Modelling, Analysis, and Control Aspects of a
Rotating Power Electronic Brushless Doubly-Fed
Induction Generator
NAVEED UR REHMAN MALIK
Doctoral Thesis in Electrical Machines and Drives
Stockholm, Sweden 2015
TRITA-EE 2015:63
ISSN 1653-5146
ISBN 978-91-7595-691-6
Laboratory of Electrical Energy Conversion (E2C),
KTH Royal Institute of Technology,
Teknikringen 33, 100 44 Stockholm,
SWEDEN
Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie doktorsexamen i måndagen den 19 Oktober 2015 klockan 10:00 i Sal F3, Kungliga Tekniska Högskolan,
Lindstedtsvägen 26, Stockholm.
© Naveed ur Rehman Malik, September 2015
Tryck: Universitetsservice US AB
iii
Abstract
This thesis deals with the modeling, analysis and control of a novel brushless generator for wind power application. The generator is named as rotating power electronic brushless doubly-fed induction machine/generator (RPEBDFIM/G).
A great advantage of the RPE-BDFIG is that the slip power recovery
is realized in a brushless manner. This is achieved by introducing an additional machine termed as exciter together with the rotating power electronic
converters, which are mounted on the shaft of a DFIG. It is shown that the
exciter recovers the slip power in a mechanical manner, and delivers it back
to the grid. As a result, slip rings and carbon brushes can be eliminated,
increasing the robustness of the system, and reducing the maintenance costs
and down-time of the turbine.
To begin with, the dynamic model of the RPE-BDFIG is developed and
analyzed. Using the dynamic model, the working principle of the generator
is understood and its operation explained. The analysis is carried out at
speeds, ±20% around the synchronous speed of the generator. Moreover, the
dynamics of the generator due to external load-torque disturbances are investigated. Additionally, the steady-state model is also derived and analyzed for
the machine, when operating in motor mode.
As a next step, the closed-loop control of the generator is considered in
detail. The power and speed control of the two machines of the generator and
the dc-link voltage control is designed using internal model control (IMC)
principles. It is found that it is possible to maintain the stability of the
generator against load-torque disturbances from the turbine and the exciter,
at the same time maintain a constant dc-link voltage of the rotor converter.
The closed-loop control is also implemented and the operation of the generator
with the control theory is confirmed through experiments.
In the third part of the thesis, the impact of grid faults on the behaviour
of the generator is investigated. The operation of the generator and its response is studied during symmetrical and unsymmetrical faults. An approach
to successful ride through of the symmetrical faults is presented, using passive
resistive network (PRN). Moreover, in order to limit the electrical and mechanical oscillations in the generator during unsymmetrical faults, the dual
vector control (DVC) is implemented. It is found that DVC to a certain extent can be used to safeguard the converter against large oscillations in rotor
currents.
Finally, for completeness of the thesis, a preliminary physical design of
the rotating power electronic converter has been done in a finite element
software called ANSYS. The thermal footprint and the cooling capability,
with estimates of the heatsink and fan sizes, are presented.
Besides, another variant of a rotating electronic induction machine which
is based on the Lindmark concept and operating in a single-fed mode is also
iv
investigated. It’s steady-state model is developed and verified through experiments.
Index Terms: Brushless doubly-fed induction generator, dual vector control, dynamic model, induction machine, internal model control, Lindmark concept, low-voltage ride-through, passive resistive network, rotating power electronic converter, rotating exciter, symmetrical faults,
synchronous machine, thermal model, unity power factor, unsymmetrical faults, vector control, wind turbines.
v
Sammanfattning
Denna avhandling handlar om modellering, analys och kontroll av en ny
typ av borstlös generator för vindkraft applikation. Generatorn benämns:
rotating power electronic brushless doubly-fed induction machine /generator
(RPE-BDFIM/G).
En stor fördel med RPE-BDFIG är att eftersläpningseffekten kan återvinnas utan släpringar och borstar. Detta uppnås genom att införa ytterligare
en maskin som kallas “exciter” tillsammans med den roterande kraftelektroniska omvandlaren, som monterades på DFIGs axeln. Det framgår att excitern
återvinner slipeffekten på mekaniskt väg, och levererar den tillbaka till nätet.
Som en följd, kan släpringar och kolborstar elimineras, vilket ökar systemets
robusthet och minskar underhållskostnaderna och turbinens stilleståndstid.
Till att börja med utvecklats och analyseras RPE-BDFIGs dynamiska
modellen. Genom den dynamiska modellen kan generatorns arbetsprincip
förstås och dess funktion förklaras. Analysen har utförts vid olika hastigheter
t.ex. vid ±20% av det synkrona varvtalet för generatorn. Dessutom undersöks
generatorns dynamik vid yttre störningar från lastens vridmoment. Vidare
härleds och analyseras maskinens stationära modell vid motordrift.
Som ett nästa steg, beaktas i detalj styrningen av generatorn i det slutna
systemet. Effekt och varvtalsreglering av de två maskinerna i systemet samt
spänningsreglering av DC mellanled har utvecklats med principer från “internal model control (IMC)”. Det framgår av resultatet att det är möjligt
att upprätthålla stabiliteten i generatorn mot lastmomentstörningarna från
turbinen och excitern, samtidigt som man håller en konstant DC mellanledsspänning på omvandlaren i rotorn. Styrningen av generatorn i det slutna
systemet har också implementerats och dess regleregenskaper bekräftas genom
experiment.
I den tredje delen av avhandlingen, har påverkan av fel på nätet på
generatorn undersökts. Generatorns drift och dess beteende under symmetriska och osymmetriska fel studerats. Ett tillvägagångssätt presenteras
för framgångsrik “ride through” genom de symmetriska felen med “passive
resistive network (PRN)”. Dessutom, i syfte att begränsa de elektriska och
mekaniska oscillationerna i generatorn under osymmetriska fel, har tekniken
“dual vector control (DVC)” tillämpats. Man har funnit att DVC i viss utsträckning kan användas för att skydda omvandlaren mot de stora oscillationerna i rotorströmmarna.
Slutligen, kompletteras avhandlingen med en preliminär design av RPE i
finita elementprogrammet ANSYS. Den termiska analysen och kylförmågan
med uppskattningar av storlekar för kylfläns och fläkt presenterats.
Dessutom, har en annan variant av den roterande elektroniska induktionsmaskinen som är baserad på Lindmarks koncept och som arbetar utan att
rotorlindningen återkopplas till nätet också undersökts. En stationär modell
för konceptet har utvecklats och verifierats genom experiment.
Acknowledgements
This project was funded by the Vindforsk Research Program who are gratefully
acknowledged.
First of all, I would like to thank my supervisor Professor Chandur Sadarangani
for his support, encouragement, and guidance during the project.
Further, I would like to express my gratitude to the steering committee members
for this project; Dr. Luca Peretti, Dr. Jouko Niiranen, and Dr. Robert Chin for
their valuable feedback and fruitful discussions.
I want to thank Prof. Lennart Harnefors for his excellent advice on the control
theory, and for continuously spending his valuable time on revising my three journal
papers. I hope we can continue with the scientific work in the future.
Special thanks to Prof. Hans Peter Nee for carefully reviewing this thesis.
I would also like to thank Dr. Alija Cosic for his help with the equipment in
the laboratory while I was working with the experimental setup. Moreover, Mats
Leksell is acknowledged for solving some of the problems, which I faced during the
implementation of the experimental setup. Dr. Oskar Wallmark too, is acknowledged for his valuable feedback on latex and on some aspects related to the control
theory of the project.
