pu for duty cycles of less than 50%, since under these conditions the SMR
behaves as a rectifier operating with an output voltage too high to facilitate rectifier
conduction.
In contrast, a duty cycle of 100% causes the transistors in Figure 3-7 to be replaced
by short circuits. This has the effect of short circuiting each phase of the SPM generator,
giving rise to a current of 1 pu, which can be viewed in Figure 3-8 and Figure 3-9.
47
CHAPTER 3: AC/DC POWER ELECTRONIC CONVERTER SIMULATION MODELS
A comparison between the analytical model of the SMR presented in Section 2.2.2
and the simulation model presented in this section can be conducted by investigating the
power versus current loci. This plot will abstract away the effect of duty cycle on the
simulated results, thus allowing a valid comparison. Figure 3-10 plots the power versus
current loci on the left side, and the Id versus Iq on the right hand plot. Points A, B and C
are once again displayed, where A was the open-circuit point, B was the maximum power
point and C was the short-circuit point. The values of I and Id at point A are 0, while at
point C their value is 1 pu. The maximum power point of the generator is equivalent to the
point at which the maximum value of Iq is produced. This operating point occurs when
I = 0.69 pu and Id = 0.53 pu.
0.5
0.5
Analytical
0.45
0.45
0.4
0.4
0.35
0.35
0.3
B
0.3
Simulated
I (pu)
0.25
0.25
q
P (pu)
B
0.2
0.2
0.15
0.15
0.1
0.1
0.05
0
A
C
0.05
A
C
0
0.5
1
0
0.5
1
Id (pu)
I (pu)
Figure 3-10: Comparison of analytical and simulated P vs I loci and I d vs. Iq loci for an ideal SPM
generator operating into a SMR with a fixed output voltage load at a generator speed of 1 pu.
0
The performance of the simulation model in comparison to the analytical model over
a range of speeds is shown in Figure 3-11. This diagram shows a comparison between the
rectifier and SMR for the phase voltage, current and output power as a function of
generator speed. The analytical performance curves of each topology is the same as that
displayed in Figure 2-9, which showed that the SMR was capable of producing output
power at low speeds, unlike the rectifier. The performance of the two techniques was
48
3.2. THREE PHASE PWM INCLUSIVE SIMULATION MODELS
similar at higher speeds. Some error between analytical and simulated values was
observed, with the maximum discrepancy between output powers obtained from these
models being 23% for the rectifier and 13% for the SMR. It should be noted that this error
was reduced for high values of generator speed, due the six-step nature of the phase
voltage under this condition.
This section has proved that the non-sinusoidal simulation model can be used with
good accuracy to predict the performance of the SMR, when utilized in conventional SMR
modulation. This non-sinusoidal simulation model can also be extended to the inverter.
The results of these simulations will be presented in the following section.
V (pu)
1
Rectifier
0.5
SMR
0
0
0.5
1
1.5
2
0
0.5
1
1.5
2
0
0.5
I (pu)
1
0.5
0
P (pu)
1
0.5
0
1
1.5
2
n (pu)
Figure 3-11: Comparison of analytical (solid) and simulated (dashed) phase voltage, current and
output power as a function of generator speed for an ideal SPM generator operating into a SMR or
a rectifier with a fixed voltage load
49
CHAPTER 3: AC/DC POWER ELECTRONIC CONVERTER SIMULATION MODELS
3.2.3 Inverter
It was shown through analysis in Section 2.2.3 that an inverter was capable of
producing two times the output power of a SMR at low generator speeds. These analytical
results were obtained based on the assumption that the phase voltage and current
waveforms of the SPM generator were sinusoids. Some form of time-stepping simulation
model was therefore required in order to verify that these analytical results were accurate.
The simulation model used to implement inverter modulation is shown in Figure
3-12. The three phase current waveforms of the generator were filtered, then passed to a
control block which generated the required duty cycles for each phase at a given instant in
time. This control block required input parameters of the required period  during which
the lower transistor for a given phase was switched on for after the positive zero-crossing
of the phase current, and d, the duty cycle of the lower switch during the 180o period when
the voltage of a given phase was being modulated. Details about the code used to generate
this control logic are given in Appendix C. This modulation strategy gave rise to a six-step
voltage waveform (see Figure 1-6d).
In Figure 2-9 it was shown that an inverter operated with maximum output power
when the phase shift  was set to 45o at low values of generator speed. This corresponds
to a power factor of 0.71. The analytical results of generator voltage, current, power factor
and output power obtained under these conditions were compared with their simulated
counterparts under maximum output power operation in Figure 3-13 for speeds in the
range 0 to 2 pu. The simulated results follow the same trends as their analytical
counterparts: at speeds below 0.71 pu, the power factor is controlled to 0.71 and the
generator voltage rises as a function of speed. For higher generator speeds, voltage is
limited to 1 pu and power factor increases towards unity.
50
3.2. THREE PHASE PWM INCLUSIVE SIMULATION MODELS
Inverter
Current
Generator Model Waveforms
VL

VDC
Constant
Voltage Load
PWM Signal Generator
d
f
Control Logic
Filtered Current
Waveforms
Figure 3-12: Three-phase non-sinusoidal simulation model of a SPM generator operating into an
inverter with a constant voltage load.
51
pf
I (pu)
V (pu)
CHAPTER 3: AC/DC POWER ELECTRONIC CONVERTER SIMULATION MODELS
1.5
1
0.5
0
0
1.5
1
0.5
0
0
B
0.5
1
0.5
1
2
1.5
2
B
A
0.5
1
Analytical
1.5
2
B
0.5
A
0
0
1.5
B
A
0.9
0.8
0.7
0
1
P (pu)
A
0.5
Sim
1
n (pu)
1.5
2
Figure 3-13: Comparison of analytical (solid) and simulated (dashed) phase voltage, current, power
factor and output power as a function of generator speed for an ideal SPM generator operating into
an inverter with a DC voltage load. Points of interest at 0.5 pu (A) and 1.5 pu (B) speed are
marked.
Points of interest are highlighted at generator speeds of 0.5 and 1.5 pu on Figure
3-13. The phase voltage, current and fundamental phase voltage at these speeds are
examined in Figure 3-14. It is apparent that the magnitude of the fundamental phase
voltage for case A is smaller than in case B. This is caused by the modulation of the phase
voltage waveform with a PWM signal. In case B, the duty cycle of the PWM signal is set
to unity in order to achieve V = 1pu. Inspection of the phase current waveforms shows that
the current waveform is more distorted at point A as the inductor voltage is more distorted
at this generator speed.
The simulations models for the semi-bridge SMR and inverter examined in this
section have used PWM to vary the magnitude of their generator phase voltage waveform.
A disadvantage of this technique is that a small simulation time step is required to model
the high frequency PWM switching. The following section will examine how simulation
52
3.3. SIMPLIFIED SIMULATION MODEL
A
V
V (pu)
1
0
10
20
30
A
1
I
0
-1
-1
10
20
t (ms)
V (fund)
0
0
0
V
-1
V (fund)
0
1
B
0
-1
I (pu)
1
30
0
5
10
5
t (ms)
10
B
I
Figure 3-14: Simulated phase voltage (including fundamental component) and current waveforms
for an SPM generator operating into a inverter with a DC voltage load at generator speeds of 0.5 pu
(A) and 1.5 pu (B)
time can be reduced by examining a simplified simulation model, which uses phase leg
averaging to model the effects of PWM switching.
3.3 Simplified Simulation Model
Extensive simulations were required to investigate the power electronic converter
topologies presented in this thesis. The simulations presented to this stage have utilised a
time-stepping simulation model where the switching components were modelled using
PWM. This complete simulation model was referred to as the PWM inclusive simulation
model. This method resulted in accurate, but time-consuming simulations.
In order to reduce the time spent on simulations and provide additional
understanding of the power electronic converter topologies used, it was decided to devise a
simplified simulation model, which abstracted the effects of PWM switching by using the
relationships which described DC-DC converters. This method was trialled with the singleswitch and semi-bridge SMR topologies.
53
CHAPTER 3: AC/DC POWER ELECTRONIC CONVERTER SIMULATION MODELS
The simplified models for the single-switch and semi-bridge SMRs could be
simulated using a time-stepping software simulation package such as PSIM®. The main
advantage from utilising these models was that the simulation time step could be increased,
due to absence of PWM. This would in turn reduce overall simulation time. For example, a
PWM frequency of 10 kHz required a maximum time step of 10 μs if the complete
simulation model was used. If the simplified model was utilized, this time step could be
increased to 50 μs. This change in time step corresponded to a decrease in simulation time
of 300%.
3.3.1 Simplified Model for Single-switch SMR
The circuit diagram of a single-switch SMR was shown in Figure 2-5b, which can be
considered as a rectifier with a boost switch added to the DC link. An equivalent circuit
model which represents the DC-DC converter as a DC transformer can be utilized [39-41].
The relationship between the DC link and output voltages and currents are provided by the
following standard boost converter equations [19]:
(3-5)
(3-6)
In these equations, d represents the duty cycle of the PWM modulation of the
transistor in the single-switch SMR. Figure 3-15 shows how these equations can be
implemented into the simulation model of the single-switch SMR, thus creating the
simplified simulation model. A variable voltage source is used in the simulation to set the
phase leg voltage as a function of duty cycle and the DC output voltage. The output current
is computed by a controlled current source using this duty cycle, and the rectifier DC link
current.
This technique of replacing the transistor-diode boost converter configuration with
the mathematical equations presented above can also be used in order to simulate the semibridge SMR. This method is described in the next section.
54
3.3. SIMPLIFIED SIMULATION MODEL
VDC = (1-d)VOUT
IOUT
IDC
E
RS
XS
I
VL
IOUT =
(1-d)IDC
VDC
+
VOUT
-
Figure 3-15: Simplified PSIM simulation model for single-switch SMR operating with a SPM
generator
3.3.2 Simplified Semi-bridge SMR Model
A close inspection of the semi-bridge SMR’s circuit diagram (Figure 3-7) shows that
the diode-transistor pairs on each phase leg are similar to the boost-converter configuration
of a single-switch SMR. Equations (3-5) and (1-1) can then be extended in order to
calculate the voltages and currents for each phase of the semi-bridge SMR. The resultant
circuit diagram for the simplified semi-bridge SMR model is given in Figure 3-16 below.
Two diodes are added around each voltage source in order to ensure that the voltage
sources will only be operational while the phase current is positive. This emulates the
operation of a semi-bridge SMR, which will only modulate the voltage waveform under
such conditions.
E
RS
XS
Va = (1-da)VOUT
IOUT = Ia’ + Ib’ + Ic’
Ia
Vb = (1-db)VOUT
Ib
Ia’ =
(1-da)Ia
Vc = (1-dc)VOUT
Ib’ =
(1-db)Ib
Ic’ =
(1-dc)Ic
+
VOUT
-
Ic
Figure 3-16: Simplified simulation model of a SPM generator with a semi-bridge SMR operating
into a fixed output voltage load
55
CHAPTER 3: AC/DC POWER ELECTRONIC CONVERTER SIMULATION MODELS
The equations used to calculate the phase voltages and output currents are given
below:
(3-7)
(3-8)
(3-9)
Here dk is the transistor PWM modulation duty cycle for a particular phase of the
simulation model.
This simplified semi-bridge SMR model could be used to simulate either
conventional SMR, or phase advance modulation. Chapter 5 will provide more discussion
on the control parameters used by this modulation technique.
3.3.3 Simplified Inverter Model
The inverter uses a similar simplified simulation model to the semi-bridge SMR.
Unlike a semi-bridge SMR an inverter is capable of producing a phase leg voltage
waveform which is positive even when the corresponding phase current is negative. This
means that the two diodes present on each phase in the left-hand side of Figure 3-16 can be
removed from the simplified inverter model, which is shown in Figure 3-17.
The same DLL block shown in Figure 3-12 was used to calculate the switching duty
cycles required for equations (3-7) and (3-8) to implement the six-step waveform shown in
Fig. 1.9d. A phase shift angle,  is introduced at the start of the SPM generator’s phase
current waveform during which d = 1. This results in a phase leg voltage Vk = 0. After
period  is over, d is controlled to a value which allows the desired phase leg voltage Vk to
be generated for 180 electrical.
56
3.4. SIMPLIFIED AND PWM INCLUSIVE MODEL COMPARISON
E
RS
XS
Va = (1-da)VOUT
IOUT = Ia’ + Ib’ + Ic’
Ia
Ib
Vb = (1-db)VOUT
Ia’ =
(1-da)Ia
Ib’ =
(1-db)Ib
Ic’ =
(1-dc)Ic
+
VOUT
Vc = (1-dc)VOUT
-
Ic
Figure 3-17: Simplified simulation model of a SPM generator with an inverter operating into a
fixed output voltage load
3.4 Simplified and PWM inclusive Model Comparison
It was expected that the simplified and PWM inclusive models should show a close
match when power converter voltage drops were neglected. It was also expected that the
simulated results obtained for both the single-switch and semi-bridge models would be
similar if they were both driven by conventional SMR modulation [21]. The simulations in
this section will be for ideal power electronic converters, with zero voltage drops. Voltage
drops can be added to the simulation models by adding the required voltage drop to the
calculated value of Vk given in (3-7).
3.4.1 Ideal Single-Switch and Semi-Bridge Comparison
This section compares the simulated results obtained when an ideal (RS  0) SPM
generator model was utilised with the simplified and complete simulation models for both
the single-switch and semi-bridge SMRs. Figure 3-18 plots the results obtained at a
generator speed of 1 pu. The top row shows a comparison of the simulated results for
phase voltage, current and output power as a function of SMR duty cycle obtained using
the simplified and complete simulation models with a single-switch or semi-bridge SMR.
The duty cycle used ranges between 0-100% in steps of 1% for the simplified model, and
steps of 10% for the complete model. The results of the PWM inclusive model are plotted
as points, whereas the simplified model is plotted as a dashed line.
The characteristics of voltage, current and output power as a function of d are very
similar to those observed in Section 3.2.2 when generator speed was set to 1 pu. It is clear
from these graphs that the simplified and PWM inclusive models have very similar results.
57
CHAPTER 3: AC/DC POWER ELECTRONIC CONVERTER SIMULATION MODELS
In addition, there is a close correspondence between the results obtained for the singleswitch and semi-bridge SMRs. This is in accordance with the conclusion made by [21].
The three points of interest marked upon these graphs are the open circuit point
(A, d = 0%), the point corresponding to maximum power with conventional SMR
modulation (B, d = 36%), and the short circuit point (C, d = 100%). The voltage and
current waveforms obtained at these points are illustrated in the second row of Figure 3-18.
The voltage and current waveforms obtained at the SMR open circuit point (A)
show a close correspondence between the simplified and PWM inclusive models. This is to
be expected, since no PWM switching occurs at this duty cycle. The same phenomenon is
experienced at the short circuit point (C), since PWM switching once again does not occur
at this duty cycle.
Single-switch
Semi-bridge
0.5
1
A
C
B
0
0
20
V (pu)
V (pu)
1
40
60
80
100
I (pu)
B
A
20
40
60
80
P (pu)
Simp
C
A
20
40
20
40
60
80
0
0
100
A
PWM
20
40
0.01
-1
0
0.01
t (s)
0.02
0
-1
I (pu)
0
0.01
B
0
0.01
t (s)
0.02
0
0.01
0.02
0
0.01
0.02
0
0.01
0.02
1
Simp
0
PWM
0
0
-1
0.02
0.01
0
-1
0.02
1
V (pu)
I (pu)
0.01
0
-1
0.02
1
0
100
1
1
C
0
80
A
-1
0.02
0
-1
0.02
60
I (pu)
0.01
V (pu)
Simp
1
V (pu)
0
1
PWM
0
0
-1
0.02
0
-1
100
C
1
C
I (pu)
0.01
V (pu)
I (pu)
0
B
1
1
I (pu)
V (pu)
V (pu)
Waveforms at
points of
interest
80
d (%)
A
B
60
Simp
A
1
0
100
0.5
B
1
80
C
d (%)
-1
60
B
0
0
100
PWM
0
0
40
0.5
P (pu)
I (pu)
C
0.5
20
1
0.5
0
0
C
B
0
0
1
Effect of duty
cycle variation
A
0.5
0
-1
0
0.01
t (s)
0.02
0
-1
t (s)
Figure 3-18: Comparison of the simulated phase voltage, current and output power as a function of
duty cycle for the single-switch and semi-bridge SMRs for a PWM inclusive (solid) and simplified
(dash) simulation models (top row). Also shown are the simulated phase voltage and current
waveforms at the open circuit (A), maximum power (B) and short circuit (C) points (bottom row)
58
3.4. SIMPLIFIED AND PWM INCLUSIVE MODEL COMPARISON
A comparison of the magnitudes of the fundamental waveforms at the conventional SMR
modulation point (B) between the simplified and PWM inclusive models are shown in
Table 3-2. There is a good correspondence for the semi-bridge model but significant
discrepancies for the single-switch model, particularly for the voltage. Since the work
presented in this thesis will use the semi-bridge SMR instead of its single-switch
counterpart, this discrepancy is not considered important.
Table 3-2 Comparison of simulated fundamental RMS voltage and current values obtained for a
single-switch and semi-bridge SMR operating at point B on Figure 3-18.
Single Switch
Simplified
Complete
Semi-Bridge
Simplified
Complete
V(fund) (pu)
0.63
0.71
0.63
0.63
I(fund) (pu)
0.71
0.69
0.69
0.69
3.4.2 Comparison of Ideal Inverter Simulation Results
Figure 3-19 shows a comparison of the values of voltage, current, power factor
angle  and output power as a function of the phase shift angle, . The simulations are
conducted for d = 0.5 and d = 0, which correspond to a 50% duty cycle or an open
circuited switch during the inverter’s conduction period. An ideal SPM generator was used
with the inverter in this test, and was operated at a constant speed of 0.71 pu.
It is clear that the value of  has no impact on the value of V, while in contrast the
value of d used does not change . Observation of the graphs confirms the expectations
that V = (1 - d) pu while  = -. The values of current and output power depend on both d
and . When d = 0, the minimum value of phase current is nearly zero, and occurs for 
values of 0o and 180o. The maximum value of phase current (2 pu) occurs when  = 90o.
For the case where d = 0.5, the maximum current still occurs when  = 90o, but has
declined to 1.5 pu.
Observation of the output power curve shows that an inverter is capable of
producing both positive and negative values of power. For  < 90o, P > 0, while for  >
90o, P < 0. This is caused by the power factor angle decreasing past -90o when  > 90o,
59
CHAPTER 3: AC/DC POWER ELECTRONIC CONVERTER SIMULATION MODELS
V (pu)
1
A
0.5
0
I (pu)
2
C
0.5
D
0
B
d=0
60
120
A
180
B
0.5
1
D
C
d=0
0
0
60
120
180
o
0
-200
d = 0, 0.5
A, D
-100
0
A
60
P (pu)
1
120
180
d=0
0
-1
B, C
D
0
0.5
60
120

B
C
180
o
Figure 3-19: Comparison of inverter voltage, current, power factor angle and output power as a
function of  for d set to 0 and 0.5 using a simplified (dashed) and complete (solid) simulation
model. The simplified simulation model was used for both sets of results.
. A value of  between 90o and 180o will therefore result in a negative
since
output power. The output power can be determined by the following equation:
(3-10)
It is clear that the difference between the simulated results obtained using the
complete and simplified inverter models are nearly identical except for small errors in the
power-factor angle at lower output power values.
The points where  = 45o and 135o with d = 0 and 0.5 are marked on Figure 3-19.
The voltage and current waveforms obtained with the simplified and complete models at
these points are shown in Figure 3-20. It is clear that the fundamental waveforms of phase
voltage and current are very similar.
60
3.4. SIMPLIFIED AND PWM INCLUSIVE MODEL COMPARISON
2
2
V (pu)
0
0
(simp, comp)
fund
5
10
V
15
20
2
-2
5
I (pu)
V (pu)
15
20
I (simp, comp)
5
10
15
20
0
I (simp, comp)
0
5
10
15
20
-2
0
2
V (simp, comp)
B
0
V (comp)
D
V (simp)
0
V
0
2
I (pu)
10
C
2
fund
5
(simp, comp)
10
15
V
20
-2
0
2
B
0
-2
(simp, comp)
2
0
-2
fund
0
A
-2
V (simp)
V (comp)
0
V
-2
C
V (simp, comp)
A
fund
5
(simp, comp)
10
15
20
I (simp, comp)
5
10
15
t (ms)
20
D
0
0
I (simp, comp)
5
10
15
t (ms)
20
-2
0
Figure 3-20: Simulated phase voltage and current obtained using the simplified and complete
inverter model for (A)  = 45o, d = 0, (B)  = 135o, d = 0, (C)  = 135o, d = 0.5, (D),  = 45o, d =
0.5. For the voltage waveforms, the fundamental component is also shown.
The findings in this section have highlighted that the simplified inverter model
produces simulated results which are very similar to the complete model. An advantage of
the simplified model is that simulation time can be reduced by abstracting the effects of
PWM switching. The inverter simulation results for the remainder of this thesis will
therefore use the simplified model.
61
CHAPTER 3: AC/DC POWER ELECTRONIC CONVERTER SIMULATION MODELS
3.5 Conclusion
This chapter introduced simulation models for the rectifier, semi-bridge SMR and
inverter and compared their predictions with analytical results based on the single-phase
equivalent circuit using a constant value for the conversion between AC and DC quantities.
The following outcomes were observed:

In the analytical model, Equation (3-4) gave the closest match with the simulation
results over a wide range of speeds.

The analytical model predicted the general trends seen in the simulated voltage,
current and power versus duty-cycle and speed graphs. In the varying duty-cycle
results there was a good correspondence at higher speeds, but significant
discrepancies at lower values of current. In the varying speed results it was found
that the simulated SMR output power was significantly lower than analytically
predicted (12.8% at rated speed). These discrepancies are likely due to the
breakdown of the assumption in the analytical model that the current waveforms
are perfectly sinusoidal.

Simplified simulation models for the inverter, single-switch and semi-bridge SMR
were introduced with the intention of reducing simulation time when compared to
the PWM inclusive model, while still taking the effects of non sinusoidal
waveforms into account. Phase leg averaging was used to model the effects of
PWM switching.

The results obtained using the simplified and complete simulation models were
found to be similar, prompting the decision to use the simplified models for
simulations in the remainder of this thesis.
The following chapter will make use of the simplified simulation models to compare
with the experimental results.
62
Chapter 4: Generator Modelling
The experiments presented in this thesis used a surface permanent magnet (SPM)
generator, which has an outer-rotor delta-connected concentrated winding with 48 poles
and 36 stator teeth. (Figure 4-1) [42]. As shown in Figure 2-1, the single-phase analytical
model of a SPM generator model consists of a back-EMF source E along with a stator
inductance LS and a stator resistance RS. The value of E is calculated for a given generator
electrical angular frequency  by the relationship E = m, where m is the generator flux
linkage.
A series of experiments were conducted to determine the machine parameters. The
open-circuit test was used to calculate m, along with the open-circuit loss torque of the
generator. A DC resistance test was then used to find RS, before a short-circuit test was
used to measure LS. These parameters were then be utilized to create analytical predictions
of the SPM generator’s performance under variable speed and load conditions. These
predictions were verified by comparing them with simulated and experimental data.
63
CHAPTER 4: GENERATOR MODELLING
Figure 4-1: SPM generator used to obtain experimental results
4.1 Parameter Testing
Figure 4-2 shows the experimental setup used for the parameter and variable load
tests presented in this chapter. A 1,500 rpm DC motor was used as the driver in this
dynamometer system, and was controlled using a variable DC supply (not shown in the
figure). A gearbox was used to couple the motor with a torque transducer and the SPM
generator under test. Rotational speeds of less than 1,000 rpm were intended for this
system, since wind turbine generators commonly operate at such speeds [43]. As a result,
the gear ratio in the gearbox was set to 1:1, since the rotational speed of the DC motor was
sufficient to drive the SPM generator.
The torque transducer used was a dual-range Himmelstein MCRT 79002V(5-2)–NF-A which offered a high torque range of 56.5 Nm and a low torque range of 11.3 Nm, and
its maximum speed capability was 15,000 rpm. Each torque range had a high-bandwidth
(500 Hz) and low-bandwidth (1 Hz) output. The high-bandwidth, low range setting was
used to obtain the torque measurements provided in this chapter. A speed output was also
available from the torque transducer, which had a frequency in Hz which was equal to the
generator speed in RPM.
64
4.1. PARAMETER TESTING
Figure 4-2: Experimental setup used for parameter and variable load testing of the SPM generator
4.1.1 Open-Circuit Test
The open-circuit test is useful for calculating the flux linkage, M of a SPM
generator, and its open-circuit losses, which are comprised of the iron losses and
mechanical losses. The experimental arrangement for the open-circuit test is shown in the
left hand side of Figure 4-3 below. The SPM generator is rotated at different speeds, and
the line-to-line open-circuit voltage and shaft torque are measured. Since the generator
under test is wound in the delta configuration, this line voltage is equal to the phase
voltage.
70
E = 0.0264 
60
50
SPM
E (V)
V
T,ω
C
40
B
30
20
A
10
0
0
Experimental Setup
500
1000
1500
 (c/s)
2000
2500
Back emf Voltage
Figure 4-3: Experimental arrangement for the open-circuit test (left), and the measured generator
back-EMF voltage as a function of generator electrical angular frequency (right). Points of interest
at 200 (A), 400 (B) and 600 (C) rpm are shown.
65
CHAPTER 4: GENERATOR MODELLING
Short-circuit
Open-circuit
20
I L (A)
E (V)
50 A
0
-20 A
-50
0
5
10
15
0
0
5
10
15
5
10
15
10
15
0
0
15
C
20
I L (A)
E (V)
10
-20 B
-50
0
0
-50
0
5
20
I L (A)
E (V)
50 B
50
0
0
-20 C
5
10
15
t (ms)
0
5
t (ms)
Figure 4-4: SPM generator experimental open-circuit line to line back-EMF voltages (left) and
short-circuit line to line current at speeds of 200 (A), 400 (B) and 600 (C) rpm.
The open-circuit line voltage measured as a function of generator electrical angular
frequency  is shown in the right hand side of Figure 4-3. As expected, the back-EMF E
increases linearly as a function of . The magnet flux linkage M is given by the slope of
the curve and is found to be 0.027 V/c/s. The line to line back-EMF waveforms obtained at
generator speeds of 200, 400 and 600 rpm are shown in the left hand side of Figure 4-4.
The sinusoidal nature of the back-EMF waveforms is evident at each of the three speeds. It
is apparent that the magnitude and frequency of the back-EMF voltage increases linearly as
a function of generator speed from these waveforms.
The shaft torque measured by the torque transducer shown in Figure 4-2 when the
generator was in open-circuit conditions is shown in Figure 4-5. The generator was spun in
both clockwise (CW) and counter clockwise (CCW) directions in order to investigate any
latent torque offset present in the readings of the transducer. Speeds in the CW direction
are shown as positive values in Figure 4-5, while those in the CCW direction are negative.
A careful examination of these results shows that a torque offset exists. This offset
was corrected by subtracting a constant of 0.05 Nm from the CW and CCW torque
readings. This value was chosen such that when the CCW torque readings are mirrored and
66
4.1. PARAMETER TESTING
1
T (Nm)
0.5
0
-0.5
-1
-1000
-500
0
n (rpm)
500
1000
Figure 4-5: Measured shaft torque obtained when the open-circuited generator was spun in the
clockwise direction (positive n) and the counter clockwise direction (negative n)
plotted, it shows a good correspondence with the CW readings, as can be seen by Figure
4-6. The corrected value of torque was then used to calculate the mechanical power loss
from the formula P = T , and is shown on the bottom of Figure 4-6. The open-circuit
power loss as a function of speed is useful for predicting the generator and system
efficiency.
T (Nm)
1
0.5
0
0
200
400
600
800
1000
600
800
1000
80
P = 4.5e-005*n2 + 0.03*n - 0.33
P (W)
60
40
20
0
0
200
400
n (rpm)
Figure 4-6: Corrected measured CW and CCW torque values as a function of speed (top), and the
measured open-circuit power loss as a function of speed.
67
CHAPTER 4: GENERATOR MODELLING
4.1.2 Resistance Test
The stator resistance RS was determined by the experimental setup shown in the left
hand side of Figure 4-7. A DC power supply was used as a controlled current source,
which supplied a current I between two of the SPM generator terminals. The resultant
voltage drop V was then measured. Given that the SPM generator was a delta-connected
machine, the following relationship could be used to calculate the resistance of each phase
winding.
(4-1)
0.8
0.7
V
0.6
A
V
SPM
PMG
+
-
0.5
R ()
I
0.4
0.3
0.2
0.1
0
0
Experimental Setup
0.5
1
I (A)
1.5
Phase Resistance
Figure 4-7: Experimental setup for the resistance test (left), and measured SPM generator phase
resistance as a function of DC input current (right).
The values of resistance obtained from these tests are plotted as a function of DC
current in the right hand side of Figure 4-7. The value of resistance is approximately 0.575
 at higher values of current. Ideally this resistance should be constant for all values of
current, but there exists some experimental error at low values. This is due to the power
analyser being used to measure current not being designed for low-current operation. The
resistance obtained for high values of current is therefore used as the stator resistance of
the SPM generator in all further analysis.
68
2
4.1. PARAMETER TESTING
4.1.3 Short-Circuit Test
The short-circuit test is a procedure which can be used to calculate the inductance of
a SPM generator. The left hand side of Figure 4-8 shows the experimental setup used for
this test. The current obtained when all three phases of the generator were short-circuited
as the generator speed was measured. The resulting line and phase current as a function of
generator speed are shown in the right hand side of Figure 4-8.
The value of generator short-circuit current asymptotes towards 16 A at high speeds.
This value can be used to calculate the reactance of the generator Xs at those speeds via
(4-2) which can in turn be used to calculate the inductance by (4-3).
(4-2)
(4-3)
20
15
T,ω
A
SPM
I L (A)
A
C
B
10
5
0
0
Experimental Setup
100
200
300
400
n (rpm)
500
600
700
Short Circuit Current
Figure 4-8: Experimental setup used for the short-circuit test (left) and comparison of SPM
generator experimental (circles) and analytical (line) current as a function of generator speed
(right). Points of interest at 200 (A), 400 (B) and 600 (C) rpm are shown.
In the above equation, e is the electrical frequency of the generator in radians per
second. The resulting inductance measured was 2.88 mH. This value of inductance and the
prior measured value of resistance was used to predict the short-circuit current as a
function of speed and is plotted in Figure 4-8.
The close correspondence with the
69
CHAPTER 4: GENERATOR MODELLING
experimental results gives confidence in the accuracy of these parameters. The short-circuit
current waveforms obtained at speeds of 200, 400 and 600 rpm are shown in the right hand
side of Figure 4-4. The short-circuit current is clearly sinusoidal, as was the back-EMF
voltage. It should be noted that while the frequency of these waveforms increases in
proportion with the generator speed, the magnitude increases only slightly. Thus the short
circuit current at these speeds is approaching the value of the characteristic current, IX,
which equivalent to the high speed short-circuit current of the generator.
4.1.4 Summary of Parameters
As stated previously, the object of the tests presented thus far in this chapter was to
obtain values of the magnet flux linkage, stator resistance and inductance of the surface
permanent magnet generator. These results are summarized in Table 4-1 below:
Table 4-1: Summary of SPM generator parameters
Parameter
Value
Magnet Flux Linkage, m (V/c/s)
0.0264
Stator Resistance, RS ()
0.576
Stator inductance, LS (mH)
2.88
Number of Poles
48
Stator Teeth
36
Open-Circuit Power Loss (W)
4.55E-5n2+0.0303n-0.33
These generator parameters could be utilized to model the performance of the SPM
generator. Figure 4-9 shows an example of the generator efficiency as a function of speed
and torque, assuming maximum torque per ampere control (Id = 0) is utilized. The
efficiency  is calculated at a given output torque T and mechanical angular speed  using
the following relationship [44],
(4-4)
70
4.2. PERFORMANCE TESTING
where Tem is the electromagnetic torque of the generator, calculated by adding the opencircuit loss torque measured in Figure 4-6 to the desired generator torque T. I is the phase
current of the generator under maximum torque per ampere conditions (i.e. I = Iq). The
required value of I for a required value of electromagnetic torque could then be calculated
by
, where k is the torque coefficient of the generator.
It is apparent that the generator efficiency increases as the torque and speed are
increased for the range shown below. Given that the SPM generator used in this thesis is
intended for small-scale wind turbine operation, the speeds at which it will be operated at
are below 500 rpm. Based on Figure 4-9, the best efficiency we can hope for in this range
is approximately 88%.
85
70
9
80
60
10
8
88
88
60
6
85
85
85
70
5
80
Torque (Nm)
7
4
3
2
60
0
200
60
60
60
0
70
70
70
1
80
80
80
400
600
Speed (rpm)
800
1000
Figure 4-9: Calculated efficiency map for the SPM generator based on the measured back-emf,
stator resistance and open-circuit loss.
4.2 Performance Testing
The primary benefit of finding the single-phase equivalent circuit parameters of a
SPM generator is that analytical and simulated predictions of the generator’s performance
71
CHAPTER 4: GENERATOR MODELLING
can then be obtained. Experimental results can be used to verify these predictions, thereby
confirming the SPM generator’s parameters.
This section will present analytical predictions of the SPM generator’s performance
when operating into a diode rectifier and a semi-bridge SMR with a fixed voltage load. The
DC load voltage for both cases was set to 42 V. Experimental results will be presented to
verify these predictions. A model of the power electronic converter system used is required
however, in order to ensure the comparison between the analytical and simulated models is
valid.
4.2.1 Power Electronic Converter Properties
The power electronic converter used in the experiments in this thesis was a threephase IGBT inverter originally intended for use in a solar electric vehicle (Figure 4-10)
[45, 46]. The inverter used Toshiba MG200J2YS50 IGBTs in the bridge of its power
converter. These devices were rated for a 600 V collector-emitter voltage, and a forward
current of 200 A. These values were significantly greater than the maximum values of
voltage and current expected from the generator under test.
The power electronic converter could be utilized in rectifier mode if the gate drive
signals to all six IGBTs were disconnected, since only the free-wheeling diodes parallel to
the switches would be operational under such a configuration. The converter could also be
operated as a semi-bridge SMR if control signals were supplied to the IGBTs on the
bottom half of the power electronic converter bridge.
Another important feature of this power electronic converter was the three LEM
current sensors present, shown in Figure 4-10. These sensors were used to measure the line
current waveforms on the input of the power electronic converter. A circuit diagram of the
power electronic converter is provided in Figure 4-11.
A summary of the important parameters of the power electronic converter are shown
in Table 4-2 below. In this table, VD is the voltage drop associated with the free-wheeling
diodes present in the converter, while VT represents the voltage drop of the IGBT. Figure
4-12 shows the measured voltage drop as a function of current for these devices. Given that
the rated current IO of the SPM generator was specified as it’s short-circuit current which
was shown to be approximately 15 A in Figure 4-8, it was decided to use the extrapolated
value of voltage drop for this value of current for both VD and VT. The resulting values
72
4.2. PERFORMANCE TESTING
were VD = 1.15 V and VT = 1.4 V. A resistive model could also be used to describe this
voltage drop, and is shown on Figure 4-12 as a dashed red line, which can be described as
a function of current by the relationship
.
The experimental results provided in the remainder of this chapter will use the fixed
voltage drop values of VD and VT. The remainder of this thesis will utilize the resistive
voltage drop approximation, VR. It should be noted that the approximation of VR will be
used for both the diode and IGBT voltage drops, since there is not much difference
between the voltage drops for the two devices.
Table 4-2: Parameters of power electronic converter
Current
IGBT
Capacitor
Sensor
Manufacturer
Toshiba
BHC
LEM
Part Number
MG200J2YS50
ALS30A152KF350 LA 100 P
Rated Values
600V, 200 A
300 V, 1500 uF
100 A
VD
1.15 V
-
-
VT
1.4 V
-
-
VR
0.0375*I+0.8 V
-
-
ESR
-
0.077 
-
73
CHAPTER 4: GENERATOR MODELLING
Figure 4-10: Power electronic converter used [45, 46]
MG200J2YS50
LA 100 P
1500 uF, 300 V
Gate Driver
(IR2130)
Figure 4-11: Circuit diagram of the power electronic converter utilized
74
4.2. PERFORMANCE TESTING
20
I = 26.7*V-21.3
18
Short-circuit line current
16
14
Diode
I (A)
12
10
8
I = 14.8*V 3D+0.364V 2D - 9.62V D + 2.92
IGBT
6
4
I = 3.49*V 3T+12.5V 2T - 16.4V T + 4.6
2
0
0.4
0.6
0.8
1
1.2
1.4
V (V)
Figure 4-12: Line current as a function of voltage drop for the free-wheeling diodes and IGBTs
present in the power electronic converter described in Table 4-2. Equations modelling each curve
as a quadratic are shown. The resistive voltage drop used to model the power electronic devices is
shown as a dashed red line.
4.2.2 Rectifier Tests
Figure 4-13 shows the experimental arrangement used to test the SPM generator
examined in this chapter with a diode rectifier using a fixed voltage load. This fixed
voltage load was represented by the arrangement showing the 42 V voltage source, diode
and resistor on the right of Figure 4-13. The 42 V source in this system was a DC power
supply, so the diode was required to provide protection from current flowing from the
generator into the power supply. A constant 42 V load is provided whilst the rectifier
output current is lower than the current passing through the resistor placed in parallel with
the 42 V supply. Once the output current exceeds the resistor current, the load voltage will
begin to increase linearly. Under this circumstance, the value of resistance was reduced,
thereby increasing the resistor current and allowing the load voltage to remain constant at
42 V.
75
CHAPTER 4: GENERATOR MODELLING
A
A
V
T,ω
+
SPM
A
V
V
42 V
-
Figure 4-13: Experimental arrangement for testing of SPM generator with diode rectifier and fixed
voltage load
The experimental setup shown here can be analysed using the single-phase
equivalent circuit for SPM generator operating into a rectifier presented in Figure 2-5. The
magnitude of the generator phase voltage V however must consider the voltage drops
present in the diode rectifier. According to [33], the magnitude of the phase voltage could
be related to the DC voltage VDC and the voltage drop per diode VD by the following
equation:
(4-5)
For the case where VD = 0, (4-5) corresponds to conversion factor of
between
VL and VDC in given in (3-4). The diagram obtained for a non ideal generator (RS  0), with
the magnitude of V set to (4-5) for a given value of VD, is shown in Figure 4-14 below
(parameters V, I, E and RS are defined in Figure 2-5).
In the study presented here, the magnitudes of V and E are know, along with the
stator resistance RS and reactance LS. The quantities which are desired are the magnuitude
of the phase current I and the angle between E and I, .
76
4.2. PERFORMANCE TESTING
y
jωLSI
E
x
 I
V
RSI
Figure 4-14: Phasor diagram used to analyse non-ideal (RS  0) SPM generator for the case where I
and V are in phase.
The value of the angle x was calculated using trigonometery to be:
(4-6)
While the law of sines was used to calculate the angle y as:
(4-7)
Equations (4-6) and (4-7) could be combined to calculate the angle  :
(4-8)
The relationship between  and I could then be expressed as follows via the use of
trigonometery:
(4-9)
77
CHAPTER 4: GENERATOR MODELLING
Where IX was the characteristic or high speed short-circuit current of the SPM
generator. Equations (4-8) and (4-9) could then be combined to provide an expression for
the magnitude of the phase current, I, in the case where there was no phase shift between I
and V.
(4-10)
This equation was valid for SPM generators operating with unity power factor loads,
such as rectifiers, switched-mode rectifiers and semi-bridge switched rectifiers (assuming
the duty cycle of the three switches in the power electronic converter bridge were held
constant). The conversion factor of 1.35 between IL and IDC shown in section 3.1 could
then be used to calculate the load current of the rectifier, and hence the output power. The
diode voltage drop VD used was 1.15 V, as given in Table 4-2. Analytical results for the
line voltage, current, output power and efficiency of the circuit in Figure 4-13 are
compared with simulated and experimental data for speeds in the range 0 to 1000 rpm in
Figure 4-15. A close correspondence is noted between all three results for all speeds in this
range. The experimental and simulated current, output power and effiicency rise above
zero at lower speeds than the analytical predicitions. This is due to the difference in
AC/DC conversion ratios highlighted in section 3.1.
Figure 4-16 shows comparisons of the analytical and simulated phase leg voltage and
line current waveforms at speeds of 600 and 1000 rpm. At each speed, the phase leg
voltage is equal to the DC link voltage while the line current waveform is positive, and is
zero when the current is negative. The line current waveform shows some distortion at the
600 rpm case, but becomes more sinusoidal as the generator speed is increased up to 1000
rpm. At high speeds, SPM generators act as constant current sources for a wider range of
load values near the short-circuit point (see Figure 2-6). Operation as a constant current
source reduces the distortion of the generator’s output current waveform.
The following section will provide details on how the analytical equation presented
in (4-10) could be used to predict the performance of a SPM generator operating with a
semi-bridge SMR.
78
4.2. PERFORMANCE TESTING
V (V)
40
20
0
0
200
400
A
B
600
800
IL (A)
20
10
0
0
200
400
600
P
800
500
B
0
1000
C
A
DC
(W)
B
C
0
200
400
A
600
800
A
B
1000
C
1000
 (%)
100
50
0
0
200
400
600
800
C
1000
n (rpm)
Figure 4-15: Comparison of analytical (line), simulated (dashed) and experimental (points) results
of a SPM generator (parameters shown in Table 4-1) operating over speed in the range 0-1000 rpm
with a 42 V DC load. Points of interest at 600 (A), 800 (B) and 1000 (C) rpm are labelled.
79
CHAPTER 4: GENERATOR MODELLING
VLeg (V)
50
50
Sim, Exp
40
40
30
30
20
20
10
10
0
B
A
0
Sim, Exp
2
4
6
8
10
0
0
2
20
Sim
IL (A)
Sim, Exp
5
10
0
0
-5
-10
-10
Exp
A
0
2
4
t (ms)
6
8
-20
4
B
0
2
t (ms)
4
Figure 4-16:Phase leg voltage and line current obtained from the SPM generator operating into a
rectifier with a 42 V DC load at speeds of 600 (A) and 1000 (B) rpm. Simulated (dashed) and
experimental (line) results are shown.
4.2.3 SMR Tests
Figure 4-17 shows the experimental setup used to test the SPM generator with a
semi-bridge SMR. A 42 V DC load is used as with the rectifier case. The analytical
equations describing the operation of a boost converter in continuous current conduction
mode provided in (3-5) and (3-6) can be used to analyse the semi-bridge SMR. This can be
achieved by considering the semi-bridge SMR as a single-switch SMR Figure 3-15. This
assumption is valid so long as all three switches in the bottom half of the semi-bridge SMR
are modulated at the same duty cycle [21].
Equation (3-5) is used to find the single-switch SMR’s rectifier output voltage VDC
for a given duty cycle d. Equation (4-5) could then be used to calculate the AC phase
voltage of the generator for a given value of VDC. The value of phase current was
calculated using (4-10) and was converted to a DC current using the IDC/IL conversion
80
4.2. PERFORMANCE TESTING
factor of 1.35 shown in section 3.1. IDC was then converted to IOUT using (3-6), thereby
allowing output power to be calculated.
A
A
V
T,ω
SPM
A
Semi-bridge
SMR
V
+
V
42 V
-
Figure 4-17: Experimental arrangement for testing of SPM generator with semi-bridge switchedmode rectifier and fixed voltage load
Chapter 3 introduced a simplified simulation model, which was designed to reduce
simulation time by modelling the PWM operation of the boost converter using equations
(3-5) and (3-6). While chapter 3 showed that a close correspondence was observed
between the results obtained with both simulations models for an ideal machine, no data
was presented for SPM generators with non-zero values of RS and VD. The simulated and
experimental results presented for an SMR utilized the generator parameters presented in
Table 4-1, and used the power electronic converter voltage drop values given in Table 4-2 .
Figure 4-18 shows the analytical, simulated and experimental results obtained for the
generator line voltage, current and output power as a function of duty cycle at a speed of
600 rpm. In each case, the duty cycle was varied from 0 to 100 %. The values of VL
followed a linear relationship based on equation (3-5).
The line current IL shown in Figure 4-18 increases as a function of d, which is
expected since (3-6) shows that the input current of a boost converter will be larger for
lower values of d. There is a larger discrepancy between the analytical, simulated and
experimental values of IL for low values of d. This is because the line current is less
sinusoidal under these conditions.
For each speed, there is an optimal value of generator duty cycle which results in
maximum output power. At 600 rpm, this optimal duty cycles is 0.35, and corresponds to
an experimental output power of 368 W. The analytical and simulated values of output
power are higher than the experimental values at low duty cycles. It is theorized that this
81
CHAPTER 4: GENERATOR MODELLING
discrepancy may be caused by the non-sinusoidal nature of the line current waveform for
low values of d.
Waveforms of the phase leg voltage and line current at the maximum power (d =
35%) and short-circuit (d = 100%) points are shown in Figure 4-19. The line current and
phase leg voltage for the open-circuit point (d = 0%) can be viewed in Figure 4-16, since a
SMR with zero duty cycle is identical to a rectifier. Observation of the open-circuit, shortcircuit and maximum power waveforms show that that the line current waveform is most
distorted at the open-circuit point, and becomes more sinusoidal as d is increased towards
100%. This finding explains the differences between the analytical and experimental and
simulated curves for low values of d in Figure 4-18.
L
V (V)
40
20
A
B
C
0
0
20
40
60
80
100
d (%)
C
10
L
I (A)
20
B
0 A
0
20
40
60
80
100
d (%)
P (W)
500
B
A
0
0
C
20
40
60
80
100
d (%)
Figure 4-18: Comparison of analytical (line), simulated (dashed) and experimental (points) SPM
generator phase voltage, current and output power as a function of SMR duty cycle, when the
output voltage was set to 42V at a speed of 600 rpm. The open circuit (A), maximum power (B)
and short circuit (C) points are labelled.
82
4.3. CONCLUSION
50
50
Exp
Sim
V
Leg
(V)
40
30
30
20
20
10
10
0
0
2
4
6
8
0
0
30
Exp, Sim
20
L
Exp, Sim
B
A
30
I (A)
40
2
10
0
0
-10
-10
-20
-20
2
4
t (ms)
8
6
8
Exp, Sim
B
A
0
6
20
10
-30
4
6
8
-30
0
2
4
t (ms)
Figure 4-19: Comparison of simulated (dashed) and experimental (line) phase leg voltage and
current waveforms obtained for a SPM generator operating under SMR modulation with duty
cycles of 30% (point A) and 100% (point B) at 600 rpm.
4.3 Conclusion
The analytical and simulated results presented in this thesis require validation in the
form of experimental results. This chapter described the SPM generator used to obtain the
experimental results in this thesis, and outlined the tests used to measure the generator’s
single-phase equivalent parameters. The power electronic converter used to obtain the
experimental results was modelled, and its losses modelled. Variable-speed tests were then
conducted with the SPM generator operating with a rectifier and a switched-mode rectifier
to validate the accuracy of the analytical and simulation models. A 42 V DC load was used
in both cases. The outcomes of the study are listed below:
 The SPM generator’s flux linkage M, stator resistance RS, and inductance, LS were
found using the open-circuit, resistance and short-circuit tests.
83
CHAPTER 4: GENERATOR MODELLING