I would also like to thank people during my exchange visit to North Carolina
State University (NCSU) Raleigh, USA. I would like to thank my supervisor there
and also a co-author of my two papers, Prof. Iqbal Husain for giving me an opportunity to work at FREEDM Systems Center, NCSU. Furthermore, I would like to
express my gratitude to the committee at ABB corporate research, Raleigh, USA,
for giving valuable feedback on my work, which I performed during my visit. For
this, special thanks goes to Dr. Waqas Arshad, Dr. Ghanshyam Shrestha, and Dr.
Hongrae Kim.
I am grateful to all my former and current colleagues at KTH, who have been
a source of help in several ways. Besides, I would like to thank Henrik Grop,
Alexander Stening, Kashif Khan, Shafigh Nategh, Andreas Krings, Noman Ahmed,
Yanmei Yao, Kalle Ilves, Shoaib Almas, and Lebing Jin for their company during
the conferences and courses.
vii
viii
Special thanks to E2C financial administrator Eva Petterson, system administrator Peter Lönn, Jesper Freiberg, and technician Jan-Olov Brännvall (late) for
assisting me with the financial, computer, and lab issues, respectively.
I would like to thank Eddie for an amazing company during indoor climbing
and for our excursions within Stockholm city, especially with regards to search for
restaurants serving good food.
Finally, I would like to express my deepest gratitude to my parents and wife
for their tremendous support and encouragement. I would also like to thank my
cricket and badminton friends Zaheer, Mati, Adnan, Wahab, and Arsalan.
Stockholm 2015
Naveed ur Rehman Malik
Contents
Contents
ix
1 Introduction
1.1 Background and Objective . . . . .
1.2 Outline of the Thesis . . . . . . . .
1.3 Main Contributions of this Thesis .
1.4 Publications . . . . . . . . . . . . .
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2 Variable-Speed Control of a Wind Generator
2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Direct- and Indirect-Drive Generator . . . . . . . . . . . . . . .
2.3 Connecting a Power Electronic Converter to a Generator . . . .
2.4 Brushless Doubly-Fed Induction Machine (BDFIM) . . . . . . .
2.4.1 Principle behind BDFIM and its Operational Evolution
2.4.2 Different Modes of BDFIM . . . . . . . . . . . . . . . .
2.5 Sizes of the Converter and Control Machine in a BDFIM . . . .
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3 Dynamic and Steady-State Model of a RPE-BDFIG
3.1 Working Principle . . . . . . . . . . . . . . . . . . . .
3.1.1 Super-Synchronous Mode . . . . . . . . . . . .
3.1.2 Sub-Synchronous Mode . . . . . . . . . . . . .
3.1.3 Synchronous Mode . . . . . . . . . . . . . . . .
3.1.4 General Comments . . . . . . . . . . . . . . . .
3.2 Dynamic Model of the RPE-BDFIG . . . . . . . . . .
3.3 Steady-State Model of the RPE-BDFIG . . . . . . . .
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4 Closed-Loop Control of a RPE-BDFIG
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4.1 Reference Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Vector Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2.1 Exciter Rotor Converter Control . . . . . . . . . . . . . . . . 33
ix
x
CONTENTS
4.2.2
4.2.3
4.2.4
4.2.5
4.2.6
DFIG Rotor Converter Control
Speed Controller . . . . . . . .
DC-Link Voltage Controller . .
Phase-Locked Loop . . . . . . .
Control Performance . . . . . .
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5 Low-Voltage Ride-Through of a RPE-BDFIG
5.1 Introduction . . . . . . . . . . . . . . . . . . . .
5.2 Grid Codes . . . . . . . . . . . . . . . . . . . .
5.3 Voltage Dips and Types of Faults . . . . . . . .
5.3.1 ABC Classification . . . . . . . . . . . .
5.4 Behaviour of the RPE-BDFIG during faults . .
5.4.1 Passive Resistive Network . . . . . . . .
5.4.2 Dual Vector Control . . . . . . . . . . .
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6 Design and Thermal Aspects of a Rotating Power Electronic
Converter (RPEC)
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6.1 Rotating Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
7 Unity Power Factor Operation of a Single-fed Induction Machine
using the Lindmark Concept
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7.1 Rotating Power Electronic Induction Drive . . . . . . . . . . . . . . 59
7.1.1 Advantage of the Lindmark Concept . . . . . . . . . . . . . . 60
8 Conclusions
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8.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
8.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
List of Figures
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Bibliography
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A Glossary of Symbols and Abbreviations
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B Summary of Publications
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C Selected Publications
C.1 Publication I . . .
C.2 Publication II . . .
C.3 Publication III . .
C.4 Publication IV . .
C.5 Publication V . . .
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CONTENTS
C.6 Publication
C.7 Publication
C.8 Publication
C.9 Publication
C.10 Publication
C.11 Publication
C.12 Publication
xi
VI .
VII .
VIII
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XII .
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Chapter 1
Introduction
This chapter presents the background, goal, and outline of the thesis.
1.1
Background and Objective
In the last two decades, electricity production through wind power has gained
momentum in Europe. This is due to a desire to gain independence from oil,
and to limit global warming from carbon dioxide emissions. The momentum has
caused improvement in the turbine technologies, and an increase in their sizes. It
is expected that if the current growth of use of the wind turbines continues, 20%
of the electricity in Europe will be supplied by wind, by 2030 [1, 2]. The major
contributor will be onshore wind, however, offshore wind power will also grow at a
much faster pace than before [1, 2]. The experiences gained from the oil industry
with regards to foundations in deep sea, will be used in order to accelerate the
growth of offshore wind turbine installations [1, 2]. Furthermore, offshore wind is
attractive as it offers better wind profile than onshore, higher wind speeds, less
visual and acoustic disturbances, and an opportunity of better energy yield per
turbine unit as larger sizes of wind turbines can be installed [1, 2].
The doubly-fed induction generator (DFIG) is one of the most famous and
widely used generator in the wind arena [5–8]. This is because the speed of the
generator is varied using a converter, that is rated at approximately 30% of the
rated power for speed variations between 20–25% [5–8]. This results in major cost
savings and reduces the size of the overall auxiliary installations of the generator,
such as harmonic filters. As seen in Figure 1.1, DFIG consists of a wound rotor
induction machine whose stator is directly connected to the grid, whereas the threephase rotor windings are connected to the power electronic converter via slip rings.
Majority of power leaves the stator unprocessed by the power electronic converter,
1
2
CHAPTER 1. INTRODUCTION
Figure 1.1: Doubly-fed induction generator (DFIG) with zoomed-in view of its slip
rings [3, 4].
whereas the remaining power corresponding to the slip of the generator, is delivered
to the grid from the generator’s rotor, via the rotor power electronic converter [5–8].
However, the generator employs slip rings and carbon brushes, which reduces the
reliability of the generator and puts limits to the amount of current that can be
transferred through the carbon brushes. Furthermore, carbon brushes wear out
and need to be replaced every few months [2]. Besides, the generated carbon
dust, if leaked in the nacelle can cause electrical hazards due to its conducting
nature [9–14]. Apart from this, the carbon dust is also blown into the generator
windings by the shaft fan, which reduces the lifetime and durability of the winding
insulation [9–14]. Thus, their absence will be of great advantage as it would reduce
the maintenance costs, and downtime of the turbine. The advantage is enhanced
for offshore installations, where the maintenance and replacement of the carbon
brushes is dependent upon weather conditions, and is also expensive.
Brushless DFIGs have been studied in the past, in order to remove carbon
brushes and slip rings, such as in [11,13,15–24]. This concept employs two machines;
the stator of one machine is connected to the grid, whereas its rotor is connected to
the rotor of the second machine, whose stator is connected to the grid through the
1.2. OUTLINE OF THE THESIS
3
power electronic converter in between (see Chapter 2). However, as pointed in [23],
the BDFIG suffers from increased size, weight, and cost, if unity or capacitive power
factor is desired at the stator terminals of the generator. Moreover, the control of
the generator is lost around the synchronous speed of the machine that is directly
connected to the grid [13, 25] (see Chapter 2). Thus, its large size and instable
regions of operation at the speeds of interest for wind power, is a major drawback.
As an alternative, a novel topology has been theoretically and experimentally
studied and investigated in this thesis. This topology offer several advantages such
as higher power density of the components and variable power factor operation. The
electromagnetic interference (EMI) to the grid will also be considerably reduced.
The generator is called as rotating power electronic brushless doubly-fed induction
generator (RPE-BDFIG). It consists of two machines (see Chapter 3). The stator
of one machine is connected to the grid and its rotor is connected to the rotor of
the second machine via back-to-back power electronic converters. The stator of the
second machine has dc field winding. The the two rotors are decoupled electrically
through the power electronic converters (see Chapter 3). The role of the second
machine is to convert slip power into mechanical power, which is delivered in an
electrical form to the grid by the first machine. Thus, the generated power is
delivered to the grid only through the stator of one machine, unlike the DFIG or
brushless DFIG.
The goal of this thesis is to study a novel generator, which can:
• Recover slip power and thereby, improve the efficiency of the system.
• Achieve dynamic and stable operation under variable-speed power generation.
• Supply variable reactive power to the grid.
• Ride through voltage dips, which occur during faults in the grid.
• Presents a preliminary design of the rotating power electronic converter.
1.2
Outline of the Thesis
The chapters in this thesis are outlined as follows:
Chapter 2 explains the basic configuration of a generic generator with respect to
its drive-train and variable-speed operation. Furthermore, a review on the working
principle of a conventional doubly-fed induction generator (BDFIG) is given.
Chapter 3 introduces the novel generator, the rotating power electronic brushless
4
CHAPTER 1. INTRODUCTION
doubly-fed induction generator (RPE-BDFIG). It explains its physical configuration and the operating principle. Moreover, it describes the active power flows with
the help of power flow diagrams. Furthermore, it derives the dynamic and steadystate models of the generator, and presents their analysis. Finally, the dynamic
and steady-state equivalent circuits based on the models are given.
Chapter 4 discusses the development of the closed-loop control of the generator.
It presents the derivation of the current, speed, and voltage closed-loop control,
and the phase-locked loop. Verification of the closed-loop controls through measurements is conducted on an 11-kW RPE-BDFIG, which is also presented.
Chapter 5 presents an investigation on the behaviour of the RPE-BDFIG, when
it is subjected to various grid faults, both symmetrical and unsymmetrical in nature. Furthermore, the analysis of the generator using passive resistive network
(PRN) in order to protect the power electronic converter during faults, is conducted. Besides, study of the generator using dual vector control (DVC) in order
to suppress oscillations in the generator, is also presented.
Chapter 6 presents the thermal design of a rotating power electronic converter
using a finite element method (FEM). The sizes of the heatsink and the shaft fan
for its cooling are estimated.
Chapter 7 introduces a steady-state model of a single-fed induction machine with a
rotating converter, based on the Lindmark concept. The verification of the steadystate model through experiments, is shown.
Chapter 8 presents the summary of the project and recommendations for future
research work.
1.3
Main Contributions of this Thesis
Thus far, this thesis has contributed in the following ways:
• It introduces and investigates the configuration of a brushless generator with
the rotating power electronic converter. A thorough analysis of the dynamic
behavior of the generator when subject to load-torque disturbances at variable
speeds, has been conducted. Furthermore, the steady-state model is also
derived and analysed.
• Closed-loop control of the generator using an 11-kW prototype has been successfully developed, analyzed, and implemented. The experimental results
1.4. PUBLICATIONS
5
confirm stable operation of the generator, and successful recovery of slip
power. Furthermore, the results demonstrate validity of the closed-loop control with regards to the dynamic performance of the generator and stable
control of the dc-link voltage, when they experience torque disturbance from
the exciter and the load machine.
• Behavior of the generator against symmetrical and unsymmetrical voltage
dips is investigated. It is seen that using proper control and external protection circuit, the generator’s rotor converter can be protected from damage,
even during extreme voltage dips. Furthermore, it is demonstrated that using
the dual vector control (DVC), the electrical and mechanical oscillations in
the generator can be reduced to a large extent.
• A preliminary thermal design and analysis of the rotating power electronic
converter has been conducted in a finite element software. The sizes of the
heating sink and shaft fan are estimated.
Note that the generator still used slip rings and brushes for the connection of
the power electronic converter. This was done in order to analyze and understand
the working principle of the topology, and confirm recovery of slip power.
1.4
Publications
The journal and conference publications are presented in an order in which they
appear in the thesis.
So far, journal publications originating from this project are:
• Malik, Naveed ur Rehman, C. Sadarangani, A. Cosic, and L. Harnefors,
“Experimental validation of a rotating power electronic brushless doubly-fed
induction generator for variable-speed operation,” accepted first version in
IEEE Trans. Energy Conv., May. 2015, and revised version resubmitted.
• Malik, Naveed ur Rehman, C. Sadarangani, A. Cosic, and L. Harnefors, “Variable reactive power control of a rotating power electronic brushless
doubly-fed generator,” submitted to IEEE Trans. Energy Conv., Aug. 2015.
• Malik, Naveed ur Rehman, C. Sadarangani, and L. Harnefors, “Lowvoltage ride-through of a 2-MW rotating power electronic brushless doublyfed generator,” submitted to IEEE Trans. on Sustainable Energy., Sep. 2015.
6
CHAPTER 1. INTRODUCTION
• Malik, Naveed ur Rehman, I. Husain, “Dynamic and steady-state 3-D
thermal design and investigation of the rotating power electronic IGBT converter,” submitted to IEEE Trans. Emerging and Selected Topics in Power
Electron., June 2015.
So far, conference publications originating from this project are:
• Malik, Naveed ur Rehman; Sadarangani, C., “Dynamic modeling and
control of a brushless doubly-fed induction generator with a rotating power
electronic converter,” XXth International Conference on Electrical Machines
(ICEM), pp. 900–906, 2-5 Sep. 2012.
• Malik, Naveed ur Rehman, C. Sadarangani, A. Cosic, “Synchronous operation of a rotating power electronic brushless doubly-fed generator,” accepted
and to be published in Annual Conference on IEEE Industrial Electronics Society (IECON), 9-12 Nov. 2015.
• Malik, Naveed ur Rehman; Sadarangani, C., “Brushless doubly-fed induction machine with rotating power electronic converter for wind power
applications,” International Conference on Electrical Machines and Systems
(ICEMS), pp. 1–6, 20-23 Aug. 2011.
• Malik, Naveed ur Rehman; Sadarangani, C., “Behavior of a brushless
doubly-fed induction generator with a rotating power electronic converter
during symmetrical voltage sags,” XXth International Conference on Electrical Machines (ICEM), pp. 865–871, 2-5 Sep. 2012.
• Malik, Naveed ur Rehman; Sadarangani, C., “Extended vector control of
a rotating power electronic brushless doubly-fed induction generator under
unsymmetrical voltage sags,” 38th Annual Conference on IEEE Industrial
Electronics Society (IECON), pp. 1793–1798, 25-28 Oct. 2012.
• Malik, Naveed ur Rehman, I. Husain, “Transient and Steady-State 3-D
Electro-Thermal Design and Analysis of the Rotating Power Electronic IGBT
Converter,” published in IEEE International Electric Machines and Drives
Conference (IEMDC), 10-13 May 2015.