Using experimental testing, it was found that the power electronic converter used
could be approximated by fixed voltage drops or an equivalent voltage drop and
resistance.

An analytical method of calculating the magnitude of the generator current I for
cases where V and I of a SPM generator were in phase was obtained using phasor
analysis. This procedure was suitable for analyzing cases where a SPM generator
was operating with a rectifier or a switched-mode rectifier.

The generator parameters and the analytical and simulation models were verified by
comparing their prediction with experimental data for the rectifier and SMR. A
close match was noted between the experimental results, and the values predicted
using analysis and simulations.
84
Chapter 5: Power Capability and Limits
of Phase Advance Modulation
Previous chapters have discussed how phase advance modulation [23] could be used
to generate increased output power with a semi-bridge switched mode rectifier (SMR)
operating into a surface permanent magnet (SPM) generator when compared to
conventional SMR modulation. This chapter describes a simplification of the phase
advance modulation strategy developed by [23], known as zero-epsilon modulation, and
present analytical methods of finding the optimal control parameters for maximum output
power at a given speed by using the optimal generator phase voltage V and power factor
angle . Finally, simulated results and experimental validation from an open-loop control
system based on a dsPIC 30F2010 microcontroller is presented to validate the analytical
findings.
5.1 Fundamental Analysis
A comparison of AC/DC converter modulation methods is shown in Figure 5-1. In
an inverter, the voltage between an input phase and the negative DC link, the phase-leg
voltage, vleg is fully-controlled, and a leading power-factor can be achieved by delaying the
85
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
phase leg voltage and hence the fundamental phase voltage, vph(fund), with respect to the
phase current waveform (see Figure 5-1a).
As an SMR has no upper transistors, it can only control the voltage of an input phase
when the corresponding input phase current is positive. During this period, the average
input phase-leg voltage is proportional to (1 – d) where d is the duty-cycle. Conventional
SMR modulation operates by driving all the lower transistors in the semi-bridge SMR at a
constant duty-cycle with an optimal value determined by the machine speed. This will give
rise to a constant average phase leg voltage VB that is only present while the phase current
waveform is positive (see Figure 5-1b). The fundamental phase voltage is thus in phase
with the phase current.
The resultant unity power-factor operation reduces the SPM
generator’s output power capability.
This limitation can be mitigated by adopting phase advance modulation (Figure 5-1c)
[23], which operates by driving the transistors in the semi-bridge SMR at a different duty
cycle for three separate periods in the phase current positive half-cycle. These periods are
known as , , and . During the  period, the duty cycle is set to unity, resulting in a zero
input phase leg voltage, which causes the SPM generator’s phase current to rise quickly. In
the  period, the duty cycle is decreased to the optimal value used by conventional SMR
modulation. Finally in the  period, the duty cycle is reduced further, resulting in a higher
phase-leg voltage VOV. The resulting stepped phase leg voltage waveform produces a
leading power-factor.
86
5.1. FUNDAMENTAL ANALYSIS
i
i
vleg
VINV
VB
vleg
t
t
vph(fund)
vph(fund)
a)
VOV
i
b)
VOV
vleg
VB
i
vLeg
t

t
 
vph(fund)
c)


vph(fund)
d)
Figure 5-1: Comparisons of phase leg (lower switch) voltage and phase current waveforms for
inverter (a), conventional SMR (b) conventional phase advance (c) and zero-epsilon modulation (d)
One of the issues of the phase advance modulation waveform in Figure 5-1c is that it
has three independent parameters (two control angles,  and , and the voltage VOV). It will
be shown in the next section that maximum output power is generally achieved with ε  0o
for generators with low values of stator resistance. Eliminating the ε parameter therefore
maintains similar maximum output power capability, while having fewer control variables.
This new technique is called zero-epsilon modulation and is shown in Figure 5-1d. It
should be noted that conventional SMR modulation is a special case of zero-epsilon
modulation where δ = 0.
When comparing the operation of the different modulation techniques shown in
Figure 5-1, it is useful to think of the power electronics as controlling the magnitude V and
phase shift  of the fundamental phase voltage with respect to the phase current. The
inverter offers complete control of the phase voltage magnitude from 0 to 1 pu and phase
shift from 0 to 90 (neglecting current limitations) as shown in the voltage-power factor
plane in Figure 5-2a. This graph also shows the optimal trajectory for maximum power
within the rated voltage and current constraints as a dashed line based on the assumption
that the rated current equals the characteristic current, which is valid for high-inductance
SPM generators as discussed in Section 2.1.1. This uses a phase shift of -45 at low speeds
which is reduced towards zero after the voltage limit is reached. With conventional
87
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
V (pu)
1
1
Optimal
Optimal
Achievable
0.5
SMR
0.5
Achievable
Inverter
0
-90
V (pu)
1
-60
-30
 (degrees)
a)
0
-90
0
-90
1
Optimal
PA
0.5
0
-60
-30
 (degrees)
b)
Optimal
ZE
Achievable
-60
-30
 (degrees)
c)
0
Achievable
0.5
0
0
-90
-60
-30
 (degrees)
d)
0
Figure 5-2: Comparison of the achievable values of V and  for inverter (a), conventional SMR (b),
conventional phase advance (c) and zero-epsilon modulation (d). The optimal maximum output
power control trajectory for an ideal SPM generator is shown as a dashed line
SMR modulation, the voltage magnitude can be controlled but the phase shift is fixed at 0
(see Figure 5-2b). This limits the allowable operating trajectory and so reduces the output
power capability. This was shown in Figure 2-9 where it was found that for an ideal SPM
generator, conventional SMR modulation produced half the output power of inverter
modulation at speeds below 0.71 pu.
The performance of the two phase advance SMR modulation algorithms
(conventional phase advance and zero-epsilon modulation) is obtained by deriving a
mathematical expression for the fundamental phase voltage waveform using Fourier
analysis [23], which is given below:
(5-1)
88
5.1. FUNDAMENTAL ANALYSIS
where n represents the harmonic number of the phase leg voltage waveform. Note that the
fundamental (n = 1) of the phase leg voltage is also equal to the fundamental of the
generator’s phase voltage.
The Fourier coefficients of the fundamental phase voltage waveform obtained from
the phase advance modulation method (Figure 5-1c) are given below:
(5-2)
(5-3)
The Fourier coefficients of the fundamental phase voltage waveform for zero-epsilon
modulation (Figure 5-1d) can be obtained by setting  to 0o in (5-2) and (5-3). These are
shown below:
(5-4)
(5-5)
A key assumption in deriving these equations is that the current waveform is
symmetrical with a positive half-cycle equal to 180. If the positive half-cycle is less than
180 this will reduce the length of the period  in Figure 5-1 and hence reduce both the
phase voltage magnitude and power factor angle.
If zero-epsilon modulation is used, it is possible to calculate the power factor angle 
and the magnitude V of the phase voltage using (5-4) and (5-5). Equation (5-6) shows the
relationship between the power factor angle  and the zero-epsilon control parameter .
Equation (5-7) expresses the per unit RMS phase voltage V, where the base value of V is
the rated voltage, while the base value of VOV is Vdc. It is apparent that  is half the value of
, while V is a function of both  and VOV. V is proportional to VOV and decays as the value
of  is increased from 0o to 180o.
89
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
(5-6)
(5-7)
Figure 5-2d shows the achievable voltage magnitude and phase shift envelope for the
zero-epsilon modulation method (see Figure 5-1d). This was calculated using (5-6) and
(5-7). Comparing Figure 5-2d and Figure 5-2a shows the achievable voltage magnitude
using zero-epsilon modulation drops rapidly as the phase shift increases. In particular, at
the optimal low-speed phase shift of  = 45, the achievable voltage magnitude (and hence
the speed at which field-weakening starts) is roughly 70% of that for an inverter.
It can be shown that conventional phase advance modulation (Figure 5-2c) has the
same voltage magnitude limitation at large phase shifts as zero-epsilon modulation. The
next section will compare conventional phase advance and zero-epsilon modulation.
5.2 Conventional Phase Advance Modulation
As stated in the previous section, conventional phase advance makes use of three
parameters, the modulation periods  and , and the duty cycle of period , d. The effects
of parameters  and  on the phase current and output power of the generator can be
examined by varying their value from 0-1800 with d set to 0o. The contour plots obtained
from these calculations and simulations are shown in Figure 5-3, for a generator speed of 1
pu which is the speed where the generator back-emf E = V. An ideal (RS = 0) SPM
generator model was used, which had a rated (1 pu) current value equal to the
characteristic current (IX). This indicates it has a high inductance, as discussed in Section
2.1.1.
The analytical results were obtained by using equations (5-6) and (5-7) to obtain the
magnitude V and power factor angle  of the phase voltage waveform. The single-phase
equivalent circuit of the SPM generator shown in Figure 2-1 was utilized in order to
calculate the phase current I obtained with these control parameters. Lastly, the voltage,
current and power factor angle were used to calculate the output power of the generator.
The simulated results shown in Figure 5-3 were obtained by using the simplified
90
5.2. CONVENTIONAL PHASE ADVANCE MODULATION
simulation model given shown in Figure 3-16. A DLL file block similar to the one used in
Figure 3-12 was used to produce the duty cycle values required at a given instant of time.
No losses were assumed in the power electronic converter.
There is a close correspondence between the analytical and simulated results. The
control parameters resulting in maximum output power while keeping within the rated
current are marked on each graph as point A, and are  = 51o,  = 0o for the analytical and
 = 50o,  = 0o for the simulated case. The analytical maximum output power is 0.79 pu,
and occurs for a phase current of 1 pu. In contrast, the simulated maximum power is 0.71
pu with a current of 1 pu.
Power
Current
180
180
0.1
120
0.7
60
60
0.8
A
1.2
A
0.6
0.2
B
0
0
1.4

0.5

Analytical
120
0.3
90

0
0
180
180
1
B
90
180

180
0.1
120
60
A
1.2

0.3
0.4

Simulated
120
0.2
0.5
0.70.6
60
A
B
0
0
90

180
0.8
0.6
0
0
1
90

B
180
Figure 5-3: Comparison of analytical and simulated contour plots of output power and phase
current for conventional phase advance modulation for an ideal high inductance SPM generator at 1
pu speed. Points showing the maximum output power while maintaining generator current at its
rated value for phase advance modulation (A) and conventional SMR modulation (B) are shown.
91
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
The control points corresponding to conventional SMR modulation ( = 0o,  =180o)
are shown on each graph as point B. For the analytical case, the output power produced by
conventional SMR modulation is 0.49 pu, while the simulated output power is 0.38 pu. The
analytical current is 0.77 pu, compared to 0.87 for the simulated case.
Examples of simulated and analytical phase current, phase leg voltage and
fundamental phase voltage waveforms are shown in Figure 5-4. The left hand side shows
the case where  and  were both set to 60o, while the right hand side displays the case for
conventional SMR modulation. The generator speed in both cases was 1 pu. It is apparent
from these figures that conventional phase advance modulation causes a larger phase
current waveform to be generated. In addition, it is observed that the positive half-cycle is
shorter than its negative counterpart. This causes the  period of the phase leg voltage
waveform to be active for a shorter length of time than anticipated, which results in a
fundamental phase voltage waveform which is smaller than the analytical value.
The generator output power observed for the phase advance modulation case shown
in Figure 5-4 is 0.48 pu, which is smaller than the maximum power value of 0.79 pu which
 = 0o,  = 180o
 = 60o,  = 60o
2
2
I (pu)
1
1
0
0
-1
-2
0
2
Analytical
-1
Analytical
4
6
8
Sim
1
V (pu)
Sim
Sim
-2
0
2
4
6
8
1
Sim (fund)
Sim
0
0
Analytical
-1
0
2
4
t (ms)
-1
6
8
Analytical,
Sim (fund)
0
2
4
t (ms)
6
8
Figure 5-4: Comparison of simulated and analytical waveforms of phase current and voltage with
conventional phase advance modulation parameters of  = 60o  = 60o (left) and conventional SMR
modulation parameters of  = 0o,  = 1800, (right) at a generator speed of 1 pu.
92
5.2. CONVENTIONAL PHASE ADVANCE MODULATION
occurred at point A of Figure 5-3. The fact that the maximum power point is achieved
while operating with an  period of 0o validates the earlier observation in Figure 5-2 that
zero-epsilon modulation is capable of operating along the same maximum power trajectory
as conventional phase advance modulation. The following section will further investigate
this concept. It should be noted that from this point onwards the terms zero-epsilon
modulation and phase advance modulation will be used interchangeably in the remaining
chapters.
5.2.1 Zero-epsilon Modulation
There are two key control parameters in zero-epsilon modulation, δ and VOV (see
Figure 5-1d). Figure 5-5 shows simulation results where  = 90o for the cases where VOV =
0.5 and 1 pu for an ideal (RS = 0) SPM generator. The delta period starts at the positive
phase current zero-crossing and during this time the phase leg voltage is kept at zero.
After 90o (about 2 ms at this speed), the phase leg voltage is set to VOV for the rest of the
positive half-cycle. The phase leg voltage and phase voltages have the same fundamental
value (note the per-unit scaling is different though). The net effect of this modulation
V
2
OV
= 1 pu
Analytical
I (pu)
1
-2
OV
= 0.5 pu
Analytical
1
0
0
-1
-1
Sim
0
2
4
6
8
Sim
Analytical
1
V (pu)
V
2
-2
Sim
0
4
6
8
Sim
1
0
2
Analytical
0
Sim (fund)
-1
0
2
4
t (ms)
Sim (fund)
-1
6
8
0
2
4
t (ms)
6
8
Figure 5-5: Simulated phase advance results with VOV = 1 (right) and 0.5 pu (left) where n = 1 pu
and  = 90o. Phase current (top), phase leg (middle) and fundamental phase voltage waveforms
(bottom) with analytical results (solid line) and simulated results (dashed line)
93
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
technique is to produce a leading power factor angle.
The simulated phase current waveform is non-sinusoidal with a smaller positive halfcycle than the negative half-cycle. The phase current waveform for the case where VOV = 1
pu is more distorted than the case where  = 60o and  = 60o with conventional phase
advance modulation, in Figure 5-4. Once again this results in a smaller magnitude
simulated phase voltage compared to the analytical prediction. The distortion of the phase
current waveform, and hence the difference in magnitude between the analytical and
simulated phase voltages, is not as pronounced in the case where VOV = 0.5 pu in Figure
5-5.
Figure 5-6 shows the comparison of the simulated and analytical phase voltage,
power-factor angle, phase current and output power for the generator at 1 pu speed for
values of VOV of 0.5 pu and 1 pu as the control parameter δ is varied from 0o to 180o. The
analytical and simulated values are compared. The difference between the analytical and
simulated V as a function of  is greater for the VOV = 1 pu case, due to the smaller positive
half cycle of the phase current waveform under these conditions. In contrast, the
simulations match the analytical results for  as a function of . A linear relationship exists
between the power-factor angle  and exists, and is given by:
as shown in
(5-6).
Figure 5-6 also shows the variation in phase current and output power as a function
of δ. The condition δ = 180 corresponds to the short-circuit case and hence the phase
current is 1 pu and the output power is zero. This is due to the characteristic current of the
SPM generator being assumed to be 1 pu. As δ is decreased, the phase current increases
above the short-circuit current, reaches a peak in the regions δ = 90 to 120, and then falls
at smaller values of δ. The power curve reaches its peak at values of δ < 70. For the
VOV = 1 pu case the current falls to zero at zero δ while the current variation is much
smaller for the VOV = 0.5 pu case. The maximum power (0.70 pu) is achieved when
 = 50o with the VOV = 1 pu case compared to a peak value of 0.45 pu for the VOV = 0.5 pu
case where  = 25o. In both these cases, the phase current was limited to 1 pu. It should be
noted that the point corresponding to maximum output power when VOV = 1pu is actually
point A in Figure 5-3. This validates the earlier assumption that zero-epsilon modulation
can be used instead of phase advance modulation, since the maximum power points
observed in Figure 5-3 occurred when  = 0o.
94
5.2. CONVENTIONAL PHASE ADVANCE MODULATION
V (pu)
1
VOV = 1 pu
0.5
0.5 pu
0
0
20
40
60
80
100
120
140
160
180
0
20
40
60
80
100
120
140
160
180
80
100
120
140
160
180
140
160
180
 (deg)
0
-30
-60
-90
I (pu)
1.5
0.5 pu
1
0.5
0
VOV = 1 pu
0
20
40
60
P (pu)
1
V
OV
= 1 pu
0.5
0.5 pu
0
0
20
40
60
80
100
 (degrees)
120
Figure 5-6: Comparison of SPM generator analytical (solid lines) and simulated (dashed lines)
phase voltage, power factor angle, , current and output power as a function of phase advance
angle δ for zero-epsilon modulation when operating with VOV values of 1 and 0.5 pu at a generator
speed of 1 pu.
Figure 5-7 shows a comparison of the analytical and simulated phase voltage versus
power-factor angle trajectories plotted from the data given in the top two graphs of Figure
5-6.
As discussed earlier, the simulated voltage magnitudes are significantly lower than
the analytical values due to the asymmetrical nature of the phase current waveforms. The
solid circles in Figure 5-7 represent the ideal (inverter) operating point for an SPM
generator at 1 pu speed (V = 1 pu,  = 26o) along with the points of maximum power for
the simulated and analytical phase advance (zero-epsilon) modulation. The simulated
trajectories are further away from the ideal operating point than their analytical
counterparts which are an indication that the simulated output power will be significantly
lower than its analytical counterpart.
95
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
1
Ideal
V (pu)
0.8
0.6
0.4
Optimal
Analytical
(VOV = 1 pu)
Optimal
Sim
(VOV = 1 pu)
Analytical
(VOV = 0.5 pu)
0.2
0
-90
Sim
(VOV = 0.5 pu)
-60
 (degrees)
-30
0
Figure 5-7: Comparison of analytical and simulated phase voltage versus power-factor angle
trajectories from Figure 5-6. The optimal (inverter) control trajectory is shown. The points show
the optimal operating points for maximum output power at 1 pu speed for the inverter and SMR
cases.
It can be concluded that conventional phase advance and zero-epsilon modulation are
capable of providing significant output power improvements when compared to
conventional SMR modulation of a semi-bridge SMR at a generator speed of 1 pu. In
addition, it was shown that the modulation parameters which result in maximum output
power for conventional phase advance modulation have values of  which are close to
zero, approximating zero-epsilon modulation. In the next section, generator and phase
advance modulation parameters will be examined to determine the optimal conditions
across all speeds.
5.3 Variable Speed Performance
The single-phase analytical models for inverter, conventional SMR modulation and
phase advance SMR modulation are shown in Figure 5-8. With conventional SMR
modulation, the SMR is represented as a variable resistive load to the SPM generator, since
it can only operate with unity power factor. The inverter and the SMR with phase advance
modulation both have the ability to operate at a leading input power-factor and are thus
represented by a variable resistive-capacitive load.
Figure 5-8 shows the phasor diagrams of the generator and converter topologies at
low and high speeds under the maximum power operation. It is assumed that the
96
5.3. VARIABLE SPEED PERFORMANCE
Single-phase Equivalent Circuit
I
ωLS
Phasor Diagram
(Low Speed)
Phasor Diagram
(High Speed)
n < 0.71 pu
n > 0.71 pu
jωLSI
E I