• Malik, Naveed ur Rehman; Sadarangani, C.; Lindmark, M., “Theoretical
and experimental investigation of the self-excited rotating power electronic
induction machine,” 37th Annual Conference on IEEE Industrial Electronics
Society (IECON), pp. 2048–2053, 7-10 Nov. 2011.
The following publication is related to the project and presents the construction
of the rotating power electronic converter and the wireless communication.
1.4. PUBLICATIONS
7
• Cosic, A.; Yao, Y.; Sadarangani, C.; Malik, Naveed ur Rehman, “Construction of a rotating power electronic converter for induction machine operation,” accepted and to be published in International Conference on Electrical
Machines and Systems (ICEMS), Oct. 2015.
The following publication is related to the project, but majority of the work
performed was part of the authors master’s thesis.
• Malik, Naveed ur Rehman; Sadarangani, C.; Cosic, A.; Lindmark, M.,
“Induction machine at unity power factor with rotating power electronic converter,” International Symposium on Power Electronics, Electrical Drives,
Automation and Motion (SPEEDAM), pp. 401–408, 20-22 Jun. 2012.
The following publications by the author may be of interest but is not part of
this thesis.
• Malik, Naveed ur Rehman; Almas, M.S.; Vanfretti, L., “Challenges of
real-time parameter estimation of a DFIG using synchrophasors,” IEEE 15th
International Conference on Environment and Electrical Engineering (EEEIC),
pp. 1939–1944, 10-13 Jun. 2015.
• Chamorro, H.R.; Nazari, M.; Babazadehi, D.; Malik, Naveed ur Rehman;
Ghandhari, M., “Consensus control for induction motors speed regulation,”
16th European Conference on Power Electronics and Applications (EPE’14ECCE Europe), pp. 1–6, 26-28 Aug. 2014.
Chapter 2
Variable-Speed Control of a Wind
Generator
This chapter briefly explains different configurations of wind power generators with
regards to speed control. Moreover, a literature review of the working principle of a
brushless doubly-fed induction generator (BDFIG) is presented.
2.1
Background
Nowadays variable speed drives (VSD’s) are receiving special attention, especially
with respect to wind power generation. This is because to obtain maximum aerodynamic efficiency from a wind turbine, it is necessary that a generator shaft adapts
its speed to the varying wind speed [26, 27]. Thus, variable speed drives (VSD’s)
are being employed in high power applications [26, 27].
It is well known that the energy extracted from wind varies cubically with
its speed, with which it flows into the turbine blades. The aerodynamic power
extracted from wind is expressed as [26, 27]
Pwt =
1
2 3
πρCp Dwt
vwind ,
8
(2.1)
where ρ, Cp , Dwt , and vwind are the specific mass of air, coefficient of power, rotor
blade diameter, and wind speed, respectively.
It is observed in (2.1) and Figure 2.1 that the maximum power is extracted
from the wind, when the generator shaft speed changes with the wind speed. The
generator speed can be varied mechanically either by pitching the turbine blades
(though at the expense of reduction in efficiency) or, electrically by varying the
shaft speed of the generator.
9
10 CHAPTER 2. VARIABLE-SPEED CONTROL OF A WIND GENERATOR
Figure 2.1: Maximum power point tracking (MPPT) curve, showing wind generator
power versus rotational speed [26].
Considering only mechanical control, e.g., pitch control, the system is slower
and less efficient. In contrast, power electronic converters are used in variablespeed drives. They offer dynamic and robust control. Doing so by electrical means,
such as through the power converter, ensures that Maximum Power Point Tracking
(MPPT) curves at various wind speeds are followed and hence, energy yield is
optimised [27,28]. This is illustrated in Figure 2.1. Furthermore, VSDs offer several
advantages over constant speed drives (CSDs) such as [27, 28]:
• Improvement in torque ripple through better control,
• Mitigation of the mechanical pulsations due to the tower effect,
• Additional flexibility of power factor control, and thus, better voltage stability
of the grid.
There are certain drawbacks of VSD’s as compared to CSD’s. VSDs in general
are more complex and bulky, and more expensive than their CSD counterpart. However, with high energy capture and better quality, the cost offsets can be overcome
within a short time-span [27, 28].
2.2. DIRECT- AND INDIRECT-DRIVE GENERATOR
(a) Direct-drive generator.
11
(b) Indirect-drive generator.
Figure 2.2: Generator and its drive-train.
2.2
Direct- and Indirect-Drive Generator
The two configurations of the mechanical drive-train of a generator are [29, 30]:
• Direct-Drive Generator: The generator, as shown in Figure 2.2a, is connected or coupled directly to a wind turbine rotor, without a gearbox in
between [29, 30], which is an advantage in terms of added reliability, and
lower maintenance costs. However, these generators are inherently designed
for low-speed operation, and therefore, have higher number of poles in the
stator, in order to produce 50/60 Hz at the stator terminals. For the same
power rating, if the number of poles are increased, speed decreases and thus
the required torque capability increases, resulting in an increase in size of the
generator. These machines can have number of poles ranging from 20 to 60,
and even higher.
• Indirect-Drive Generator: In these type of drives, the generator is coupled
to the wind turbine via a gearbox [29, 30], as shown in Figure 2.2b. The
gearbox steps up the low speed of the wind turbine rotor to a high speed
of the generator shaft. Therefore, the generator is designed for relatively
high speeds and low torques, for the same power rating, as compared to the
direct-drive generators. Less number of poles are required in order to produce
required frequency at the stator terminals. As a result, these generators are
12 CHAPTER 2. VARIABLE-SPEED CONTROL OF A WIND GENERATOR
smaller than their direct-drive counterparts. Normally such machines consists
of four, six, or eight poles. The gearbox can have 1.5 steps to 3 steps. It can
be of planetary or helical type.
2.3
Connecting a Power Electronic Converter to a
Generator
The power electronic converter for speed control purposes can be connected to a
generator in two configurations, i.e., either to the stator windings of the generator
or, to the rotor windings of the generator (in the latter case only if the rotor has
three-phase windings). These two configurations are summarized as follows [30].
• Stator-Connected Converter: The converter is directly connected to the
stator and has at least the same power rating as the power rating of the
generator, because whole of the generated power flows from the stator to
the power converter and into the grid [30]. The full-scale converter provides
better controllability of the generator during stator voltage transients and
grid faults. However, cost of the overall system increases. Furthermore, large
filters are needed in order to reduce electromagnetic interference (EMI) to the
grid.
• Rotor-Connected Converter: The converter is connected to the threephase rotor windings of the generator [5–8]. This configuration for variablespeed control is only possible in an induction machine (i.e., it is necessary that
the rotor windings carries three-phase ac currents). In this configuration,
the converter size reduces and is rated according to the magnitude of the
slip power. Thus, the size of the converter depends on the speed variation
from the synchronous speed. The converter power rating is normally 25% to
30% of the power rating of generator, for ±20% speed variations around the
synchronous speed. Converter size can increase if the following requirements
are imposed on the generator [5–8]:
– Rotor shall provide reactive power to the generator, e.g., the stator terminal is to operate at unity or leading power factor.
– Rotor converter shall handle transients in current and voltages during
the disturbances in the grid.
The partially-rated converter is connected to rotor by means of carbon brushes
and slip rings, which increases the maintenance costs and decreases the reliability of the generator [9–11, 13, 14, 17]. The doubly-fed induction generator
(DFIG), which is one of the most widely used generator in the wind industry,
2.4. BRUSHLESS DOUBLY-FED INDUCTION MACHINE (BDFIM)
13
belongs to this configuration. One way to get rid of slip rings and carbon
brushes is to use a brushless drive which is explained in the following section.
2.4
Brushless Doubly-Fed Induction Machine (BDFIM)
The concept of the brushless doubly-fed induction machine/generator (BDFIM/G)
dates back to the beginning of the 20th century. One of the first inventors of the BDFIM was Hunt [31,32], and later Creedy [33,34] developed it further. Broadway [15]
and Smith [35] also studied it further and made improvements. The BDFIM relies
on the same principle as today’s slip-ring DFIG. It is useful in a sense that it has
provision of recovering slip power without slip rings and carbon brushes. This is a
major advantage, since in certain applications, dust generated from carbon brushes
is prohibited. Apart from that, the maintenance costs of slip rings and carbon
brushes are high, which are uncalled for in offshore application [9–11, 13, 14, 17],
where maintenance is tedious and dependent upon weather conditions.
The BDFIM is a combination of two machines; main machine and the auxiliary/control machine [11, 13, 16–24], as shown in Figure 2.3. The main machine
is connected to the grid, whereas the rotors of the two machines are connected in
cascade. The stator of the control machine is connected to the grid via a converter.
The slip power of the main machine is delivered to the grid through the control
machine and the power converters. As a result, the efficiency increases as slip power
is recovered. At the same time, it is compact and without slip rings and carbon
brushes, which minimizes maintenance [11, 13, 16–24]. Generally, as is also the case
with slip-ring DFIG, the BDFIM has an advantage over stator-connected converter
drives in that the bulk of electric power which is supplied to the grid, leaves unprocessed by the power electronic converter. As a result, a smaller converter is
required and less harmonics are injected into the grid, thereby improving the power
quality.
2.4.1
Principle behind BDFIM and its Operational Evolution
In a BDFIM, the main and control machines can be connected with each other in
two ways, which are explained as follows.
• The main and control machines are connected in a non-inverted
configuration [31–33]:
– This configuration was used in the beginning of the 20th century, in
order to operate the machine at three different speeds, i.e., around synchronous speed of the main machine, around synchronous speed of the
control machine, and synchronous speed of the two machines connected
14 CHAPTER 2. VARIABLE-SPEED CONTROL OF A WIND GENERATOR
Figure 2.3: Configuration of the BDFIM.
in cascade [31–33]. In this configuration, the stator of the main machine
is connected directly to the grid. The rotor of the main machine is connected through slip rings to the stator of the control machine. The rotor
of the control machine is short-circuited via slip rings. The main machine
supplies its own magnetization as well as that of the control machine.
For the two machines which are wound for the same number of poles,
the cascade set rotates at half the speed of the individual machine, if it
were connected alone [31–33].
• Main machine is connected in a non-inverted configuration, whereas
the control machine is connected in an inverted configuration:
– This configuration was born when Hunt realized that the slip-rings are
no longer required, if the rotor of the main machine is connected to the
rotor of the control machine, similar to a modern-day BDFIG [31–33].
This has been one of the most common brushless configuration in use in
the beginning of the 20th century, for variable speed control by means of
variable resistor banks [31–33]. It must be noted that since the control
machine is connected in an inverted configuration, two of the three rotor
winding terminals are swaped and connected in reverse, i.e., abc winding
terminals of the first rotor is connected to acb winding terminals of the
second rotor, see Figure 2.3. Similar, to the non-inverted configuration,
2.4. BRUSHLESS DOUBLY-FED INDUCTION MACHINE (BDFIM)
15
for the two machines which are wound for the same number of poles, the
cascade set rotates at half the speed of the individual machine, if it were
connected alone [31–33].
Instead of connecting two separate machines together, the two machines can be
integrated into a single frame known as single-frame brushless doubly-fed induction
machine (SF-BDFIM). There are two ways of doing this [31–33]:
• The stator windings are fitted in one frame. The stator is divided into alternate segments and primary and secondary windings are placed alternately
in the stator. The primary windings are connected directly to the mains,
whereas the secondary stator windings are connected to the resistors or a
converter for speed control purposes. Through suitable spacing of the two
stator windings, the two stator fields are not interlinked magnetically, and
are only coupled through the agency of the rotor. However, the size of the
machine increases [31].
• The stator windings are fitted in one frame sharing the same iron path. The
two stator windings are inserted in the same slot. The numbers of poles of
the two stator winding must be different, in order to avoid direct coupling
(transformer effect) between them. The fields of the two stator windings must
only couple with each other through the rotor, for torque production [31].
The disadvantages of a BDFIM are mainly [31, 33]:
• High cost, size, and weight.
• Low efficiency mainly due to higher copper losses.
• Small overload capacity due to low power factor.
• Increased magnetic leakage.
2.4.2
Different Modes of BDFIM
There are two modes of operation in a BDFIM. These are explained as follows [13]:
• Cascade Induction Mode: The stator of one machine is connected to
the grid, whereas the stator of the other machine is short-circuited. The
two stators are still linked magnetically through the rotor. Machine behaves
similar to an ordinary induction machine and speed changes with load [13].
16 CHAPTER 2. VARIABLE-SPEED CONTROL OF A WIND GENERATOR
• Cascade Synchronous Mode: This is the mode in which the modern-day
BDFIM is always used. In this mode, the stator of the main machine (Stator 1) is connected to the grid, whereas stator of the control machine (Stator 2)
is connected to the grid, via an electronic converter. A specially designed rotor (such as a nested-loop rotor [15]) is used, which magnetically couples the
two stators. The aim of the specially designed rotor is as follows [13, 15]:
– Currents in Stator 1 (having p1 number of poles) should induce currents
in the rotor such that the induced currents in the rotor produces a magnetic field, which should have a harmonic component corresponding to
p2 number of poles. The p2 pole harmonic component couples with the
p2 pole field in the winding of Stator 2 (composed of p2 number of poles).
– Similarly, currents in Stator 2 should induce currents in the rotor such
that the magnetic field produced by the rotor contains a harmonic component of p1 number of poles. This ensures the magnetic coupling of the
rotor with stator 1. Hence, the machine is able to generate torque.
As a result, varying torque is produced at constant speed and the torque can
be controlled by the power electronic converter [13].
Besides, if a dc current is fed through the converter, the machine behaves as
a conventional synchronous machine, though the rotor still has ac currents.
This is a special case of the cascade synchronous mode, and the speed of the
machine is referred to as the natural speed.
In a cascade synchronous operation, the currents of same frequency flow through
the two rotors, and thus the following relation must always be satisfied [13, 15].
ωm =
ω1 + ω2
,
p1 + p2
(2.2)
where ω1 is the grid frequency and ω2 is the frequency of the currents, injected
by the power electronic converter, which is connected to the stator of the control
machine.
Observing (2.2), it is deduced that the rotor speed can be changed by varying
the frequency through the power electronic converter. This is only possible when
the two rotor windings carry currents of the same frequency, thereby coupling the
two stators. From (2.2), it is also seen that the BDFIM is essentially a low speed
machine, due to the high pole number count.
2.5. SIZES OF THE CONVERTER AND CONTROL MACHINE IN A BDFIM
17
2.5
Sizes of the Converter and Control Machine in a
BDFIM
As mentioned previously, the doubly-fed drives are attractive due to smaller power
rating of the converter. However, the size of the converter is subject to certain limitations as discussed in Section 2.3. As far as large wind generators are concerned, it
becomes necessary that the generator has some means of supplying reactive power
in order to operate at variable power factor, e.g., unity. This condition can have serious consequences on the size of the converter and the control machine itself [36,37].
There are different ways of managing the sizes of the converter and the control
machine [36, 37], some of which are listed as follows.
• Consider a scenario in which, if a back-to-back bidirectional converter is considered, the control machine side converter handles active power as well as the
reactive power. This is for the case, when the reactive power is generated by
the control machine and its converter, whereas the grid-side converter handles only active power [36]. This implies that the grid-side converter can be
made smaller than the machine-side converter. Thus, the size of the control
machine and its converter grows due to an increase in the voltage and current requirements for the reactive power control. In this case, the size of the
machine-side converter is a function of:
– Variable speed deviation from the synchronous speed, as it determines
the amount of active (slip) power in an induction machine.