V

jωLSI
RL
Inverter
E
1
jC
V
n < 1.41 pu
E
SMR
E
RL
I
Phase
Advance
V
jωLSI
I
45o
V
I= 0.71 pu,  = 0o
V <= 1 pu
n < 0.5 pu
ωLS
RL
E
V
I = 1 pu,  = 45o
V <= 1 pu
ωLS
I
E
45o
I
1
jC
V
jωLSI
E
I 45o V
I = 1 pu,  = 45o
V <= 0.71 pu
I,V = 1 pu
0o <  < 45o
n > 1.41 pu
E
jωLSI
 I
V
V=1pu,  = 0o
0.71 pu < I < 1 pu
n > 0.5 pu
E
jωLSI

I
V

I = 1 pu, 0o <  < 45o
0.71 pu < V <= 1 pu
Figure 5-8: Comparison of single-phase equivalent circuit, and phasor diagrams for an ideal (RS =
0) SPM generator at low and high speeds operating with inverter, SMR and phase advance
modulation.
generator’s short-circuit current equals it’s rated current. The base speed (1 pu) is defined
as the speed at which the back-emf equals rated voltage, as calculated in equation (2-14).
The effect of stator resistance is neglected.
The low-speed phasor diagrams for phase advance and inverter modulation are
identical. In both cases, a power-factor angle  = -45 is used to maintain the current in
phase with the back-emf to obtain maximum torque per ampere. The primary difference
97
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
between the two methods is the speed where field weakening starts, which corresponds to
0.71 pu for inverter modulation and 0.5 pu for phase advance modulation.
The equivalent circuits of the three modulation techniques can then be used to
calculate the values of the required V, I, , power factor and P as a function of generator
speed corresponding to maximum output power within the voltage and current limits for
an ideal SPM generator. The results are shown in Figure 5-9. It is apparent that prior to its
field weakening speed of 0.5 pu, phase advance modulation is capable of matching the
inverter’s optimum V, I, power factor and hence P. Between this speed and 0.71 pu the
inverter’s V continues to rise at the same rate, while the V of phase advance modulation
rises at a slower rate. This discrepancy causes the inverter to generate more output power.
The inverter’s V is limited at 1 pu after 0.71 pu speed, which causes the difference in
output power between phase advance and inverter modulation to reduce.
V (pu)
1
Inv
0.5
0
PA
SMR
0
0.5
1
1.5
2
I (pu)
1
SMR
0.5
0
0
0.5
o
0
2
1
1.5
2
1
1.5
2
1.5
2
Inv
0
0.5
1
pf
1.5
PA
-40
SMR
PA
0.8
Inv
0
1
P (pu)
1
SMR
-20
0.6
PA, Inv
0.5
Inv
0.5
PA
SMR
0
0
0.5
1
n (pu)
Figure 5-9: Comparison of phase voltage (V), current (I), power factor angle (), power factor (pf)
and output power (P) corresponding to maximum output power as a function of generator speed for
an ideal (RS = 0) SPM generator operating with an inverter and conventional (SMR) and phase
advance (PA) modulation
98
5.3. VARIABLE SPEED PERFORMANCE
As shown in Figure 5-9 at speeds below 0.71 pu, the SMR produces half the voltage
of an inverter, 0.71 of the current, and 1.41 times the power factor. These factors cause the
output power of a SMR to be half that of an inverter. This discrepancy reduces after the
inverter enters the field weakening range.
The reults obtained for phase advance modulation in Figure 5-9 form a key
contribution of this thesis. While [20] and [24] analysed the optimal performance of a SPM
generator operating under conventional SMR and inverter modulation, no work has been
completed on the optimal performance of phase advance modulation of a semi-bridge
SMR. These results indicate that significant output power gains can be expected over
conventional SMR modulation at low generator speeds. The following section will
investigate how the zero-epsilon modulation parameters required for the generation of
maximum output power can be derived.
5.3.1 Optimisation of Parameters
It is possible to utilize the phasor diagrams to derive expressions for the optimal
values of V and  as a function of speed for inverter and phase advance modulation. Figure
5-10 shows the low speed phasor diagram used for both inverter and phase advance
modulation. Using the assumption that base speed is the speed at which the back-emf
equals rated voltage given in equation (2-14), then the induced voltage E has the same perunit value as the speed n. It is assumed that the characteristic current is equal to rated
current, and that the machine is operating at rated current (I = Io = 1 pu) , then the voltage
drop across the stator inductance LsI has the same per unit value as the speed.
These assumptions produce the normalized phasor diagram on the right of Figure
5-10, which gives rise to
pu and  = 45o. For the zero-epsilon modulation case,
equations (5-6) and (5-7) can be used to show that the required parameters are  = 90o and
VOV = 2n pu.
99
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
jLsI
E
n pu
45o
n pu
I
V

I = 1 pu
V pu
45o
Figure 5-10: Low speed phasor diagrams for inverter and phase advance modulation at rated
current under maximum power operation
jLsI
E
n pu
n pu

I

V

I = 1 pu

V pu
Figure 5-11: High speed phasor diagrams for inverter and phase advance modulation at rated
current under maximum power operation
Figure 5-11 shows the phasor diagram at high speeds which is used to calculate the
required value of  under field-weakening conditions, where the value of V is constrained.
Using the diagram on the right side, the value of  can be as:
(5-8)
For an inverter, field weakening occurs when V = 1 pu, which further simplifies the
result in the above equation. The solution required for the zero-epsilon implementation of
phase advance modulation is determined by (5-7), with VOV set to its limiting value of 1 pu.
The value of V determined by this expression is a function of . Equations (5-6) and (5-7)
can be used with equation (5-8) to calculate:
(5-9)
The value of  obtained can then be used to calculate the required V for the zeroepsilon implementation of phase advance modulation using (5-7). This value is:
100
5.3. VARIABLE SPEED PERFORMANCE
(5-10)
Once the values of V and  have been obtained, the output power can be calculated
by:
(5-11)
Table 5-1 provides a summary of the analytical results obtained for inverter, phase
advance and conventional SMR modulation. The parameters of each modulation technique
which will be examined are the values of V ,, VOV and . The values of VOV and  are not
shown for inverter modulation, since these parameters are not used. It should be noted that
conventional SMR modulation can be viewed as a subset of phase advance modulation,
where the value of  is always controlled to zero.
Table 5-1: Summary of analytical results for an ideal SPM generator operating at maximum power
when using an inverter or SMR modulated under either phase advance or conventional SMR
modulation
Inv (nb = 0.71 pu)
n < nb
n < nb
n > nb
SMR (nb = 0.5 pu)
n < nb
1
V

n > nb
PA (nb = 0.5 pu)
45o
n > nb
1
45o
VOV
2n

90o
0o
0o
1
1
0o
0o
101
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
5.3.2 Comparison Betweeen Analysis and Simulations
The analytical results for phase advance modulation shown in Table 5-1 were
compared with the simulated optimal values of  and VOV in Figure 5-12. The simulated
parameters were obtained by conducting a two-dimensional sweep of parameters  and
VOV, and selecting the parameters which resulted in maximum generator output power
while keeping the current below the rated value.
There is a close correspondence between the analytical and simulated results at high
generator speeds, but significant errors at speeds below 0.5 pu. This is caused by the nonsinusoidal nature of the phase current waveforms at low speeds, which result in smaller
phase leg voltage and fundamental phase voltage waveforms than predicted.
Sim
0.5
Analytical
V
OV
(pu)
1
0
0
0.5
1
1.5
2
0
0.5
1
n (pu)
1.5
2
 (degrees)
180
120
60
0
Figure 5-12: Comparison of simulated (dashed lines) and analytical (solid lines) optimal VOV and 
to maximize output power for zero-epsilon modulation.
Figure 5-13 shows the simulated and analytical phase current waveforms obtained
using the optimal values of VOV and  for speeds of 0.5 (A), 1 (B) and 1.5 (C) pu. It is clear
that the simulated phase current waveforms are heavily distorted at lower speeds, which
could cause the differences seen in Figure 5-12.
102
5.3. VARIABLE SPEED PERFORMANCE
The optimal modulation parameters shown in Figure 5-12 were used to compute the
simulated maximum output power obtained by the use of zero-epsilon modulation on an
ideal SPM generator as a function of speed. This is shown in Figure 5-14 along with the
analytical curves from Figure 5-9 and simulated results for conventional SMR modulation.
The points corresponding to 0.5 (A), 1 (B) and 1.5 (C) pu speed are also shown on the
graph. It was observed that the simulated results are about 10% less than analytical
predictions at low to medium generator speeds. Despite this difference, it is clear that there
is a significant increase in output power when the simulated results for conventional SMR
I (pu)
modulation are compared with those for phase advance modulation.
Sim
1
0
-1
A
0
I (pu)
Analytical
0.005
5
Sim
1
0.01
10
0.015
15
0.02
20
B: n = 1 pu
0
-1
B
0
Analytical
0.002
0.004
2
4
0.006
6
0.008
8
0.01
10
C: n = 1.5 pu
Sim
1
I (pu)
A: n = 0.5 pu
0
-1
0
C
Analytical
2
4
(s)
tt (ms)
8
6
x 10
-3
Figure 5-13: Analytical and simulated phase current waveforms obtained using optimized zeroepsilon modulation with an ideal SPM generator at a speeds of 0.5 pu (top), 1 pu (middle) and 1.5
pu (bottom).
103
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
1
Inv
(analytical)
0.9
C
ZE
(analytical)
0.8
0.7
SMR
(sim)
B
P (pu)
0.6
ZE
(sim)
0.5
0.4
SMR
(analytical)
A
0.3
0.2
0.1
0
0
0.5
1
n (pu)
1.5
2
Figure 5-14: Analytical and simulated output power versus speed for an ideal SPM generator
operating with an inverter and a SMR with conventional and phase advance (zero-epsilon)
modulation. The current waveforms corresponding to points A, B and C are shown in Figure 5-13
5.4 Implementation of the Control System
The implementation of the phase advance modulation techniques described in this
chapter requires the construction of hardware and software modules. In the following subsections the details of the design and construction of these modules are explained.
5.4.1 Zero-Crossing Detection Circuit
Phase advance modulation for each phase of a SPM generator must be conducted
during the positive half cycle of the corresponding phase current waveform. It is thus
desirable that a control signal be generated at the positive zero-crossing of the phase
current waveforms.
LEM LA 100P Hall-effect current sensors were used to measure the phase currents.
They produced an output current which was passed through a 100 load resistor to
produce a voltage signal with a scaling of 10 V/A.
A comparator was used to produce the current zero-crossing signal. Hysteresis was
used to avoid noise on the signal causing multiple transitions. This was achieved by the
104
5.4. IMPLEMENTATION OF THE CONTROL SYSTEM
positive feedback resistors R1 and R2 which gave rise to a hysteresis band of about 0.4 V.
Figure 5-15 shows the design of this comparator circuit.
The comparator was operating with +-12 V power rails and so the resistors and diode
on the comparator output were used to provide the desired 0-5V output signal for the
microcontroller.
R2: 9.5k
+12V
+
+5V
10k 
1k 
+
IA
100 
R1: 220
6.8k 
-12V
4.7k 
VO
-
Figure 5-15: Circuit diagram for a comparator with hysteresis, producing an output voltage of +5V
when IA < 0 A and 0 V when IA > 0 A
5.4.2 Control Circuitry
A controller capable of implementing phase advance modulation was required in
order to provide experimental verification of the results presented in this chapter. The
Microchip dsPIC30F2010 microcontroller [47] was chosen as it had sufficient digital input
channels, PWM output channels and timers to implement phase advance modulation.
Figure 5-16 shows a simplified circuit diagram used for the control system. The
outputs of the three zero-crossing detection comparators, ZCD1-3, are presented to the
microcontroller as digital inputs. The user was able to choose the required phase advance
modulation parameters by using SW1 and SW2, which increased and decreased a
particular parameter, and SW3 which was used to select or confirm the particular value of
a parameter. The microcontroller was then able to utilise the zero-crossing information,
and supplied phase advance modulation parameters to determine the required PWM duty
cycle of each of the transistors in the bottom half of the semi-bridge SMR. These PWM
output signals were present on pins PWM1, PWM2 and PWM3 of the microcontroller.
A 16 character, two line LCD screen was used to display the current operating mode
and the phase advance or conventional SMR parameters. An issue with the implementation
of the LCD screen was that its parallel interface required more digital outputs than were
105
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
available in the microcontroller. The solution was to use the SPI interface on the
microcontroller to transmit the data required by the LCD to a 7HC164 shift register, which
converted it into parallel form.
The switches SW1 and SW2 were used to increase and decrease control parameters
respectively. The parameter  was varied from 0o to 90o in steps of 5o, while VOV was
controlled by controlling the duty cycle during this period from 0% to 100% in steps of
5%. SW3 was used to confirm the parameters entered by a user. A PWM switching
frequency of 10 kHz was utilized.
The tasks executed by the microcontroller in this system required significant amounts
of code to function. This software will be examined in the next section.
+5V GND
10 k
SPI
+5V
GND
ZCD1
ZCD2
ZCD3
PWM1
PWM2
Q0
Q1
Q2
Q3
GND
+5V
Q7
Q6
Q5
Q4
+5V
74HC164
dsPIC 30F2010
GND
15 pF
15 pF 20 MHz
PWM3
+5V
GND
+5V
GND
+5V
GND
GND
GND
Displaytech 16B2
GND
SW2
SW1
10 k
10 k
GND +5V
GND +5V
SW3
10 k
GND +5V
+5V
10 k
GND
Figure 5-16: Simplified circuit diagram for control electronics system
106
Q7
Q6
Q5
Q4
Q3
Q2
Q1
Q0
5.4. IMPLEMENTATION OF THE CONTROL SYSTEM
5.4.3 Software Design
The key functions performed by the dsPIC 30F2010 microcontroller used were to
accept input parameters for the value of δ and VOV from users, and to determine the correct
value of duty cycle at which to operate at a given instant. Figure 5-17 shows a flow chart
of the software developed to implement phase advance modulation.
The three inputs from the zero-crossing detection circuit were used as change
notification (CN) interrupts, which triggered at either the rising or falling edge of the phase
current waveform. When a rising edge was encountered, the period required for the δ phase
was calculated based on the user’s input parameters, and stored in a timer. The controller
then tested if the current waveform was still in the positive half cycle (i.e. no falling edge
interrupt had been encountered on the phase current waveform). At this point, d was set to
either 1 or dφ based on whether the period of δ had finished. The value of d was set to zero
during the negative half cycle of the phase current waveform. It should be noted that
conventional SMR modulation could be achieved by setting the δ period to zero, and
varying the duty cycle dφ.
One of the limitations of the software systems and control hardware presented in this
section was that it was not trivial to reprogram the microcontroller, or adjust the
parameters of the zero crossing detection circuit. To obtain a much more flexible
development platform, a dSPACE based system has been developed which will be
examined in Chapter 6.
107
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
START
Measure
Current
Waveform
else
Rising
Edge
Calculate δ
period
I>0
t< δ
end
time
else
else
D=0
D = dφ
D=1
Figure 5-17: Flow chart for software used to implement phase advance modulation on dsPIC
30F2010 microcontroller
5.5 Experimental Results
The generator and IGBT power electronic converter presented in Chapter 4 were
utilized in this section. (see Table 4-1and Table 4-2 for parameters) The simplified
simulation model for a semi-bridge SMR given in Section 3.3.2 was utilized in order to
108
5.5. EXPERIMENTAL RESULTS
obtain simulated results with the power converter voltage drops set to the values specified
by Table 4-2 and the generator stator resistance set to the value in Table 4-1.
5.5.1 Rated Speed Performance
Figure 5-18 shows a comparison of the simulated and experimental line current and
phase leg voltage waveforms for three operating points at rated speed (490 rpm).

VOV
I (A)
VLEG (V)
50
20
40
Sim
0o
21 V
Exp
30
0
20
-20
0
2
Sim
10
Exp
4
t (ms)
6
8
0
0
2
4
t (ms)
6
8
6
8
6
8
50
20
40
Exp
30o
21 V
Exp
30
0
20
0
2
Sim
10
Sim
-20
4
t (ms)
6
8
0
0
2
4
t (ms)
50
20
40
Exp
0
70o
Exp
30
20
42 V
Sim
-20
0
2
Sim
10
4
t (ms)
6
8
0
0
2
4
t(ms)
Figure 5-18: Conventional (δ = 0o, VOV = 21V), and phase-advance SMR modulation (δ = 30o, VOV
= 21V and δ = 70o, VOV = 42V). Simulated and experimental line current and phase leg voltage
waveforms at 490 rpm.
The experimental waveforms show a good correspondence with the simulated ones.
Note that the simulation does not model the PWM. The line current magnitude, output
power and length of the positive half cycle for the three cases are summarized in Table 5-2.
109
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
The case where δ = 0 and VOV = 21 V corresponds to conventional SMR modulation.
The current waveform has a rms magnitude of 9 A, is sinusoidal and largely symmetrical.
An experimental output power value of 259 W was achieved under these conditions.
When the control angle  is increased to 30o while VOV is unchanged at 21 V the
asymmetry in the stator current waveform increases and the rms value increases from 9 A
to nearly 13 A. The output power increases by about 9% compared to conventional SMR
modulation.
As the control parameters are increased to  = 70o and VOV = 42 V, the distortion in
the phase current is pronounced and the phase current increases to about 14 A. The output
power increases substantially to about 55% greater than conventional SMR modulation.
This corresponds to the maximum achievable power with phase-advance modulation at this
speed.
Figure 5-19 shows the simulated and experimental phase voltage, current and output
power as a function of δ at 1 pu speed for VOV values of 42 V and 21 V. The simulated
results are similar to those shown in Figure 5-6 except they include the effect of stator
resistance and device voltage drops.
There is a good correspondence between the
simulated and experimental results. The points corresponding to the cases in Figure 5-18
are labelled as A, B and C respectively in the power graph. Point C refers to the maximum
generator power obtained at rated speed.
Table 5-2: Summary of the performance results for the case shown in Figure 5-18

VOV
I
P
Positive Cycle
00
21 V
9.04 A
259 W
180o
300
21 V
12.89 A
283 W
180o
700
42 V
13.59 A
402 W
170.1o
110
5.5. EXPERIMENTAL RESULTS
V (V)
40
VOV = 42 V
20
0
VOV = 21 V
0
20
40
60
80
100
120
140
160
180
0
20
40
60
80
100
120
140
160
180
120
140
160
180
I (A)
15
10
5
0
500
P (W)
A
C
250
B
0
0
20
40
60
80
100
 (degrees)
Figure 5-19: Comparison of simulated (dashed lines) and experimental (symbols) generator phase
voltage, current and output power as a function of δ for VOV values of 1 and 0.5 when zero-epsilon
modulation was used at a speed of 490 rpm
5.5.2 Variable Speed Performance
The above testing was repeated for a range of speeds between 100 to 1,000 rpm to
experimentally determine the optimum values of control parameters to maximize the
output power. The results are summarized in Figure 5-20 which shows the simulated and
experimental optimal control parameters VOV and δ, and the resultant output power and
system efficiency. On the output power graph, the simulated inverter output is shown for
comparison. The simulated results all include the effect of stator resistance and device
voltage drops.
At speeds above 200 rpm, there is a close match between the simulated and
experimental values of VOV and . At lower speeds, greater values of VOV and  are
required than predicted by the simulations. This is likely caused by the non-sinusoidal
nature of current waveforms at lower speeds.
111
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
VOV (V)
50
 (degrees)
0
0
200
400
600
800
1000
0
200
400
600
800
1000
150
100
50
0
1000
P (W)
Inverter
500
ZE
0
0
200
400
SMR
600
800
1000
600
800
1000
1

SMR
0.5
ZE
0
0
200
400
n (rpm)
Figure 5-20: Comparison of simulated and experimental (circles) optimal VOV and , maximum
output power and system efficiency as a function of generator speed obtained using zero-epsilon
modulation. Experimental (squares) and simulated efficiency and power results are shown for
conventional SMR modulation, while the simulated inverter output power is also displayed.
Simulated and experimental data for the output power obtained with zero-epsilon and
conventional (non phase advance) SMR modulation, along with simulated results for
inverter modulation are also shown. An examination of the power curves shows that zeroepsilon modulation produces an output power which is approximately half way between
the results for inverter and conventional SMR modulation.
The efficiencies offered by conventional SMR and zero-epsilon modulation as a
function of generator speed are comparable, with maximum values of 0.8 for conventional
SMR modulation, at a generator speed of 800 rpm, compared to 0.75 for zero-epsilon
modulation at 860 rpm.
The results obtained could also be plotted in the V- plane, which enabled an
investigation of the similarities between inverter modulation and conventional (non phase
advance) and zero-epsilon SMR modulation to be conducted. V was measured as the rms
112
5.5. EXPERIMENTAL RESULTS
of the fundamental voltage waveform, while  was obtained by using a power analyser to
measure the phase shift between V and I. The results are plotted in Figure 5-21. The
significant difference between the ideal analytical curve and the simulated results is due to
the effect of stator resistance and device voltage drops.
It is clear that zero-epsilon modulation is capable of matching the inverter’s operating
points for low values of V (low speeds), but is unable to generate large phase shift angles 
for values of V between 15 to 30 V. At higher voltages (speeds), there is again a reasonable
correspondence between the simulated inverter curve and the simulated and experimental
results for zero-epsilon modulation. These findings verify the results found in Figure 5-20,
which showed that zero-epsilon modulation provided a closer match to an inverter’s output
power at low and high generator speeds.
40
35
Ideal (RS = 0)
30
Inv
V (V)
25
SMR
20
ZE
15
10
5
0
-50
-40
-30
 (degrees)
-20
-10
0
Figure 5-21: Comparison of simulated (dashed) V- loci corresponding to maximum power
generation for the SPM generator operating with an inverter, as well as a semi-bridge SMR using
zero-epsilon modulation and conventional (non phase advance) modulation. Experimental results
for zero-epsilon (circles) and conventional SMR (squares) are also shown, along with the optimal
trajectory for an ideal SPM generator (RS = 0).
113
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
5.6 Conclusion
This chapter investigated the use of phase advance modulation for surface permanent
magnet (SPM) generators operating with a switched-mode rectifier (SMR). The control
and performance were compared with the results obtained from conventional SMR and
inverter modulation. The SMR has the advantage over the inverter as it does not require
explicit rotor position information. The key results are as follows.

The phase voltage-power factor angle plane was shown to provide a convenient
graphical means for visualizing both the PM generator control requirements to
maximize the output power at different speeds, as well as the power electronics
control limitations.

With conventional SMR modulation only unity power factor operation is possible
however phase advance SMR modulation can achieve leading power factors (similar
to an inverter but with not as much control flexibility) and hence improved output
power.

A simplified phase advance modulation technique called zero-epsilon modulation
was introduced and shown to offer comparable maximum output power to the
standard phase advance modulation technique.

Analytical results based on Fourier series calculations and assuming symmetrical
current waveforms were used to calculate the required phase advance modulation
parameters to maximize the output power.

Though analytically the output power with phase advance modulation should closely
approach that with an inverter, simulations showed that the output power is reduced
significantly by due to the non-symmetrical current waveforms. A similar effect was
observed with conventional SMR modulation. A good correspondence between the
simulated and experimental results was found.

The results were validated experimentally on a small PM generator. It was found
that at rated speed, phase advance modulation improved the output power by 60%
compared to conventional SMR modulation.
114
5.6. CONCLUSION
This chapter has examined maximizing the generator output power at different
speeds. The next chapter will examine the issue of producing a particular output power at
maximum efficiency at a desired speed. This control approach is of importance to wind
turbine generators and automotive alternators.
115
CHAPTER 5: POWER CAPABILITY AND LIMITS OF PHASE ADVANCE MODULATION
116
Chapter 6: Maximum Torque per Ampere
Control of Phase Advance Modulation
The previous chapter focussed on determining the phase advance modulation control
parameters required for the generation of maximum power at a given speed for a SPM
generator. This control strategy is not suitable in applications such as wind power
generation, since in such a situation the SPM generator is usually commanded by a
maximum power point tracking algorithm to produce a value of torque which results in
maximum turbine output power for a given wind speed.
Maximum torque per ampere control is an algorithm which produces a commanded
value of torque at a given speed using the smallest possible phase current. This control
strategy effectively minimizes the copper losses of the SPM generator, and thereby
maximizes efficiency if the generator iron losses are assumed to be constant.
In this study, the required generator control parameters for maximum torque per
ampere control at a given value of torque and speed will be determined analytically by
determining the values of Id and Iq, then transforming these quantities to the generator
voltage V and power factor angle . Maximum torque per ampere control is achieved by
setting the generator’s Id to the minimum value possible whilst allowing the generator
output V and I to remain below their limiting values. In addition, transformations used in
117
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
the previous chapter will then be used to calculate the required values of  and VOV
required. Simulations obtained using the simplified simulation model presented in Chapter
3 will be used to determine the validity of this analytical approach. Experimental results
verifying the analytical and simulated findings presented throughout this chapter will also
be shown. A number of experimental results obtained under both open-loop and closedloop current feedback control modes will be given.
6.1 Analytical Methods
Maximum torque per ampere control of SPM generators generally requires operation
with a leading power factor. As a result, this method can only be utilized by the semibridge SMR topology operating under phase advance modulation, and the inverter. The
rectifier and SMR used with conventional modulation are not applicable for this technique
since they can only operate at unity power factor. The following sections will outline the
methods used to compute the control parameters required for maximum torque per ampere
control with inverter and phase advance modulation.
6.1.1 Inverter Modulation
Equations (6-1) and (6-2) show the d and q-axis voltage equations for an SPM
generator including resistance. The equations are derived from the phasor diagram shown
in Figure 2-2a. The generator sign convention is used, which causes the terms with Id and
Iq to have opposite signs to those observed with the conventional motor sign convention.
(6-1)
(6-2)
These equations are used to analytically determine the SPM generator parameters
required for maximum torque per ampere control.
A number of assumptions are made in order to simplify the analysis. Firstly, the rated
angular speed o is defined such that the induced voltage at this speed Mo is equal to the
rated voltage of the generator, Vo. Secondly, it is assumed that the SPM generator is
designed such that the characteristic current Ix, that is, the high-speed short circuit current
118
6.1. ANALYTICAL METHODS
(
), is equal to the generator rated current, Io. This assumption implies a machine
with a high stator inductance, generally associated with a fractional-slot stator winding
which is applicable to the machine under test [48-50]. Finally it is assumed that the phase
currents are purely sinusoidal.
Using the above assumptions, it is found that M and LS are unity under this per-unit
system. The rated generator speed in rpm, no is chosen to correspond to o so that the
values of n and  in per unit are the same and hence are interchangeable. The simplified
per-unit Vd and Vq voltage equations are shown below:
(6-3)
(6-4)
Hence, the magnitude of the stator voltage V can be given by:
(6-5)
Maximum torque per ampere control is achieved when Id is either set to zero, or the
minimum value allowable when keeping V less than 1 pu. The expression for V when Id = 0
becomes:
(6-6)
Cases where V > 1 pu indicates that V is greater than the rated voltage, Vo. This
scenario is encountered as the generator per unit speed n and commanded Iq are increased.
The value of V can be controlled to Vo for a given value of n and Iq by introducing a nonzero value of Id.
Figure 6-1 shows examples of how Id affects the value of V for an ideal (RS = 0) SPM
generator for different values of Iq and n. These images show that increasing the value of Id
119
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
1.5
V (pu)
n = 1 pu
1
0.75 pu
0.5
0.5 pu
I = 1 pu for all cases
0.25 pu
q
0
0
0.2
0.4
0.6
0.8
1
1.5
I = 1 pu
V (pu)
q
1
0.75 pu
0.5
0.25 pu
0.5 pu
n = 1 pu for all cases
0
0
0.2
0.4
0.6
0.8
1
Id (pu)
Figure 6-1: Comparison of V as a function of Id for the case where Iq was held constant and n was
varied (top image) and n was held constant at 1 pu while Iq was varied (bottom)
up to 1 pu reduces the value of V for the cases where Iq was kept constant at 1 pu and n was
varied, and vice versa. The rated voltage Vo is plotted on these graphs as a dashed line. For
the case in the upper image, when n = 0.75 pu and Iq = 1 pu, the value of V with Id = 0
control is 1.06 pu. In order to reduce this value to 1 pu, or Vo, an Id of 0.12 pu should be
introduced. For the case where n = 1 pu, and Iq = 0.25 pu in the bottom image, an Id of 0.14
pu was required to keep the generator output voltage to its rated voltage Vo.
Another issue that should be considered when non-zero values of Id are utilized to
reduce V is that the magnitude of the generator current, I increases as Id grows larger. Care
must therefore be taken to ensure that I does not exceed its rated value, Io. Figure 2-4
illustrates the effects of current and voltage limits in the d-q plane. It is apparent that
increasing the value of Id reduces the maximum value of Iq which can be generated while
maintaining I < Io. As a result, the smaller of the two possible solutions for Id which allows
for V to be below its rated value should be chosen.
Equation (6-5) can be expressed as a quadratic which can be solved for the required
Id assuming V is set to the rated voltage, Vo. This is shown in (6-7). Given that this
expression is a quadratic, two solutions of Id will be found. As stated previously, choosing
120
6.1. ANALYTICAL METHODS
the larger value of Id will result in a larger value of I, so the solution for Id with the smaller
magnitude is always utilized.
(6-7)
The analytical expressions provided above could be simplified by setting the stator
resistance RS to zero. Equation (6-6) could then be simplified to the following expression
for Id = 0 control.
(6-8)
If Iq is set to the rated value of current (that is, the maximum generator output power
is sought) the magnitude of the stator voltage is equal to
n, which is identical to the
expression found in Chapter 5. The quadratic equation shown in (6-7) for the case where Id
 0 could also be simplified using the RS = 0 assumption, and is given below.
(6-9)
The value of SPM generator power factor angle,  for given values of Id, Iq, Vd and
Vq is given below in equation (6-10). This expression was derived by analysing the phasor
diagram presented in Figure 2-2a. The first tan-1 function in the equation represents the
angle between I and Id, while the second represents the angle between V and Vd. The
difference between these two angles is the power factor angle, .
(6-10)
Equation (6-10) can be simplified for the case where Id = 0. The function
will become /2, whereas Vq/Vd can be calculated by (6-3) and (6-4) to be:
121
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
(6-11)
As a result, the expression for  will be given as:
(6-12)
If the value of Iq was set to the rated current, and the stator resistance was set to zero,
the value of  would be 45o, which is identical to the value derived in Chapter 5 for
maximum output power at speeds below the field weakening value.
The analysis in this section has shown how the required values V and  can be
computed for a SPM generator requiring a particular value of q-axis current Iq (that is,
torque) to be generated at a given speed n when an inverter was used. The next section will
examine the additional issues encountered when a semi-bridge SMR with phase advance
modulation was used.
6.1.2 Phase Advance Modulation
The inverter is constrained by its maximum allowable values of V and I for a given
set of operating conditions. Phase advance modulation has an additional parameter which
is constrained, VOV. The equations linking the generator V and  to the phase advance
modulation control parameters VOV and  were given by (5-6) and (5-7) in the previous
chapter.
The value of  is calculated by using the power factor angle  calculated for inverter
modulation under a given operating speed n and required Iq in (5-6). This value of  is then
utilized to evaluate the required value of VOV from (5-7). The maximum value of VOV is
constrained by the DC link voltage of the semi-bridge SMR, VDC.
This section has described the analytical techniques required to compute the control
parameters  and VOV required for an SPM generator operating with a required Iq at a speed
n. The next section will compare the performance of maximum torque per ampere control
when using inverter and phase advance modulation.
122
6.1. ANALYTICAL METHODS
6.1.3 Comparison of Inverter and Phase Advance Modulation
Figure 2-4 showed the voltage and current limits of a SPM generator in the d-q
current plane, where the current limit circle had a radius of 1 pu and was centred on the
origin of the d-q current plane. The radius of this current limit circle was found to remain
constant as generator speed was varied. In contrast, the voltage limiting circle was centred
on the point where Id = 1 pu and Iq = 0 (due to the assumption that the rated current Io was
equal to the characteristic current, Ix) , and was found to contract in size as generator speed
was increased.
Analysis of inverter modulation presented in Chapter 2 showed that the inverter was
only capable of operating whilst V < 1 pu. In contrast, analysis of phase advance
modulation in Chapter 5 showed that a SPM generator using this strategy could only
operate while VOV < 1 pu.
Figure 6-2 plots the voltage and current limit constraints for inverter and phase
advance modulation on the d-q current plane for generator speeds of 0.5, 0.71, 1 and 2 pu.
RS is assumed to be zero for these calculations. The voltage limiting circles for inverter
operation correspond to the V = 1 pu circles. For n < 0.71 pu an inverter is capable of
generating an Iq value of up to 1 pu, while maintaining Id = 0. For the speeds of 1 pu and 2
pu, some amount of Id is required in order to ensure the SPM generator’s operating point is
within the voltage limiting circle.
The voltage limit regions for phase advance modulation are presented by the VOV = 1
limits in Figure 6-2. Unlike the V = 1 regions, which remain circles at all generator speeds,
the VOV = 1 operating area consists of two intersecting ellipses (shaded) for the lower speed
values. As speed increases, the ellipses contract, with the smaller ellipse eventually
disappearing entirely while the larger ellipse becomes centred around the Id = 1, Iq = 0
point in a similar fashion to the V = 1 pu circle. In fact, at a generator speed of 2 pu the VOV
= 1 pu and V = 1 pu circles are identical, indicating that the performance of a SPM
generator using inverter or phase advance modulation at this speed should be nearly
identical.
123
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
Figure 6-2: Comparison of d-q axis current plots for inverter and phase advance modulation,
showing the limits for I = 1 pu, V = 1 pu and VOV = 1 pu at speeds of 0.5, 0.71, 1 and 2 pu. The
operating region possible with phase advance modulation is shown as the shaded area
The requirement for non-zero Id at higher values of generator speed can be further
illustrated by Figure 6-3. The graph on the left hand side of this figure shows Id and Iq as a
function of generator torque for the case where n = 0.5 pu. Torque values of up to 1 pu can
be generated by both topologies without introducing any Id. If we compare this figure to
the top left graph of Figure 6-2 (where n = 0.5 pu) it can be seen that at this speed Iq values
of up to 1 pu can be obtained when V < 1 pu and VOV < 1 pu.
The graph of Id and Iq as a function of T when n = 1 pu is shown on the right hand
side of Figure 6-3. In this case, Id is required in order to generate torque for both the phase
advance and inverter modulation cases. The phase advance modulation case requires a
greater value of Id to achieve a given value of torque. This too can be explained by Figure
6-2, which shows that the V = 1 limiting circle requires a smaller value of Id to generate the
124
6.1. ANALYTICAL METHODS
1.2
1.2
1
1
Id, I q (pu)
0.8
0.8
I q (PA, Inv)
I q (PA,Inv)
0.6
0.6
0.4
0.4
I d (PA)
0.2
0.2
I d (PA, Inv)
0
0
0.5
T (pu)
I d (Inv)
1
0
0
0.5
T (pu)
1
Figure 6-3 : Comparison of SPM generator Id and Iq as a function of generator torque at speeds of
0.5 pu (left) and 1 pu (right).
maximum value of Iq while remaining within the current limiting circle compared to the
VOV = 1 locus.
The optimal values of V and  for an ideal (RS = 0) SPM generator at speeds of 0.5
and 1 pu using either inverter or phase advance modulation are shown in Figure 6-4 as a
function of generator torque. In addition, Figure 6-4 displays the required values of the
phase advance modulation parameters VOV and .
At 0.5 pu speed, V and VOV had not yet reached their limiting values of 1 pu for any
value of T. As a result, there was no difference between the curve of V as a function of T
for inverter and phase advance modulation. When the generator speed was increased to 1
pu, the values of V and VOV had already reached their limiting values. Observation of the
graph of  as a function of T at both speeds shows that  is proportional to the value of T
required. Equation (5-5) showed that increasing  reduced the maximum value of V. As a
result, it is no surprise that V reduces as a function of T for phase advance modulation at 1
pu generator speed.
The maximum torque which could be achieved using phase advance modulation
within rated voltage and current was equal to 1 pu for n = 0.5 pu, but dropped to 0.8 pu
when n was raised to 1 pu. It should be noted that despite the difference in V, the values of
 obtained using each technique is similar up till the maximum torque achievable by phase
125
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
V (pu)
1
Inv (1 pu)
PA (1 pu)
0.5
0
PA, Inv (0.5 pu)
0
0.2
0.4
0.6
0
PA (1 pu)
0.8
1
Inv (1 pu)
o
-20
PA, Inv (0.5 pu)
-40
0
0.2
0.4
0.6
I (pu)
1
0.8
1
Inv (1 pu)
PA (1 pu)
0.5
PA, Inv (0.5 pu)
VOV (pu)
0
0
0.2
0.4
1
0.6
1
PA (1 pu)
0.5
0
0.8
PA (0.5 pu)
0
0.2
0.4
0.6
0.8
1
100

o
PA (0.5 pu)
50
PA (1 pu)
0
0
0.2
0.4
0.6
0.8
1
T (pu)
Figure 6-4: Comparison of V and  obtained using inverter and phase advance modulation at speeds
of 0.5 and 1 pu as a function of generator torque. The current magnitude and required phase
advance modulation parameters VOV and  are also shown.
advance modulation. This is because equation (5-6) is not dependant on V. The curves of 
as a function of T are also related to  through equation (5-6).
Contour plots of the T and I obtained as V and  are varied are shown in Figure 6-5
and Figure 6-6 for speeds of 0.5 and 1 pu respectively for an ideal SPM generator. The
optimal operating trajectories for inverter and PA modulation found in Figure 6-4 are
plotted on these figures, along with the trajectory used by conventional SMR modulation.
126
6.1. ANALYTICAL METHODS
0.8
0.8
0.7
0.7
PA, Inverter
0.6
V (pu)
0.5
0.6
1
PA, Inverter
0.5
0.8
1.4
0.4
0.4
0.8
0.6
0.3
1.2
0.3
SMR
1
SMR
0.4
0.2
0.2
0.1
0
0.2
-40
-30
-20