– Power factor of the stator of the main machine at which it is operated.
Converter size will increase as the power factor requirements on the
terminal of the main machine are changed from inductive to unity to
capacitive.
• There is another technique through which the control machine and the converter size can be controlled, and at the same time power factor to the grid
can be maintained at unity. The idea is to use the same converter size for both
the machine-side converter and the grid-side converter. The main machine
is allowed to draw lagging reactive power from the grid, while the grid-side
converter supplies the equivalent amount of the reactive power (VARs) to the
grid, which is consumed by the main machine. In this way, the net reactive
power drawn from the grid is zero. This strategy has an advantage in that the
size of the control machine is reduced. This is because the control winding
voltage can be reduced as less reactive power is supplied from the control
machine [36]. However, optimisation analysis has to be done with regards to
the machine and converter sizes.
18 CHAPTER 2. VARIABLE-SPEED CONTROL OF A WIND GENERATOR
• For the case, when the main machine in the BDFIG is allowed to draw reactive
power from the grid, the control machine and power electronic converter does
not need to supply reactive power. Therefore, the size of the control machine
and the converters can be reduced, but at the expense of the size of the main
machine, which increases.
Chapter 3
Dynamic and Steady-State Model
of a RPE-BDFIG
This chapter presents the derivation and analysis of the dynamic and steady-state
model of the generator. The analysis has been conducted at rated torque and various
speeds.
This chapter is based on Publication I, Publication II, Publication III, Publication IV, and the author’s licentiate thesis [3].
3.1
Working Principle
The rotating power electronic brushless doubly-fed induction generator (RPE-BDFIG)
was invented by L. Gertmar and A. Nysveen [38]. It is based on the same operating principle as the conventional doubly-fed induction generator (DFIG) and the
brushless doubly-fed induction generator (BDFIG). The RPE-BDFIG comprises of
two machines; one is the main machine referred to as DFIG, and the second is the
control machine referred to as exciter, as shown in Figure 3.1. The DFIG consists
of a three-phase winding in the stator and a three-phase winding in the rotor. In
contrast, the exciter consists of a three-phase winding in the rotor, and a dc field
winding in the stator. The two machines are coupled mechanically and therefore,
share the same shaft. The stator of the DFIG is connected to the grid, whereas the
three-phase winding of the DFIG rotor is connected to the three-phase winding of
the exciter, through the two power electronic converters.
The back-to-back insulated gate bipolar transistor (IGBT) converter is used, in
order to interconnect the DFIG and exciter three-phase rotor windings, i.e., one of
the converter is connected to the three-phase DFIG rotor windings, whereas the
19
20
CHAPTER 3. DYNAMIC AND STEADY-STATE MODEL OF A
RPE-BDFIG
Figure 3.1: Configuration of the rotating power electronic converter brushless
doubly-fed induction generator (RPE-BDFIG).
other is connected to the three-phase rotor windings of the exciter. Due to the
rotor mounted converter, the two rotor windings are electrically decoupled. Thus,
the the two rotor windings operate at different frequencies. As a result, currents of
any frequency can be injected in the rotor windings, as explained in Publication
III, unlike BDFIG where dc currents cannot be injected in the rotor.
As is the case with the DFIG and BDFIG, the RPE-BDFIG also operates in
super- and sub-synchronous modes. The two modes are explained in terms of active
power only.
3.1.1
Super-Synchronous Mode
In this mode, the speed of the generator is higher than the synchronous speed of
the DFIG, e.g., for a 4-pole generator and 50 Hz grid frequency, the speed is higher
than 1500 rpm. The power flows out from the stator of the DFIG and into the
grid, and from the rotor of the DFIG towards the rotor of the exciter via the power
electronic converter, as shown in Figure 3.2a. The power which enters the exciter
rotor windings is converted into mechanical torque, which is added to the shaft,
being shared by both the DFIG and the exciter. The added torque is used by the
DFIG to generate electrical power, which is then delivered to the grid via its stator.
As a result, the slip power is recovered with the help of the exciter. The exciter
acts as a motor in the super-synchronous mode.
3.1. WORKING PRINCIPLE
(a) Super-synchronous mode.
(b) Sub-synchronous mode.
Figure 3.2: Active power flow in the the RPE-BDFIG.
21
22
CHAPTER 3. DYNAMIC AND STEADY-STATE MODEL OF A
RPE-BDFIG
(a) Direction of rotation of the magnetic field in the super-synchronous
mode.
(b) Direction of rotation of the magnetic field in the sub-synchronous
mode.
Figure 3.3: Modes of operation.
Figure 3.3a show the direction of the flux vector in the different parts of the
generator system. It is observed that in the super-synchronous mode, the direction
of the flux vector produced by the slip frequency currents in the DFIG rotor, is
opposite to the rotational speed of the generator. This is because, since the rota-
3.1. WORKING PRINCIPLE
23
Turbine Torque (Nm)
2200
Speed (rpm)
2000
1800
1600
1400
1200
1000
40
60
80
100
120
Time (sec)
140
0
−50
−100
−150
−200
−250
40
160
0
−100
−200
−300
40
60
80
100
120
Time (sec)
80
100
120
Time (sec)
140
160
140
160
(b) Turbine torque.
Exciter Torque (Nm)
RPE−BDFIG Torque (Nm)
(a) Shaft speed.
60
140
(c) RPE-BDFIG torque.
160
50
0
−50
−100
40
60
80
100
120
Time (sec)
(d) Exciter torque.
Figure 3.4: Simulation results for the operation of a 37-kW RPE-BDFIG, in the
super-synchronous mode.
tional speed is greater than 1500 rpm, the flux vector rotates so as to produce the
grid frequency at the stator terminals, which is fixed by the grid. Concerning the
exciter, since it is an inverted configuration, the flux vector produced by the stator
field winding is at standstill. As a consequence, to maintain stable operation, the
exciter rotor converter must inject current of frequency equal in magnitude to the
rotor speed in electrical radians per second, but in the opposite direction to the
rotor’s rotation.
Figure 3.4 shows the results of a step response of the load torque of a 4-pole
37-kW RPE-BDFIG in the super-synchronous mode of operation. Figure 3.4a show
the speed response of the generator, illustrating that the RPE-BDFIG is operating
in the super-synchronous mode. Figure 3.4b, Figure 3.4c, and Figure 3.4d show
the turbine torque, RPE-BDFIG generated torque, and exciter torque responses,
respectively. It is observed that in the super-synchronous mode, the torque gener-
24
CHAPTER 3. DYNAMIC AND STEADY-STATE MODEL OF A
RPE-BDFIG
ated by the RPE-BDFIG is the sum of the turbine torque and the exciter torque,
emphasizing motor operation of the exciter. The DFIG slip power is used to generate exciter torque, which is added to the shaft and thereafter used by the DFIG
to produce electrical power (see Publication II, and Section 3.2).
3.1.2
Sub-Synchronous Mode
In this mode, the speed of the generator is less than the synchronous speed of the
DFIG, e.g., for a 4-pole generator and 50 Hz grid frequency, the speed is less than
1500 rpm. The majority of power leaves the stator of the DFIG, unprocessed by
the power converter. However, some percentage of power, which corresponds to the
slip of the generator, must be supplied to the DFIG for its proper operation, see
Figure 3.2b. This is done by the exciter, which consumes fraction of the mechanical
torque supplied by the turbine, converts it into electrical power, and delivers it to
the DFIG. Thereafter, the power in the rotor of the DFIG is delivered to the grid
through its stator, by induction means. As a result, slip power recovery scheme is
also successful in this mode of operation. The exciter behaves as a generator in the
sub-synchronous mode.
From Figure 3.3b, it is observed that in the sub-synchronous mode, the direction
of the flux vector produced by the slip frequency currents in the DFIG rotor, is in
the same direction as the rotational speed of the generator. This is because, since
the rotational speed is less than 1500 rpm, the flux vector rotates so as to produce
the grid frequency at the DFIG stator terminals. Concerning the exciter, since
it is fed by dc-voltage, the flux vector produced by the stator dc field winding is
at standstill. As a consequence, for stable operation, the exciter rotor converter
must inject current of frequency equal in magnitude to the rotor speed in electrical
radians per second, but in the opposite direction to the rotor’s rotation.
Similar to the analysis in the super-synchronous mode, Figure 3.5a show the
speed response of the generator, illustrating its operation in the sub-synchronous
mode, whereas Figure 3.5b, Figure 3.5c, and Figure 3.5d show the turbine torque,
RPE-BDFIG generated torque, and exciter torque responses, respectively. It is
observed that the torque generated by the RPE-BDFIG is the difference of the
turbine torque and the exciter torque, emphasizing generator operation of the exciter. The exciter uses fraction of the torque supplied by the turbine to generate
electric power, which corresponds to the slip power. The slip power is then supplied
to the DFIG rotor and is delivered to the grid via induction means through the
RPE-BDFIG stator (see Publication II, and Section 3.2).
A thorough analysis of the super- and sub-synchronous modes during the transient
conditions has been conducted in Publication I and Publication II, whereas
3.1. WORKING PRINCIPLE
25
Turbine Torque (Nm)
2200
Speed (rpm)
2000
1800
1600
1400
1200
1000
40
60
80
100
120
Time (sec)
140
0
−50
−100
−150
−200
−250
40
160
0
−100
−200
−300
40
60
80
100
120
Time (sec)
80
100
120
Time (sec)
140
160
140
160
(b) Turbine torque.
Exciter Torque (Nm)
RPE−BDFIG Torque (Nm)
(a) Shaft speed.
60
140
(c) RPE-BDFIG torque.
160
50
0
−50
−100
40
60
80
100
120
Time (sec)
(d) Exciter torque.
Figure 3.5: Simulation results for the operation of a 37-kW RPE-BDFIG, in the
sub-synchronous mode.
analysis of the generator during steady-state conditions is conducted in Publication IV.
3.1.3
Synchronous Mode
The synchronous mode is a special advantage of the RPE-BDFIG as compared to
the BDFIG. The conventional BDFIG is unstable at the synchronous speed of the
main machine, whereas the RPE-BDFIG is stable at this speed. This is a major
advantage as it implies that the state of the machine is predictable at all points
of operation. Thus, the RPE-BDFIG offers better control performance and power
quality when the generator shaft speed crosses the synchronous speed of the DFIG.
Publication III presents the operational analysis of the RPE-BDFIG during
CHAPTER 3. DYNAMIC AND STEADY-STATE MODEL OF A
RPE-BDFIG
26
60
8000
Frequency [Hz]
Output Power [W]
10000
6000
4000
2000
0
0
40
20
Stator Frequency
DFIG Rotor Frequency
Exciter Rotor Frequency
0
20
40
60
Input Torque [Nm]
(a) Generated power.
0
0.05
Time [sec]
0.1
(b) Frequency of currents in the three windings.
Figure 3.6: Measurements results of the operation of an 11-kW RPE-BDFIG during
the synchronous mode.
the synchronous mode. The results are summarized in Figure 3.6a which show
that the RPE-BDFIG can produce electrical power of sufficient magnitude at the
synchronous speed, emphasizing stable operation. Furthermore, Figure 3.6b shows
the frequencies in the stator and the two rotor windings of the RPE-BDFIG.
3.1.4
General Comments
Observing the super- and sub-synchronous modes of operation, it is seen that the
main machine, i.e., DFIG shows the same operational principle as the conventional
DFIG. However, in the conventional slip-ring DFIG and BDFIG, the slip power
recovery scheme is electrical in nature, similar to a Scherbius drive [39, 40]. In contrast, in the RPE-BDFIG, the slip power recovery scheme is realized by mechanical
means, similar to a Kramer drive [39].
Besides, it is seen that the RPE-BDFIG is relatively a high-speed machine as
compared to the BDFIG (see Chapter 2 and Publication III). This is because the
speed of the RPE-BDFIG is only dictated by the poles of the DFIG and not the
exciter, unlike the BDFIG. Moreover, the mechanical torque of the exciter acts as
an additional torque, which needs to be taken into consideration when designing the
control of the generator (see Chapter 4). Thus, during super-synchronous operation,
the torque of the turbine is less than the torque of the DFIG, because a fraction
of the torque is also contributed by the exciter. On the other hand, in the subsynchronous mode, the torque rating of the wind turbine needs to be higher than
the torque rating of the DFIG, i.e., ideally it is sum of the torque rating of the
DFIG and the exciter.
3.2. DYNAMIC MODEL OF THE RPE-BDFIG
27
(a) d-axis equivalent circuit.
(b) q-axis equivalent circuit.
Figure 3.7: dq dynamic model of the RPE-BDFIG.
3.2
Dynamic Model of the RPE-BDFIG
This section presents the dq dynamic model of the RPE-BDFIG, which is based
on Park’s equivalent circuit [41]. The voltages, currents, and fluxes of the stator
and two rotors of the RPE-BDFIG are transformed to a fictitious reference frame,
which rotates in synchronism with one of the state-variable of the RPE-BDFIG. As
a result, the generator inductances, which in the stationary reference frame are a
function of the rotor position, become independent of the rotor position, after the
dq transformation [41]. This is an added advantage, since the complexity of the time
varying differential equations of the generator are reduced, and the mathematical
model is simplified [41]. This transformation is given in Chapter 4, whereas the
derivation and analysis of the dynamic model is given in Publication II, which
presents the simulation results on how the system responds to torque steps during
sub- and super-synchronous operation.
The equivalent circuit of the dynamic model is shown in Figure 3.7, whereas
Figure 3.8a, Figure 3.8b, Figure 3.9a, and Figure 3.9b show the simulation results
from the developed dynamic model of the 37-kW RPE-BDFIG.
Figure 3.8a and Figure 3.8b show the response of a step on the turbine torque on
the mechanical power supplied by the turbine and the generated electrical power by
the RPE-BDFIG, respectively, at 1800 rpm (i.e., in the super-synchronous mode).
It is seen that the generated electrical power is approximately equal (minus the
CHAPTER 3. DYNAMIC AND STEADY-STATE MODEL OF A
RPE-BDFIG
Stator Power (kW,kVAr)
28
Turbine Power (kW)
60
40
20
0
−20
−40
−60
40
60
80
100
120
Time (sec)
140
160
50
40
Active power
Reactive power
30
20
10
0
−10
40
60
80
100
120
Time (sec)
140
160
(a) Mechanical power supplied by the turbine. (b) RPE-BDFIG’s generated power delivered to
the grid.
Figure 3.8: Turbine and REP-BDFIG stator power in the super-synchronous mode,
at 1800 rpm.
resistive and friction losses) to the supplied mechanical power. This show that the
slip power recovery scheme is successful. Furthermore, Figure 3.9a and Figure 3.9b
show the DFIG rotor power (slip power), and the power which flows from the
DFIG rotor through the rotor power electronic converter into the exciter rotor,
respectively. It is seen that the rotor powers are 20% of the generated power due to
20% slip. The exciter rotor power is converted into mechanical power, re-generated
as electrical power by the DFIG, and delivered to the grid via the stator. Note that
the rotor resistive losses are considered in the analysis, whereas the rotor converter
losses are neglected.