-10
0.1
0
0
-40
-30
o
-20

-10
0
o
Figure 6-5: Contour plots of torque (left) and current (right) as functions of V and  for an SPM
generator at a speed of 0.5 pu. Trajectories indicating the optimal modulation parameters for
inverter, phase advance and conventional SMR modulation are also shown
1
1
Inverter
0.9
Inverter
0.9
0.6
PA
0.8
PA
0.8
0.8
0.8
0.7
0.7
V (pu)
0.6
0.6
0.6
0.5
0.5
1
1.2
0.4
0.4
SMR
0.4
SMR
0.3
0.3
0.2
0.2
0.2
0.1
0
0.1
-40
-30
-20
o
-10
0
0
-40
-30
-20
o
-10
0
Figure 6-6: Contour plots of torque (left) and current (right) as functions of V and  for an SPM
generator at a speed of 1 pu. Trajectories indicating the optimal modulation parameters for inverter,
phase advance and conventional SMR modulation are also shown.
127
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
The open circuit point is found when V is at its maximum value while  = 0o. The
current is zero at this point, and increases as the values of V and  change from this point.
The SMR is only capable of operating at a unity power factor, and as a result remains on
the  = 0o line while V is modified. In contrast, inverter and phase advance modulation are
able to control the SPM generator’s power factor angle. The short circuit points are
obtained when V = 0 and appear on Figure 6-5 and Figure 6-6 as the x-axis of the contour
plots. The current at the short circuit points is 1 pu for both speeds, since RS = 0 for an
ideal SPM generator.
At 0.5 pu speed (Figure 6-5) both phase advance and inverter modulation have the
same operating trajectory. This is because the values of V and VOV used by inverter and
zero-epsilon modulation respectively at this speed do not exceed 1 pu. At 1 pu speed, the
phase advance trajectory diverges from the inverter trajectory for higher values of torque
with a smaller V being available as  becomes more negative. This is because  is being
increased in order to increase  for phase advance modulation. Equation (5-5) shows that
the maximum V capability is reduced as  increases.
The optimal values of V and  shown in Figure 6-4 correspond to the optimal curves
shown in Figure 6-5 and Figure 6-6. This finding proves that the analytical equations
presented earlier in this chapter describe maximum torque per ampere control. The
following section will investigate whether the analytical values of V and  corresponding
to maximum torque per ampere control will be validated by simulations.
6.2 Simulation Results
As stated previously, the analytical results were based on sinusoidal assumptions for
V and I, which was not necessarily valid for all operating conditions. These simulated
results were based on an ideal (RS = 0) generator model and a power electronic converter
with no voltage drops. Figure 6-7 shows a comparison between the analytical and
simulated values of V and I as a function of generator torque obtained at a speed of 1 pu.
The optimal analytical values of  and VOV shown in Figure 6-4 were utilized to obtain the
simulated curve. There is a close correspondence between the simulated and analytical
current values. There is a larger error, however, between the results obtained for the
voltage. The simulated values of voltage are consistently smaller than the analytical values.
128
6.2. SIMULATION RESULTS
1
A
B
V (pu)
Sim
Analytical
0.5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1
B
I (pu)
0.8
A
0.6
Sim
0.4
Analytical
0.2
0
0
0.1
0.2
0.3
0.4
T (pu)
0.5
0.6
0.7
0.8
Figure 6-7: Comparison of simulated and analytical results of generator voltage and current as a
function of torque for an ideal SPM generator operating at a speed of 1 pu using phase advance
modulation. Points of interest at 0.4 and 0.8 pu torque are shown.
This phenomenon was encountered in the previous chapter, and was found to be
caused by the non-symmetrical nature of the phase current waveform. Examples of the
current and voltage waveforms for torque values of 0.4 pu (A) and 0.8 pu (B) are shown in
Figure 6-8. It is apparent that the simulated current waveforms in both cases are again nonsinusoidal, which explains the difference between the simulated and analytical curves in
Figure 6-7.
The values of simulated and analytical generator torque as a function of the
commanded value of torque, T*, are shown in Figure 6-9. It is apparent that the simulated
value of torque is greater than the analytical result for low values of torque command, and
is higher for larger values of T*. The simulated torque is greater for low T* because in this
range, the current waveform is less symmetrical than at higher values of T*. The shorter
positive half-cycle of the phase current reduces the terminal voltage V and hence increases
the phase current I (see Figure 6-8). The simulated T becomes smaller than the analytical
value at high values of T* as the reduction in terminal voltage V does not change the phase
129
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
current magnitude but changes its phase shift. This causes, the value of current required to
generate a given value of torque to be greater than for the simulated case as can be viewed
by graph on the right of Figure 6-9. This is likely due to the simulated results requiring a
greater level of Id than their analytical counterparts for larger values of T.
2
2
A
I (pu)
1
B
Analytical
1
Analytical
0
0
-1
-1
Sim
Sim
-2
0
6
12
1.5
V
V (pu)
0.5
Leg
(Sim)
-0.5
-0.5
-1.5
0
6
t (ms)
V
0.5
0
Sim (fund)
6
12
B
1
0
-1
0
1.5
A
1
-2
12
-1.5
(Sim)
Sim (fund)
-1
Analytical
Leg
Analytical
0
6
t (ms)
12
Figure 6-8: Comparison of simulated and analytical phase current (top), and simulated and
analytical fundamental phase voltage along with simulated phase leg voltage (bottom) for an ideal
SPM generator operating at 1 pu speed for torque values of 0.4 pu (A) and 0.8 pu (B)
130
6.3. IMPLEMENTATION OF CONTROL ALGORITHMS
0.9
1.5
PA
(calc)
0.8
0.7
PA
(calc)
SMR
(calc)
1
0.5
I (pu)
T (pu)
0.6
PA
(sim)
PA
(sim)
0.4
0.3
SMR
(sim)
Inv
(calc)
0.5
0.2
0.1
0
0
0.5
T* (pu)
1
0
0
0.5
T (pu)
1
Figure 6-9: Comparison of analytical and simulated generator torque as a function of torque
command, T*, along with generator current as a function of torque for inverter, SMR and phase
advance modulation at a generator speed of 1 pu for an ideal (RS = 0) SPM generator
The graph of current as a function of generator torque shows that there is not much
difference between the three power electronic converter topologies at low torque values.
Phase advance modulation is capable of producing increased amounts of generator torque
when compared to the SMR, but less torque when compared to inverter modulation.
This section has examined the effects of non-sinusoidal waveforms on performance
capability compared to the analytical techniques presented earlier in this chapter for
achieving maximum torque per ampere control. The following section will show how a
phase-advance modulation control system was implemented.
6.3 Implementation of Control Algorithms
The analytical equations presented in Section 6.1 provided methods of calculating
the phase advance modulation parameters required to generate a commanded value of
torque under maximum torque per ampere conditions. This section will investigate how
these equations could be implemented in a realistic control algorithm.
131
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
6.3.1 Open-Loop Control Algorithm
Figure 6-10 shows a block diagram of the control system which was used to generate
the control signals required for maximum torque per ampere control of a SPM generator
using phase advance modulation. The torque command T* and the generator speed n are
used to calculate the required generator voltage V and power factor angle, via lookup
tables. The voltage look-up table utilizes equations (6-6) and (6-7), while the power factor
angle  look-up table uses (6-10). These values are then used to calculate the required
phase advance modulation parameters VOV and  using equations (5-6) and (5-7). The
PWM controller uses these parameters, along with the positive zero-crossing information
of the phase currents, to determine the required duty cycle for each of the three phases at a
given instant. The Simulink program used to implement this control system is given in
Appendix B.
Power
Electronics
Generator
I1
n
I2
I3
d1 d2 d3
vwind
I_Feedback
+
-
I*
_Lookup
MPPT
*
V_Lookup
Iq*
-2
PWM
Controller
I
k
+
+
OLD
NEW
VOV _Calc
V*
VOV
Figure 6-10: Block diagram of the control system used to implement phase advance control in a
standalone wind turbine system. The components required to implement closed-loop current
control are shown as dashed lines
132
6.3. IMPLEMENTATION OF CONTROL ALGORITHMS
6.3.2 Closed-Loop Control Algorithms
The T vs. T* results in Figure 6-9 showed that the simulated torque obtained using
the analytical equations in Section 6.1 had some discrepancies when compared to the
analytical results. It was predicted that some form of closed-loop control would be required
to correct these errors in an experimental system. Two methods of closed-loop control
which will be examined in this section are current feedback control and beta or current
positive half-cycle feedback control, which will be presented in the following subsections.
6.3.2.1 Current Magnitude Feedback Control
A refinement of the open-loop torque control scheme is to use generator line current
magnitude feedback. The magnitude was obtained using a FFT operation within Simulink.
It is acknowledged that other methods such as using the peak value of the filtered current
waveform would be more suitable for low-cost implementation. For the purposes of
laboratory testing, however, the FFT was deemed to be sufficient.
The dashed lines in Figure 6-10 showed how the closed-loop current feedback
control system was implemented. A current error signal I was computed by subtracting
the measured stator current magnitude I from the expected stator current magnitude I* (see
below). This error signal was then multiplied by a gain k, before being added to the
commanded value of. A measured current which is larger than the commanded current
causes the value of  to be reduced. The parameter was used as the control parameter
instead of VOV because previous results in Chapter 5 had shown that the value of current is
primarily dependant on this variable.
The value of I* was calculated using the SPM generator model (Section 2.1.1):
(6-13)
where Iq* is obtained from the commanded torque, and * was found by the following
equation [23]:
133
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
(6-14)
. The values of V*and * were calculated using
In this equation,
lookup tables for given values of generator speed and commanded torque. The Simulink
programs used to implement closed-loop current feedback control are also given in
Appendix B.
6.3.2.2 Beta Feedback Control
It has been stated in Chapter 5 that a key difference between the analytical, simulated
and experimental phase current waveforms obtained using phase advance modulation was
that the positive half cycle of these waveforms in the simulated and experimental cases
were often smaller than their negative counterparts. Figure 6-11 shows the effects of a
non-symmetrical phase current waveform when phase advance modulation is utilized.
A parameter  is defined as the time difference between the negative zero crossing
of the positive half cycle of a symmetrical and non-symmetrical phase current waveform. It
VLeg
VOV
I

V

VOV
VLeg
I



V
Figure 6-11: Comparison of the effects of symmetrical (top) and non-symetrical (bottom) phase
current waveforms on phase advance modulation. The phase current I, and resulting fundamental
phase voltage V is shown.
134
6.3. IMPLEMENTATION OF CONTROL ALGORITHMS
is apparent that the time which the generator’s phase leg to ground voltage, VLeg is high is
reduced by the length of . This change results in a smaller magnitude of the fundamental
phase voltage, V, as can be observed in Figure 6-11. The value of the power factor angle 
between I and V is also reduced.
It is possible to use Fourier analysis to quantify the changes to V and  encountered
when  is introduced. The Fourier coefficients, a1 and b1 will be defined as shown below.
(6-15)
(6-16)
The value of V can then be calculated as:
(6-17)
The value of power factor angle  is given as:
(6-18)
Equations (6-17) and (6-18) show that increasing  reduces the value of V and the
magnitude of  obtained. As a result,  must be increased to keep  at its desired value,
while VOV must in turn be increased to compensate for the new value of  and the addition
of . The new value of  is given by:
(6-19)
The required new value of VOV can then be calculated by using (6-17) to keep V at its
desired value.
135
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
(6-20)
Thus it can be seen that the new value of VOV will become larger as  increases.
There is a problem, however, since VOV cannot be increased indefinitely and is limited by
the DC link voltage, VDC.
6.3.3 Simulation Results
The previous section showed that beta feedback control was a promising control
strategy for correcting the phase advance modulation control parameters  and VOV based
on the lack of symmetry in the SPM generator’s phase current waveform. This technique
however depended on the negative zero crossing of the phase current waveform being
clearly defined. The simulated phase current waveform for an ideal SPM generator
operating at a speed of 1 pu while generating a torque of 0.4 pu in Figure 6-8 showed that
there was no clear transition between the positive and negative half cycles. This “flat”
region in the current waveform could cause significant errors in the value of beta estimated
by the controller.
This issue with the shape of the phase current waveform meant that it was difficult
to implement beta feedback control. In contrast, the current magnitude feedback method
was found to function adequately even with the same irregularly-shaped waveforms. As a
result, the closed-loop simulated results presented in the next section will all utilize the
current magnitude feedback technique.
6.4 Experimental Results
This section will examine the implementation of the maximum torque per ampere
control algorithms presented in this chapter, and compare the experimental results obtained
with analytical and simulated values. Figure 6-12 shows the arrangement of hardware used
in these experiments. It should be noted that a different dynamometer arrangement was
used in this section than the one used earlier in Chapter 4 and Chapter 5. The SPM
136
6.4. EXPERIMENTAL RESULTS
generator and power electronic converter used were the same as those examined in Chapter
4:, whose parameters were listed in Table 4-1and Table 4-2 respectively.
The resistive voltage drop was used to model the IGBT losses. The simulated results
which will be shown in this section will include stator resistances. The open-circuit power
loss used to calculate simulated and experimental efficiency values will be obtained from
Figure 6-13 which is presented later in section 6.4.2.
The first test which was conducted was an open circuit test to find the zero offset of
the torque transducer and determine the open circuit power loss of the generator.
Torque
Transducer
Induction
Motor
+
Power
Electronic
Converter
SPM
Generator
Line
Current
T, 
42 V
PWM
Signals
dSPACE
System
A/D
Conversion
Control
Parameters
PC
Figure 6-12: Hardware block diagram for experimental setup using the dSPACE control system
The generator was then connected to the SMR and load and operated at a constant
speed. The phase advance modulation parameters were varied manually in order to
determine the maximum possible efficiency achievable for each value of torque. Next, a
series of open-loop tests were conducted to examine how closely the generator torque
followed the commanded torque. Lastly, closed-loop tests were completed in order to
determine how much of an improvement in torque error was achieved when compared to
the open-loop case.
137
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
6.4.1 Control Algorithm Implementation
A dSPACE control system [51] was used to implement the control algorithm for the
results given in this chapter. The advantages of using a dSPACE system are as follows:

Reduction of required hardware construction. The dSPACE system possesses
analog to digital inputs and PWM outputs, which could be used to read the
analog sensors and produce PWM signals accordingly.

Programming for the dSPACE system was done in Simulink instead of C. This
allowed the use of many existing function blocks in Simulink, for example Fast
Fourier Transform and relay blocks (which performed the task of the comparator
with hysteresis described in the previous chapter).

Graphical user interface (GUI) design using the dSPACE Control Desk program.
This allowed a convenient method of displaying and adjusting the control
parameters of the system via a PC. This was in contrast to the dsPIC30F2010
system, which required LCD display and push buttons to display and modify
parameters.
The main disadvantage of using a dSPACE system was that such a system was only
suitable for laboratory testing, and hence not suitable for a small-scale wind turbine
system. This was largely due to the system’s size and the requirement for a control PC.
6.4.2 Preliminary Results
The dynamometer arrangement used in this chapter is different to the one described
in Chapter 4 and Chapter 5. The key differences were that an induction machine was used
instead of a DC motor, and no gearbox was present (see Figure 6-12).
The first test was to measure the DC offset of the torque transducer and the opencircuit loss of the generator. The torque obtained as the generator was rotated clockwise
(positive speeds) and counter clockwise (negative speeds) under open-circuit conditions is
shown on the left hand side of Figure 6-13. The torque offset was found using the same
techniques as shown in section 4.1.1and was -0.158 Nm, which is used to correct the
measured values. The open-circuit power loss as a function of generator speed for the
clockwise case is shown on the right hand side of Figure 6-13, based on torque readings
which had been corrected for the offset. A quadratic function was
138
0.6
35
0.4
30
0.2
25
0
20
P (W)
T (Nm)
6.4. EXPERIMENTAL RESULTS
-0.2
15
-0.4
10
-0.6
5
-0.8
-500
0
n (rpm)
500
CW
CCW
0
0
500
n (rpm)
Figure 6-13: Comparison of open-circuit loss torque (left) and power loss (right) as a function of
speed for the experimental setup shown in Figure 6-12. Power loss is plotted for both clockwise
and counter clockwise rotation (corrected for torque offset).
used to fit the experimental points. Based on this function, the open-circuit power loss at
rated generator speed (490 rpm) is 28.4 W.
The plots of phase current and system efficiency as a function of generator torque are
shown in Figure 6-14 for the rated speed case (490 rpm). The upper plot of Figure 6-14
shows a comparison between the generator current as a function of torque for conventional
SMR, PA and inverter modulation. Experimental results are shown for the SMR and PA
cases. The curves in this image closely resemble the ideal simulated results found Figure
6-9, which showed that while PA modulation was capable of producing higher values of
torque than SMR modulation, it cannot match the performance of an inverter.
It was also observed that there is a linear relationship between current and torque at
low torques for all three modulation techniques. This is caused by the value of Id being
small relative to Iq in this range. As the generator torque is increased, SMR and phase
advance modulation require higher values of current than the inverter for a given value of
torque. This indicates that field weakening control is being utilized for the PA case, where
larger values of Id are introduced to limit VOV to its rated value.
139
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
12
PA
8
I (A)
SMR
Inv
4
0
0
6
12
18
1
Inv
0.8

0.6
0.4
SMR
PA
0.2
0
0
6
12
18
T (Nm)
Figure 6-14: Comparison of analytical (solid), simulated (dashed) and experimental (symbols)
generator phase current and system efficiency as a function of torque for conventional SMR, phase
advance and inverter modulation at a generator speed of 490 rpm. The analytical and simulated
results include generator copper and open-circuit losses.
The lower graph in Figure 6-14 shows a comparison of the system efficiency as a
function of generator torque for SMR, PA and inverter modulation. The simulation results
predicted a similar efficiency for inverter and PA modulation with a lower efficiency for
the SMR. These simulation results include the effects of generator copper losses, the opencircuit loss shown in Figure 6-13 and the resistive model for power converter voltage drops
given in Chapter 4. The difference between PA and SMR modulation was confirmed
experimentally. The maximum experimental efficiency for PA modulation was 78% at a
torque of 7.3 Nm while the maximum efficiency for the SMR was 71% at 5.6 Nm. The
analytical efficiency map provided in Figure 4-9 showed that the maximum efficiency this
generator could obtain under inverter modulation was 88%. It was expected that the
experimental efficiency values would be lower than their analytical counterparts due to
some of the unmodeled losses in the system, such as stray resistances.
140
6.4. EXPERIMENTAL RESULTS
6.4.3 Results of Open-Loop Control Scheme
Figure 6-15 shows an example of the results obtained when the equations given in
Section 6.1 were used to calculate the SMR control parameters used to drive the SPM
generator at a required torque for speeds of 245 (0.5 pu) and 490 (1 pu) rpm corresponding
to 0.5 pu and 1 pu speeds.
Observation of the control parameters VOV and  showed that there was a seemingly
linear relationship between  and T*, while VOV was subject to much smaller variation. As
expected, the required values of  and VOV increased as a function of T*. VOV was limited
by the DC link voltage (42 V). A close correspondence was observed between the
simulated and experimental open-loop results at this range validating the correctness of the
look-up table implementation. The control parameters required to generate torque values of
5 and 10 Nm at generator speeds of 245 and 490 rpm are labelled on Figure 6-15 as points
A-D.
100
B
80
245 rpm
A

o
60
40
n = 490 rpm
C
20
0
0
2
4
6
45
(V)
OV
8
10
12
n = 490 rpm
40
V
D
D
C
35
30
25
20
A
0
2
4
245 rpm
B
6
T* (Nm)
8
10
12
Figure 6-15: Comparison of control parameters  and VOV computed by the open-loop controller
as a function of command torque T* at speeds of 245 and 490 rpm. Simulated results (dashed
lines) and experimental measurements (symbols).
141
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
The phase leg voltages and phase current waveforms observed at points A and B
corresponding to half of base speed are shown in Figure 6-16. The simulated phase leg
voltage displays the average value of the PWM waveform, which causes the difference
between the experimental and simulated voltage waveforms. The measured peak phase
current matches the simulated value well for the 10 Nm case but there is a significant
discrepancy at 5 Nm. The phase current waveforms for both the experimental and
simulated case clearly exhibit a shorter positive half-cycle than the negative half-cycle,
especially at the higher torque value.
Similar conditions are also observed for the waveforms obtained when the generator
speed was set to 490 rpm in Figure 6-17. The main difference was that the value of VOV
was set to VDC in this range which caused the phase leg voltage waveform to not utilize
PWM. This meant that the waveforms obtained for the phase leg voltage through
simulations and experiments had the same peak value. A significant discrepancy is again
noted between the experimental and simulated line current waveforms at a commanded
torque of 5 Nm (point C).
50
40
30
Exp
20
Sim
0
5
t (ms)
30
Sim
0
5
t (ms)
5
t (ms)
10
B
Sim
0
-10
10
0
0
10
I (A)
VLeg (V)
Exp
20
Exp
20
B
40
0
-20
10
50
Sim
-10
10
0
A
10
I (A)
VLeg (V)
20
A
10
-20
Exp
0
5
t (ms)
10
Figure 6-16: n = 245 rpm experimental and simulated phase leg voltage and line current waveforms
obtained when using phase advance modulation with a torque command 5 Nm (A) and 10 Nm (B)
142
6.4. EXPERIMENTAL RESULTS
50
20
C
C
10
30
20
I (A)
VLeg (V)
40
Exp
Sim
0
10
-10
0
-20
Exp
Sim
0
2
t (ms)
4
0
2
t (ms)
4
50
D
D
20
Exp
Sim
30
I (A)
VLeg (V)
40
20
Exp
Sim
10
0
0
-20
0
2
t (ms)
4
0
2
t (ms)
4
Figure 6-17: n = 490 rpm experimental and simulated phase leg voltage and line current waveforms
obtained when using phase advance modulation with a torque command of 5 Nm (C) and 10 Nm
(D)
The results of actual torque T shown as squares as a function of torque command T*
obtained using the open loop control system are plotted in Figure 6-18 and Figure 6-19 at
generator speeds of 245 rpm and 490 rpm respectively. At 245 rpm, the maximum
deviation between commanded (analytical) and actual (experimental) open-loop torque is
20%, and is obtained at a T* value of 9 Nm. At 490 rpm, the maximum error is 51% and
occurs when T* = 6 Nm. The differences between the analytical values of torque and
current and the simulated and experimental results under open-loop conditions were caused
by the assumption of sinusoidal current waveforms used in the analytical model. Figure
6-16 and Figure 6-17 clearly show that the simulated and experimental current waveforms
are asymmetrical which cause large errors in the generated value of fundamental phase
voltage, and hence phase current magnitude and generator torque errors. As stated
previously, closed-loop control strategy based on current magnitude feedback was
implemented to reduce these errors.
143
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
15
T (Nm)
OL
10
CL (exp)
OL (sim)
5
Analytical
CL (sim)
0
0
2
4
6
8
10
12
15
OL
IL (A)
10
CL (exp)
OL (sim)
5
CL (sim)
Analytical
0
0
2
4
6
T* (Nm)
8
10
12
Figure 6-18: Comparison of analytical (solid), simulated (dashed) and experimental (points)
generator torque as a function of command torque using open-loop and closed-loop control at 245
rpm
15
T (Nm)
OL
10
CL
OL (sim)
CL (sim)
5
Analytical
0
0
2
4
6
8
10
12
15
OL
10
IL (A)
CL
OL (sim)
CL (sim)
5
Analytical
0
0
2
4
6
T* (Nm)
8
10
12
Figure 6-19: Comparison of analytical (solid), simulated (dashed) and experimental (points)
generator torque as a function of command torque using open-loop and closed-loop control at 490
rpm
144
6.4. EXPERIMENTAL RESULTS
6.4.4 Closed-Loop Current Feedback Results
A method of implementing closed-loop torque control via current magnitude
feedback was introduced in Section 6.3.2.1. This method calculated the expected generator
current magnitude for a given torque command by utilizing the generator speed, and the
open loop zero-epsilon control parameters  and VOV. This current reference was then
compared to the measured value of generator current, and the error was used to adjust .
Figure 6-20 compares the commanded control parameter  obtained through closed-loop
control with its open-loop counterparts. It is apparent that there is little difference between
the closed-loop and open-loop  values at 245 rpm, which indicates that the open-loop
generator torque T should be close to the command torque T*. The discrepancy between
these parameters is larger for the 490 rpm case. This indicates that the closed-loop control
method should have a larger effect on the results for this case.
100
n = 245 rpm
Exp (CL)
Open Loop
60

o
80
40
20
0
Sim (CL)
0
2
4
100
6
8
12
n = 490 rpm
Exp (CL)
80
Sim (CL)
60
Open Loop

o
10
40
20
0
0
2
4
6
T (Nm)
8
10
12
Figure 6-20: Comparison of the values of the values of  obtained with open-loop and closed-loop
controllers at speeds of 245 and 490 rpm. Points of interest at 5 Nm (A) and 10 Nm (B) are
highlighted
145
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
Analytical, simulated and experimental torque and line current obtained as a function
of commanded torque obtained using the closed-loop controller were shown earlier in
Figure 6-18 for a generator speed of 245 rpm. As stated earlier, there is a close
correspondence between the open-loop and closed-loop model. Observation of these
results shows that the closed-loop current controller significantly reduces the difference
between T* and T. The maximum error for the closed-loop case is 5%, which occurs at a
commanded torque of 7 Nm. This is significantly lower than the maximum open-loop error
of 20% which occurred when T* = 9 Nm.
Figure 6-19 also showed the closed-loop current control results at 490 rpm. The
difference between the open-loop torque and the commanded value is greater at this speed
than at 245 rpm. Closed-loop control produces a maximum discrepancy of 21% which
occurs when T* = 4 Nm, which is lower than the deviation of 51% when T* = 6 Nm
obtained under open-loop control. Examination of the line current results under open-loop
control shows that the difference between these values and the desired current increases as
a function of T* up to a point of approximately 6 Nm, after which the difference reduces.
A comparison of the torque error obtained using open-loop and closed-loop control
methods at generator speeds of 245 and 490 rpm are shown in Table 6-1. The results have
shown that the closed-loop controller proposed in this paper is capable of providing a close
match between the commanded and resultant values of generator torque. A comparison of
the efficiencies obtained using this closed-loop controller with the maximum efficiency
obtained by varying the generator’s control parameters manually to find the maximum
efficiency point was performed in order to determine whether the control methods shown
previously actually operate under maximum torque per ampere conditions. This
comparison is shown in Figure 6-21. It is apparent that there are minimal differences
between the efficiency values obtained at both speeds.
Table 6-1: Maximum torque error under open-loop and closed-loop control
Maximum Torque Error
245 rpm (0.5 pu)
490 rpm (1 pu)
Open-loop
20%
51%
Closed-loop
5%
21%
146
6.5. CONCLUSION
100
 (%)
80
Manual
60
40
CL
20
0
0
2
n = 245 rpm
4
6
8
10
12
10
12
100
 (%)
80
60
Manual
40
CL
20
0
n = 490 rpm
0
2
4
6
T (Nm)
8
Figure 6-21: Comparison of system efficiency as a function of generator torque obtained by
varying the control parameters manually to find the maximum efficiency point (circles) and using
the closed-loop controller (squares)
6.5 Conclusion
This chapter examined the analysis and implementation of phase advance modulation
of a switched-mode rectifier (SMR) as a low-cost controller for the surface permanent
magnet (SPM) generators used in small wind turbines. To avoid the need for a rotor
position sensor, it used voltage control rather than the more conventional current control.
It is necessary for the controller to generate a commanded value of torque whilst
minimizing copper losses. The key results obtained are as follows:
 The required SMR phase advance modulation control parameters VOV and  to produce a
desired value of torque from a SPM generator under maximum torque per ampere
conditions were determined analytically using the required operating trajectory in the
voltage magnitude/power-factor angle plane.
147
CHAPTER 6: MAXIMUM TORQUE PER AMPERE CONTROL OF PHASE ADVANCE MODULATION
 The allowable operating loci in the d-q current plane for phase advance control was
investigated and it was shown that the VOV = 1 pu limit is a tighter constraint than the
terminal voltage V = 1 pu.
 The analytical methods for determining the optimal control parameters was implemented
experimentally in an open-loop fashion and showed a significant difference between the
actual versus commanded torque with a maximum error of about 50% at rated speed.
 Closed-loop control using the generator line current magnitude was shown to give
improved performance with a maximum error of about 20% at rated speed.
 The closed-loop current feedback scheme was found to operate close to the maximum
possible efficiency trajectory.
148
Chapter 7: Conclusion
7.1 Summary
The limited availability and environmental impact of fossil fuels has caused
renewable energy sources such as wind energy to become highly sought after. Small-scale
wind turbines are often used for power generation for household, maritime and remote area
applications, and are rated in the order of several kilowatts. Such wind turbines often
operate under stand-alone configurations with surface permanent magnet (SPM)
generators.
Small-scale wind turbines with SPM generators commonly operate at variable
speeds, which results in the production of variable frequency output power. Some form of
AC/DC power electronic converter is required to convert this AC power into a DC value.
Commonly used power electronic converters are the rectifier, single-switch and semibridge switched-mode rectifier (SMR), and the inverter. The rectifier has the lowest cost of
these topologies and requires no control, but is unable to produce output power at low
generator speeds.
The two SMR topologies are capable of producing output power at low speeds, but
require generator speed information. The cost of the SMR topologies is also greater than
149
CHAPTER 7: CONCLUSION
the rectifier due to the requirement of controllable power electronic switches. The inverter
topology has a higher cost than the SMR, and requires generator rotor position
information. This topology is however capable of producing more power than the SMR
variants at low generator speeds. The inverter’s high output power capability is due to its
ability to generate a leading phase shift on the generator phase current waveform.
A semi-bridge SMR is similar to a three-phase inverter except it does not possess
controllable switches in the upper half of each phase leg. This means that the voltage in
each phase leg can only be controlled when the corresponding phase current is positive. In
conventional SMR control a constant duty cycle is applied to each switch. This technique
produces an average phase leg voltage which is constant over the positive phase current
half-cycle. As a result of these restrictions, the SMR operates with a unity power factor.
In phase advance modulation, the duty cycle of the switches (and thus the resultant
phase leg voltage) is varied (usually in stepwise fashion) over the positive current halfcycle. This produces a phase shift between the phase voltage and current and hence causes
a leading power-factor to be obtained. A leading power factor is necessary to maximise the
power capability of a given SPM generator operating with a limited voltage and current
rating.
Previous studies had obtained analytical models for the fundamental components of
the phase voltage and current waveforms of a SPM generator operating with a semi-bridge
SMR controlled under phase advance modulation. This thesis introduced a simplified
method of phase advance control and used the equivalent circuit model of a SPM generator
to derive the control parameters required for command of the generators output power and
torque. An important assumption made in the analysis is that the generator has high
inductance, that is its characteristic (high-speed short-circuit) current is equal to its rated
current. For convenience, speeds were normalised with a base speed equal to the speed at
which the back-emf equals the rated generator voltage.
In the first part of the work the optimal SMR phase advance modulation control
parameters (VOV, ) for generating the maximum output power at a given speed were
determined by selecting those parameters which would produce the optimal generator
voltage (V) and power factor angle () comparable to those required under inverter
modulation. These calculated parameters were verified by simulations using a simplified
(neglecting PWM effects) model, and experimental results with a high-inductance SPM
150
7.2. KEY RESULTS AND ORIGINAL CONTRIBUTIONS
generator and a microcontroller based open-loop control system. The experimental results
showed an output power increase of 60% at generator rated speed when compared to
conventional SMR modulation.
In the second part of the work, the phase advance modulation parameters required to
generate a commanded value of torque at a given speed while minimizing copper losses
were determined by implementing maximum torque per ampere control. This process was
achieved by selecting the values of V and  which would give rise to the minimum value of
the SPM generator d-axis current, Id. An open-loop controller and a closed-loop controller
using generator current feedback were implemented using a dSPACE system. The closedloop current controller improved the torque error observed under open loop control by up
to 30% at rated generator speed without compromising the system efficiency.
7.2 Key Results and Original Contributions
The major results demonstrated in this thesis are as follows:
1.
Analysis of the performance of SPM generators operating with AC/DC power
electronic converters such as the rectifier, SMR and inverter showed that while the
SMR with conventional modulation offered greater values of output power at low
speeds when compared to a rectifier, it only produced half the output power capability
of an inverter at speeds below 0.71 pu. The increased performance of the inverter was
due to its ability to produce a leading phase shift (power-factor) on the SPM
generators phase current with respect to its phase voltage at low speeds. The inverter
could achieve this shift due to its controllable upper phase-leg.
2.
Phase advance modulation of a semi-bridge SMR was applied to a SPM generator,
rather than the Lundell alternator and interior permanent magnet (IPM) generators
which were used in previous studies. Phase advance modulation generated increased
output power capability when compared to conventional SMR modulation. The
variation of the generator phase leg voltage during the positive half cycle of the phase
current resulted in a phase shift being applied to the fundamental value of V, thereby
emulating the leading power-factor operation of an inverter.
151
CHAPTER 7: CONCLUSION
3.
Time stepping simulation models created using PSIM were used to verify the
analytical findings. It was found that the analytical conversion ratios used to convert
between AC and DC quantities were not constant for all values of voltage and current.
This phenomenon caused differences between simulated and analytical results. A
simplified simulation model was introduced, which used phase-leg averaging to
remove the need to model PWM signals, thereby reducing simulation time.
Comparisons between the results obtained for simplified and complete simulation
models were made, and showed minimal differences between the two techniques.
4.
A modified version of phase advance modulation known as zero-epsilon modulation
was introduced, which used a reduced number of control parameters. This reduction
made it simpler to determine the control parameters required for maximum power
transfer by choosing these values to generate V and  which would produce maximum
output power. It was shown analytically that with an ideal SPM generator, a semibridge SMR operating with this modulation technique was able to produce the same
level of output power as an inverter at generator speeds below 0.5 pu. Simulation
results showed that the phase current waveforms produced using this technique were
asymmetrical, with a shorter positive half cycle than its negative counterpart. This
discrepancy gave rise to smaller simulated values of V than predicted, thereby creating
differences between the simulated and analytical results. Experimental results
comparing conventional SMR modulation and the new phase advance modulation
technique showed an increase in output power of 60% at rated speed, while
maintaining a near identical value of efficiency.
5.
Maximum torque per ampere control of a SPM generator was demonstrated for phase
advance modulation. The required control parameters were calculated by determining
the required values of V and  to minimize Id at a given generator speed based on the
equivalent circuit model of the SPM generator. An open loop control system
implementing the proposed algorithm analysis was completed using a dSPACE
controller. Errors between the commanded and actual values of torque using this
method were up to 50%. A closed-loop control algorithm relying on generator line
152
7.3. SUGGESTIONS FOR FURTHER RESEARCH
current feedback was then implemented which reduced the maximum error to 20%,
while keeping generator efficiency close to its maximum value.
6.
The use of the V- plane of a SPM generator to define the operating regions utilized
by different AC/DC power electronic converters, and the values resulting in maximum
output power. The use of this plane allowed for simple analysis to calculate the phase
advance modulation parameters resulting in maximum output power.
7.3 Suggestions for Further Research
Further research to improve the ability of the algorithm to follow a torque command
can be conducted by utilizing the width of a SPM generator’s phase current positive half
cycle as a feedback parameter in a closed-loop control system. It has been shown that this
parameter has a substantial effect on the magnitude of V in a semi-bridge SMR. Note that
analysis has already been given in this thesis about how this parameter could be used to
calculate adjusted values of the phase advance modulation control parameters. This control
strategy was not implemented since simulations showed that the negative zero-crossing of
the phase current waveform was not defined clearly.
The performance of a semi-bridge SMR operating under phase advance modulation
control in a grid-connected application can also be examined. This was not examined as
the scope of this thesis focussed on stand-alone applications.
153
CHAPTER 7: CONCLUSION
154
Appendix A: Microcontroller Code
The microcontroller code used the implement phase advance modulation on a
dSPIC 30F2010 based control system was originally designed by Chong-Zhi Liaw.
Changes were required to this code however in order to ensure it could work with the
hardware arrangement shown in Figure 5-16.
CNpins.c
This file contained the interrupt handlers for the change notification pins used to detect the
zero crossings of the phase current waveforms. These interrupt handlers were used to set
the duty cycles of the bottom half of the semi-bridge SMR to the required values for a
givne interval.
#include "h\p30f2010.h"
#include "h\common.h"
// Define Phase Current Sign inputs
#define Ia PORTBbits.RB1 // CN3
#define Ib PORTBbits.RB2 // CN4
#define Ic PORTBbits.RB3 // CN5
void CN_Init(void);
void _ISR _CNInterrupt( void ); // CN handler
volatile unsigned int Ia_prev;
volatile unsigned int Ib_prev;
volatile unsigned int Ic_prev;
155
APPENDICES
volatile unsigned long period_alpha;
volatile unsigned long period_epsilon;
void CN_Init(void) {
// Clear previous values of phase current
Ia_prev = 0;
Ib_prev = 0;
Ic_prev = 0;
TRISBbits.TRISB1
ADPCFGbits.PCFG1
TRISBbits.TRISB2
ADPCFGbits.PCFG2
TRISBbits.TRISB3
ADPCFGbits.PCFG3
=
=
=
=
=
=
1;
1;
1;
1;
1;
1;
// Set Ia as digital input
// Set Ib as digital input
// Set Ic as digital input
// SETUP TIMERS
T1CON = 0x0010;
TMR1 = 0;
PR1 = 0xFFFF;
IFS0bits.T1IF = 0;
IEC0bits.T1IE =
1;
IPC0bits.T1IP = 6;
//Setup Timer1 for 1:8 prescale
//Clear timer counter
//Set period
//Clear timer interrupt flag
//Enable timer interrupt
//Set timer priority to 6
T2CON = 0x0010;
TMR2 = 0;
PR2 = 0xFFFF;
IFS0bits.T2IF = 0;
IEC0bits.T2IE =
1;
IPC1bits.T2IP = 6;
//Setup Timer2 for 1:8 prescale
//Clear timer counter
//Set period
//Clear timer interrupt flag
//Enable timer interrupt
//Set timer priority to 6
//TRISFbits.TRISF2 = 0; //set RF2 as output
T3CON = 0x0010;
TMR3 = 0;
PR3 = 0xFFFF;
IFS0bits.T3IF = 0;
IEC0bits.T3IE =
1;
IPC1bits.T3IP = 6;
//Setup Timer3 for 1:8 prescale
//Clear timer counter
//Set period
//Clear timer interrupt flag
//Enable timer interrupt
//Set timer priority to 6
// SETUP CN PINS TO DETECT CURRENT ZERO-CROSSINGS
CNEN1 = 0x038;
CNPU1 = 0;
IFS0bits.CNIF = 0;
IPC3bits.CNIP = 7;
IEC0bits.CNIE = 1;
/*Enable CN interrupt on CN3,4,5 */
// Disable pull-ups on CN pins
/*Reset CN interrupt flag */
// Set CN interrupt priority to 7
// Enable CN interrupt
}
/*-------------------------------------------------------------------Function Name: CNInterrupt
Description:
CN pin ISR - handles detection of phase current
zero-crossings
156
APPENDIX A: MICROCONTROLLER CODE
Inputs:
None
Returns:
None
----------------------------------------------------------------------*/
void _ISR _CNInterrupt( void ) {
unsigned int dummy;
IFS0bits.CNIF = 0;
/*Reset CN interrupt flag
*/
dummy = PORTB;
// Read PORTB to clear CN mismatch flag
if (Ia != Ia_prev) {
// Zero-crossing detected on phase A
Ia_prev = Ia;
if (Ia == 1) {
// positive zero-crossing
if (!a_suppress) {
//
led1 = 1;
if (param_alpha > 0) {
// ENTER ALPHA INTERVAL
a_interval = 1;
PR1 = period_alpha;
// Set timer to alpha period
PDC1 = duty_alpha;
TMR1 = 0;
// Reset timer value
T1CONbits.TON = 1;
// Activate timer
} else if (param_epsilon > 0) {
// ENTER EPSILON INTERVAL
a_interval = 2;
PR1 = period_epsilon;
// Set timer to epsilon period
PDC1 = duty_epsilon;
TMR1 = 0;
// Reset timer value
T1CONbits.TON = 1;
// Activate timer
} else {
// ENTER PHI INTERVAL
a_interval = 3;
PDC1 = duty_phi;
}
}
} else {
// negative zero-crossing
// ENTER INACTIVE INTERVAL
a_interval = 0;
PDC1 = duty_epsilon;
T1CONbits.TON = 0;
// Deactivate timer (important)
a_suppress = 1;
// Activate zero-crossing suppression
PR1 = period_suppress;
157
APPENDICES
// Set timer to suppress period
T1CONbits.TON = 1;
// Activate Timer
}
}
if (Ib != Ib_prev) {
// Zero-crossing detected on phase B
Ib_prev = Ib;
if (Ib == 1) {
// positive zero-crossing
if (!b_suppress) {
if (param_alpha > 0) {
// ENTER ALPHA INTERVAL
b_interval = 1;
PR2 = period_alpha;
// Set timer to alpha period
PDC2 = duty_alpha;
TMR2 = 0;
// Reset timer value
T2CONbits.TON = 1;
// Activate timer
} else if (param_epsilon > 0) {
// ENTER EPSILON INTERVAL
b_interval = 2;
PR2 = period_epsilon;
// Set timer to epsilon period
PDC2 = duty_epsilon;
TMR2 = 0;
// Reset timer value
T2CONbits.TON = 1;
// Activate timer
} else {
// ENTER PHI INTERVAL
b_interval = 3;
PDC2 = duty_phi;
}
}
} else {
// negative zero-crossing
// ENTER INACTIVE INTERVAL
b_interval = 0;
PDC2 = duty_epsilon;
T2CONbits.TON = 0;
// Deactivate timer
b_suppress = 1;
// Activate zero-crossing suppression
PR2 = period_suppress;
// Set timer to suppress period
T2CONbits.TON = 1;
// Activate Timer
}
}
if (Ic != Ic_prev) {
// Zero-crossing detected on phase C
158
APPENDIX A: MICROCONTROLLER CODE
Ic_prev = Ic;
if (Ic == 1) {
// positive zero-crossing
if (!c_suppress) {
if (param_alpha > 0) {
// ENTER ALPHA INTERVAL
c_interval = 1;
PR3 = period_alpha;
// Set timer to alpha period
PDC3 = duty_alpha;
TMR3 = 0;
// Reset timer value
T3CONbits.TON = 1;
// Activate timer
} else if (param_epsilon > 0) {
// ENTER EPSILON INTERVAL
c_interval = 2;
PR3 = period_epsilon;
// Set timer to epsilon period
PDC3 = duty_epsilon;
TMR3 = 0;
// Reset timer value
T3CONbits.TON = 1;
// Activate timer
} else {
// ENTER PHI INTERVAL
c_interval = 3;
PDC3 = duty_phi;
}
}
} else {
// negative zero-crossing
// ENTER INACTIVE INTERVAL
c_interval = 0;
PDC3 = duty_epsilon;
T3CONbits.TON = 0;
// Deactivate timer
c_suppress = 1;
// Activate zero-crossing suppression
PR3 = period_suppress;
// Set timer to suppress period
T3CONbits.TON = 1;
// Activate Timer
}
}
}
void CN_Enable(void) {
IEC0bits.CNIE = 1;
}
void CN_Disable(void) {
IEC0bits.CNIE = 0;
}
// Enable CN interrupt
// Disable CN interrupt
159
Appendix B: dSPACE Simulink Programs
The experimental results shown in Chapter 6 were obtained using a dSPACE based
controller. This system required Simulink programs to control its operation. These files are
presented in this section.
160
APPENDIX B: DSPACE SIMULINK PROGRAMS
Open Loop Controller: This file shows the design for an open loop control system,
where the required values of  and VOV are calculated via lookup tables for a commanded
value of torque and a measured speed.
161
APPENDICES
PA_Control: This block generates the required duty cycle for an input current
waveform and control parameter set at a given instant of time.
162
APPENDIX B: DSPACE SIMULINK PROGRAMS
Closed Loop Current Feedback System: Similar to the open loop system, except
that a reference current calculator block is used to calculate the magnitude of the reference
current, which is compared with the magnitude of the measured current obtained using a
FFT operation.
163
APPENDICES
Reference Current Calculator: This program calculates the reference current
required for the closed loop controller by implementing (6-13) and (6-14).
164
APPENDIX B: DSPACE SIMULINK PROGRAMS
Appendix C: Code Used to Generate
Simulation .DLL File
// Variables:
//
t: Time, passed from PSIM by value
//
delt: Time step, passed from PSIM by value
//
in: input array, passed from PSIM by reference
//
out: output array, sent back to PSIM (Note: the values of
out[*] can
//
be modified in PSIM)
// The maximum length of the input and output array "in" and "out"
is 20.
//
Warning:
Global
variables
(t,delt,in,out)
//
are not allowed!!!
above
the
function
simuser
#include <math.h>
__declspec(dllexport) void simuser (t, delt, in, out)
// Note that all the variables must be defined as "double"
double t, delt;
double *in, *out;
//in[0] = Required value of duty cycle during conduction period
//in[1] = Required value of theta (in degrees)
//in[2] = frequency
//in[3], in[4], in[5] = phase A,B and C current
//out[0], out[1], out[2] = The three duty cycles required
{
double dCond, theta, f,period;
165
APPENDICES
//flags for rising edge
static int actionFlag1,actionFlag2,actionFlag3=0;
static
double
D1,D2,D3,
condStartTime1,condStartTime2,condStartTime3,endTime1,endTime2,endTime3,I
line1,Iline2,Iline3,tDelay;
dCond = in[0];
theta = in[1];
f = in[2];
Iline1 = in[3];
Iline2 = in[4];
Iline3 = in[5];
//We should note - for the bottom half, Vleg = (1-D)Vout
//For the top half, Vleg = D*Vout
//D1,D2,D3 correspond to the BOTTOM HALF transistors
//These signals are logically inverted in PSIM
//period of positive half-cycle current waveform
period = 1/(2*f);
//The time corresponding to the delay of theta
tDelay = theta/180*period;
//I need to reset the timers at every rising edge
if (Iline1 > 0.01 && actionFlag1 == 0) //rising edge
{
//we are now in the positive half cycle
actionFlag1 = 1;
//The time at which we should begin conduction
condStartTime1 = t+tDelay;
//The time at which we stop conducting
endTime1 = condStartTime1+period;
}
else if(Iline1 < -0.01 && actionFlag1 == 1)//falling edge
{
actionFlag1 = 0;
}
if (Iline2 > 0.01 && actionFlag2 == 0) //rising edge
{
//we are now in the positive half cycle
actionFlag2 = 1;
//The time at which we should begin conduction
condStartTime2 = t+tDelay;
//The time at which we stop conducting
endTime2 = condStartTime2+period;
}
else if(Iline2 < -0.01 && actionFlag2 == 1)//falling edge
{
actionFlag2 = 0;
}
if (Iline3 > 0.01 && actionFlag3 == 0) //rising edge
{
//we are now in the positive half cycle
actionFlag3 = 1;
//The time at which we should begin conduction
condStartTime3 = t+tDelay;
//The time at which we stop conducting
endTime3 = condStartTime3+period;
}
166
APPENDIX B: DSPACE SIMULINK PROGRAMS
else if(Iline3 < -0.01 && actionFlag3 == 1)//falling edge
{
actionFlag3 = 0;
}
if(actionFlag1 == 1 && Iline1 > 0) //positive half cycle for phase
1
{
if(t < condStartTime1)
{
//set the duty cycle to unity before conduction
D1 = 1;
}
else //we are in the conduction period
{
D1 = 1-dCond;
}
}
else //negative half cycle for phase 1
{
if(t < endTime1) //we are still in conduction period of an
inverter
{
//D4 = top half, D1 = bottom half
D1 = 1-dCond;
}
else //make the phase leg voltage zero
{
D1 = 1;
}
}
if(actionFlag2 == 1 && Iline2 > 0) //positive half cycle for phase
2
{
if(t < condStartTime2)
{
//set the duty cycle to unity before conduction
D2 = 1;
}
else //we are in the conduction period
{
D2 = 1-dCond;
}
}
else //negative half cycle for phase 2
{
if(t < endTime2) //we are still in conduction period of an
inverter
{
D2 = 1-dCond;
}
else //make the phase leg voltage zero
{
D2 = 1;
167
APPENDICES
}
}
if(actionFlag3 == 1 &&
Iline3 > 0) //positive half cycle for phase
3
{
if(t < condStartTime3)
{
//set the duty cycle to unity before conduction
D3 = 1;
}
else //we are in the conduction period
{
D3 = 1-dCond;
}
}
else //negative half cycle for phase 3
{
if(t < endTime3) //we are still in conduction period of an
inverter
{
D3 = 1-dCond;
}
else //make the phase leg voltage zero
{
D3 = 1;
}
}
out[0] = D1;
out[1] = D2;
out[2] = D3;
}
168
Appendix D: Relevant Publications
This appendix contains the abstracts of two conference papers which summarise the
contents of chapters 5 and 6 of this thesis.
169
APPENDICES
C.1 Output Power Capability of SMR with Phase Advance Paper
This paper entitled “Output Power Capability of Surface PM Generators with
Switched-Mode Rectifiers” was presented at the IEEE International Conference on
Sustainable Energy Technologies in Sri Lanka, December 2010.
A
Pathmanathan, M., Soong, W.L. & Ertugrul, N. (2010) `Output power capability of surface
PM generators with switched-mode rectifiers' in Sustainable Energy Technologies
(ICSET), 2010 IEEE International Conference, Kandy, Sri Lanka, pp.1-6.
NOTE:
This publication is included on page 170 in the print copy
of the thesis held in the University of Adelaide Library.
It is also available online to authorised users at:
http://dx.doi.org/10.1109/ICSET.2010.5684437
170
APPENDIX C: RELEVANT PUBLICATIONS
C.2 Maximum Torque Per Ampere Control Paper
This paper entitled “Maximum Torque per Ampere Control of Phase Advance
Modulation of a SPM Wind Generator” was presented at the IEEE Energy Conversion
Congress and Exposition in Phoenix, Arizona, September 2011.
A
Pathmanathan, M., Soong, W.L. & Ertugrul, N. (2011) `Maximum Torque per Ampere
Control of Phase Advance Modulation of a SPM Wind Generator' in Energy Conversion
Congress and Exposition (ECCE), 2011 IEEE, Phoenix, Arizona, pp. 1676-1683.
NOTE:
This publication is included on page 171 in the print copy
of the thesis held in the University of Adelaide Library.
It is also available online to authorised users at:
http://dx.doi.org/10.1109/ECCE.2011.6063984
171
References
[1] G. Alexander, “Overview: The Context of Renewable Energy Technologies” in
Renewable Energy Power for a Sustainable Future, 1st Edition, G. Boyle, Ed. Oxford:
Oxford University Press, 1996, pp. 1-40.
[2] C.V. Nayar, S.M. Islam, H. Dehbonei, K. Tan and H. Sharma, “Power Electronics for
Renewable Energy Sources” in Power Electronics Handbook: Devices, Circuits, and
Applications, 2nd Edition, H.M. Rashid, Ed. Burlington: Academic Press, 2007, pp. 673716.
[3] D. Taylor, “Wind Energy” in Renewable Energy Power for a Sustainable Future, 1st
Edition, G. Boyle, Ed. Oxford: Oxford University Press, 1996, pp. 267-314.
[4] J.M. Carasco, E. Galvan, and R. Portillo, “Wind Turbine Applications” in Power
Electronics Handbook: Devices, Circuits, and Applications, 2nd Edition, H.M. Rashid, Ed.
Burlington: Academic Press, 2007, pp. 737-768.
172
[5] F.D. Bianchi, H. De Battista, and R.J. Mantz. Wind Turbine Control Systems:
Principles, Modelling and Gain Scheduling Design. Advances in Industrial Control,
Springer, 2006.
[6] C. Tang. Analysis and Modelling of the Effects of Inertia and Parameter Errors on
Wind Turbine Output Power, Master’s Thesis, School of Electrical and Electronic
Engineering, Faculty of Engineering, Computer and Mathematical Sciences, The
University of Adelaide, Australia, 2009.
[7] E. Hau. Wind Turbines: Fundamentals, Technologies, Application and Economics.
New York: Springer, 2000.
[8] G.M. Masters. Renewable and Efficient Electric Power Systems. Hoboken, New Jersey,
John Wiley & Sons, 2004.
[9] S. Matthew. Wind Energy: Fundamentals, Resource Analysis and Economics. Verlag
Berlin Heidelberg: Springer, 2006.
[10] A. Grauers, “Efficiency of Three Wind Energy Generator Systems,” IEEE
Transactions on Energy Conversion, vol. 11, no. 3, 1996, pp. 650–657.
[11] S. Muller, M. Deike and R.W. De Doncker, “Doubly Fed Induction Generator
Systems for Wind Turbines”, IEEE Industry Applications Magazine, May/June 2002.
[12] L.H. Hansen, F. Blaabjerg, H.C. Christensen, U. Lindhard, and K. Eskildsen,
“Generators and Power Electronic for Wind Turbines,” Proceedings of the IEEE Industrial
Electronics Conference, vol. 3, 2001, pp. 2000–2005.
[13] L. Holdsworth, X.G. Wu, J.B. Ekanayake, and N. Jenkins, “Comparison of Fixed
Speed and Doubly-fed Induction Wind Turbines during Power System Disturbances”, IEE
Proc-Generation. Transmission and Distribution, Vol. 150, No. 3, May 2003, pp. 343-352.
173
[14] M.S Vicatos and J.A. Tegopolous, “Steady State Analysis of a Doubly-fed Induction
Generator Under Synchronous Operation”, IEEE Transactions on Energy Conversion, Vol.
4, No. 3, Sep. 1989, pp. 495-501.
[15] A.J. Thomas. A Doubly-Fed Permanent Magnet Generator for Wind Turbines.
Master’s Thesis, Department of Electrical Engineering and Computer Science,
Massachusetts Institute of Technology, Massachusetts, USA, June 2004.
[16] T. Ackermann. Wind Power in Power Systems. Chichester: John Wiley & Sons, 2005
[17] A.J. Mitcham and N. Grum, “An Integrated LP Shaft Generator for the More Electric
Aircraft”, IEE Colloquium on All Electric Aircraft, June 1998, pp. 8/1-8/9.
[18] E. Muljadi, S. Drouilhet, R. Holz and V. Gevorgian, “Analysis of Permanent Magnet
Generator for Wind Power Battery Charging”, IEEE Industry Applications Conference,
Oct. 1996, Vol. 1, pp. 541-548.
[19] N. Mohan, T.M. Undeland and W.P. Robbins. Power Electronics: Converters,
Applications and Design. John Wiley & Sons, Singapore, 1989.
[20]
D.M. Whaley, W.L. Soong and N. Ertugrul “Investigation of Switched-Mode
Rectifier for Control of Small-Scale Wind Turbines”, IEEE Industry Applications Society
Annual Meeting 2005, Vol. 4, pp 2849-2856.
[21] D.J. Perreault and V. Caliskan, “Automotive Power Generation and Control,” IEEE
Transactions on Power Electronics, vol. 19, no. 3, 2004, pp. 618–630.
[22] C.Z. Liaw, D.M. Whaley, W.L. Soong, and N. Ertugrul, “Implementation of
Inverterless Control of Interior PermanentMagnet Alternators”, IEEE Transactions on
Industry Applications, vol. 42, no. 2, Mar. - Apr., 2006, pp. 536 – 544.
174
[23] J. Rivas, D.J. Perreault, and T. Keim, “Performance Improvement of Alternators With
Switched-Mode Rectifiers,” IEEE Transactions on Energy Conversion, vol. 19, no. 3,
2004, pp. 561–568.
[24] C.Z. Liaw, W.L. Soong and N. Ertugrul “Low-Speed Output Power Improvement
of an Interior PM Automotive Alternator”, IEEE Industry Applications Society Annual
Meeting 2006, Vol. 1 pp 27-34.
[25] W.L. Soong and N. Ertugrul, “Inverterless High-Power Interior Permanent-Magnet
Automotive Alternator,” IEEE Transactions on Industry Applications, vol. 40, no. 4, JulAug 2004, pp. 1083–1091.
[26] G. Venkataramanan, B. Milkovska, V. Gerez, and H. Nehrir, “Variable Speed
Operation of Permanent Magnet Alternator Wind Turbine Using a Single Switch Power
Converter,” Transactions of the ASME, Journal of Solar Energy Engineering, vol. 118, no.
4, Nov. 1996, pp. 235–238.
[27]
D.M. Whaley, G. Ertasgin, W.L. Soong, N. Ertugrul, J. Darbyshire, H. Dehboeni,
C.V. Nayar, “Investigation of a Low-Cost Grid-Connected Inverter for Small-Scale Wind
Turbines Based on a Constant-Current Source PM Generator”, IEEE 32nd Annual
Conference on Industrial Electronics, Paris 2006 pp. 4297-4302.
[28]
A.M. De Broe’, S. Drouilhet, V. Gevorgian, “A Peak Power Point Tracker for
Small Wind Turbines in Battery Charging Applications”, IEEE Transactions on Energy
Conversion, Vol. 14, No. 4, December 1999, pp. 1630-1635, pp. 1220-1225.
[29] M.F. Rahman, D. Patterson, A. Cheok and R. Betz, “Motor Drives” in Power
Electronics Handbook: Devices, Circuits, and Applications, 2nd Edition, H.M. Rashid, Ed.
Burlington: Academic Press, 2007, pp. 858-933.
175
[30] R.F. Schiferl and T.A. Lipo, “Power Capability of Salient Pole Permanent Magnet
Synchronous Motors in Variable Speed Drive Applications”, IEEE Transactions on
Industry Applications, Vol. 26, January/February 1990, pp. 115-123.
[31] T. Sebastian and G.R. Slemon, “Operating Limits of Inverter-driven Permanent
Magnet Motor Drives”, IEEE Transactions on Industry Applications, Vol. 23, March/April
1987, pp. 327-333.
[32] S. Morimoto, Y. Takeda, T. Hirasa and K. Taniguchi, “Expansion of Operating Limits
for Permanent Magnet Motor by Current Vector Control Considering Inverter Capacity”,
IEEE Transactions on Industry Applications, Vol. 26, No. 5, September/October 1990,
pp. 866-871.
[33]
V. Caliskan, D.J. Perreault, T.M. Jahns, J.G. Kassakian, “Analysis of Three-Phase
Rectifiers, with Constant-Voltage Loads”, IEEE Transactions on Circuits and Systems – I:
Fundamental Theory and Applications, Vol. 50, No. 9, September 2003.
[34] D.M. Whaley, W.L. Soong, N. Ertugrul, “Extracting More Power from the Lundell
Car Alternator”, Australasian Universities Power Engineering Conference, Brisbane,
Australia, September 2004.
[35] T.M. Jahns and V. Caliskan, “Uncontrolled Generator Operation of Interior PM
Synchronous Machines Following High-Speed Inverter Shutdown,” IEEE Transactions on
Industry Applications, vol. 35, no. 6, Nov./Dec. 1999, pp. 1347–1357.
[36] W.L. Soong and T.J.E. Miller, “Theoretical Limitations to the Field-weakening
Performance of the Five Classes of Brushless Synchronous AC Motor Drive”, Conference
on Electrical Machines and Drives, Sep. 1993, pp. 127-132.
[37] T.M. Jahns, G.B. Kliman, and T.W. Neumann, “Interior Permanent-Magnet
Synchronous Motors for Adjustable Speed Drives, IEEE Transactions on Industry
Applications, Vol. IA-22, No. 4, July/August 1986, pp. 738-747.
176
[38] C.-Z. Liaw, W.L. Soong, B.A. Welchko, and N. Ertugrul, “Uncontrolled generation in
interior permanent-magnet Machines,” IEEE Transactions on Industry Applications, vol.
41, no. 4, Jul./Aug. 2005, pp. 945–954.
[39] R.D. Middlebrook and S. Cuk, “A General Unified Approach to Modelling SwitchingConverter Power Stages, IEEE Power Electronics Specialists Conference, June 1976, pp.
18-34.
[40] V. Vorperian, “Simplified Analysis of PWM Converters Using Model of PWM
Switch Part 1: Continuous Conduction Mode”, IEEE Transactions on Aerospace and
Electronic Systems, Vol. 26, No. 3, May 1990, pp. 490-496.
[41] E. van Dijk, H.J.N. Spruijt, D.M. O’Sullivan, and J.B. Klaasseens, IEEE Transactions
on Power Electronics, Vol. 10, No. 6, November 1995, pp. 659-665.
[42] D.M. Whaley. Low-Cost Small-Scale Wind Power Generation. PhD. Thesis, School of
Electrical and Electronic Engineering, Faculty of Engineering, Computer and
Mathematical Sciences, The University of Adelaide, Australia, February 2009.
[43] B.J. Chalmers, W. Wu and E. Spooner, “An Axial-Flux Permanent Magnet Generator
for a Gearless Wind Energy System”, IEEE Transactions on Energy Conversion, Vol. 14,
No. 2, June 1999, pp. 251-257.
[44] W.L. Soong. PM Machines: Parameter Measurement and Performance Prediction,
available at http://www.eleceng.adelaide.edu.au/research/power/pebn/ on 19th April 2012.
[45] L. Cha, Solar Electric Vehicle Propulsion System, Final Year Project Report, School
of Electrical and Electronic Engineering, Faculty of Engineering, Computer and
Mathematical Sciences, The University of Adelaide, Australia, 2003.
177
[46] C.H. Li, Solar Electric Vehicle Propulsion System, Final Year Project Report, School
of Electrical and Electronic Engineering, Faculty of Engineering, Computer and
Mathematical Sciences, The University of Adelaide, Australia, 2003.
[47] dsPIC 30F2010 datasheet, available at
http://ww1.microchip.com/downloads/en/devicedoc/70118e.pdf on 19th April, 2012.
[48] A.M. EL-Refaie and T.M. Jahns, “Optimal flux weakening in surface PM machines
using concentrated windings,” IEEE Transactions on Industry Applications, vol .41, no. 3,
May-Jun 2005, pp. 115-123.
[49] A.M. EL-Refaie, T.M. Jahns, P.J. McCleer and J.W. McKeever, “Experimental
verification of optimal flux weakening in surface PM machines using concentrated
windings,” IEEE Transactions on Industry Applications, vol. 42 Mar-Apr 2006, pp. 443453.
[50] A.M. EL-Refaie, Z.Q. Zhu, T.M. Jahns, D. Howe, “Winding Inductances of Fractional
Slot Surface-Mounted Permanent Magnet Brushless Machines,” Industry Applications
Society Annual Meeting, October 2008, pp. 1-8.
[51] dSPACE website, available at http://www.dspace.com/en/inc/home.cfm on 19th April
2012.
[52] S. Heier. Grid Integration of Wind Energy Conversion Systems. John Wiley & Sons,
2nd Edition, 2006
[53] J.W. Dixon, “Three-phase Controlled Rectifiers” in Power Electronics Handbook:
Devices, Circuits, and Applications, 2nd Edition, H.M. Rashid, Ed. Burlington: Academic
Press, 2007, pp. 201-243.
[54] B.K. Bose. Power Electronics and Motor Drives: Advances and Trends. Burlington:
Academic Press, 2006.
178
[55]
D. Krahenbuhl, C. Zwyssig, J.W. Kolar, “Half-Controlled Boost Rectifier for Low-
Power High-Speed Permanent Magnet Generators”, IEEE Transactions on Industrial
Electronics, Vol. 58, No. 11, November 2011, pp. 5066-5074.
[56]
J. Kikuchi, M.D. Manjrekar, T.A. Lipo, “Performance Improvement of Half
Controlled Three Phase PWM Boost Rectifier”, Power Electronics Specialists Conference
(PESC), Vol. 1, August 1999, pp. 319-324.
[57]
J. Kikuchi, M.D. Manjrekar, T.A. Lipo, “Complementary Half Controlled Three
Phase PWM Boost Rectifier for Multi-DC-Link Applications”, Applied Power Electronics
Conference and Exposition (APEC), Vol. 1, 2000, pp. 494-500.
179