Furthermore, Figure 3.10 show unity power factor operation of the generator,
thereby confirming that with the help of the rotating exciter and converters, the
rotor of the DFIG can be used to generate reactive power, self-excite the DFIG, and
if need be, reactive power can even be delivered to the grid. The unity power factor
operation is also shown in Figure 3.8b, where the stator reactive power drawn from
the grid is zero.
Similar trend is observed for the operation of the RPE-BDFIG during the subsynchronous mode, as shown in Publication II.
3.3
Steady-State Model of the RPE-BDFIG
Publication IV presents the steady-state model of the RPE-BDFIM, when operated as a motor. The model is based on induction principles, as it is function of
slip. Hence, it is seen that the generator looses control at the synchronous speed of
10
5
0
−5
−10
−15
−20
40
60
80
100
120
Time (sec)
140
160
Exciter Rotor Power (kW)
DFIG Rotor Power (kW)
3.3. STEADY-STATE MODEL OF THE RPE-BDFIG
29
20
15
10
5
0
−5
−10
40
(a) DFIG rotor power.
60
80
100
120
Time (sec)
140
160
(b) Exciter rotor power.
Stator Power Factor (pu)
Figure 3.9: DFIG rotor and exciter power at 1800 rpm.
1
0.5
0
−0.5
−1
40
60
80
100
120
Time (sec)
140
160
Figure 3.10: Power factor at the RPE-BDFIG stator terminals at 1800 rpm.
the RPE-BDFIG. However, in reality, as we know from Publication III, that this
is not true. The steady-state model is inadequate as it does not consider the synchronous operation of the RPE-BDFIM. This is because at synchronous speed, slip
in the steady-state model is zero, resulting in zero torque. In reality, however, the
characteristics of the machine change from an induction machine to a synchronous
machine. Thus, in the steady state, mathematics considering the synchronous operation of the generator needs to be included, in order to predict the performance of
the generator during the synchronous mode. In the thesis, the dynamic model presented in Publication I and Publication II covers all three modes of operation,
including the synchronous mode which is specifically dealt within Publication III.
Chapter 4
Closed-Loop Control of a
RPE-BDFIG
This chapter presents the derivation, development, hardware implementation, and
measurement results of the closed loop control of the RPE-BDFIG. The control
employs current, speed, dc-link voltage controllers, and a phase-locked loop.
This chapter is based on Publication I, Publication II, Publication III, Publication V, and the author’s licentiate thesis [3].
With the advent of the vector control method, the dynamic control performance
of an ac machine was considerably enhanced. This is because the slowly varying
flux component (due to inherent large time constant) is controlled independently of
torque, similar to a separately excited dc machine [41]. Due to the aforementioned
reasoning, in this thesis, the vector control approach is adopted in a synchronous
reference frame, in order to control the RPE-BDFIG.
4.1
Reference Frames
The generator is controlled in a closed-loop fashion using the field oriented vector
control. In the first step, the three-phase quantities of the generator are expressed
in a two-phase stationary reference frame, the αβ frame. This is achieved using
Clarke’s transformation [41], expressed as
#
"
1 − 12 − 21
√
√
Tαβ = K
,
(4.1)
3
0
− 23
2
where K =
this thesis.
2
3
refers to the amplitude invariant transformation, which is used in
31
32
CHAPTER 4. CLOSED-LOOP CONTROL OF A RPE-BDFIG
Figure 4.1: Reference frames for the control of the RPE-BDFIG.
The quantities in an αβ coordinate system produce the same effect in the generator as the quantities in a three-phase abc reference frame. However, the analysis
of the generator becomes simpler in an αβ coordinates, since the three-phase quantities are reduced to the two-phase quantities. The common practice of fixing the
αβ frame is by aligning the α axes to phase a of the three-phase windings [41].
The variables in the αβ reference frame are further transformed to a coordinate
system, which rotates in synchronism with a state-variable of the generator, such
as flux or voltage. As a result, implementation of the proportional-integral (PI)
controller becomes possible, since for these controllers, the state-variables of the
generator must have dc values in steady-state. The transformation from the stationary reference frame to the synchronous reference frame is commonly referred
to as Park’s transformation [41], expressed as
"
Tdq =
cos θ
sin θ
−sin θ
cos θ
#
.
(4.2)
Accordingly, if one of the axes is aligned with the stator flux, the active and
reactive powers of the generator are controlled independently, thereby resulting
in a high dynamic performance of the generator. This is similar to mimicking
a dc machine, which is the main motivation for implementing the control in the
synchronously rotating dq frame [41].
The choice of reference frames used for the control of the RPE-BDFIG is illustrated in Figure 4.1.
4.2. VECTOR CONTROL
33
Figure 4.2: Closed-loop current control and model of the exciter.
4.2
Vector Control
Closed-loop control of the generator is necessary, since the total dynamic behavior
of the generator is affected by the interaction of the dynamics of the DFIG and
the exciter. This is because the exciter also exerts a fraction of the torque on the
shaft and therefore, the DFIG needs to handle the torque transients both from the
turbine and the exciter. This demands design of controllers which are fast, robust,
and stable. Therefore, the need of vector control.
The control of the generator is implemented in the dq frame, where the d-axes
is aligned with the grid flux and the q-axes is in quadrature. As a result, the
reactive power is controlled through the component of the current in the d axes,
whereas the active power is controlled through the component of the current in
the q axes. In this way, the flux and torque controlling current components are
controlled independently.
In order to realize vector control of the RPE-DFIG, two current controllers,
one speed controller, one voltage controller, and a phase-locked loop are all that
are needed for proper control of the generator. These controllers are explained in
detail in Publication I and summarized in the following sections.
As mentioned above, two current controllers are designed; one controls the DFIG
rotor converter, whereas the other controls the exciter rotor converter. Each of the
two current controllers, uses two independent proportional-integral (PI) regulators,
in order to control the d- and q-axes rotor winding currents, respectively.
4.2.1
Exciter Rotor Converter Control
The main aim of the exciter rotor converter is to control the dc-link voltage and
handle the slip power of the DFIG.
The electrical transfer function of the exciter is based on its electrical dynamic
34
CHAPTER 4. CLOSED-LOOP CONTROL OF A RPE-BDFIG
model, and is written as
Gc,exc (s) =
i00
3dq (s)
(s)
v00
3dq
=
1
00 .
R300 +jω3 L00
3 +sL3
(4.3)
00
where v3dq
, i003dq , R300 , and L003 are the exciter rotor voltage, rotor current, rotor
winding resistance, and rotor leakage inductance, respectively.
The cross-coupling coefficient jω3 L003 is cancelled by using jω3 L003 in the positive
closed-loop path. Furthermore, as shown in Figure 4.2, the active damping coefficient for the exciter Ra2 is used in the closed-loop path of the Gc,exc (s), in order
to improve the dynamic performance of the exciter model [42, 43]. Incorporating
the cross-coupling cancellation and active damping effects, the modified transfer
function is obtained as
G0c,exc (s) =
i00
3dq (s)
v00
(s)
3dq
=
1
.
R300 +Ra2 +sL00
3
(4.4)
Using the IMC design method, the current controller for the exciter is obtained
using the transfer function in (4.4) [42, 43]. Placing the exciter current controller
Fc,exc (s) in a cascade configuration with the exciter electrical model G0c,exc (s), and
solving from output of the exciter model to the input of the current controller, see
Figure 4.2, gives the closed-loop transfer function as
G0cl,exc (s) =
α
α
Fc,exc (s)G0c,exc (s)
c,exc
c,exc /s
=
=
.
0
1 + Fc,exc (s)Gc,exc (s)
s + αc,exc
1 + αc,exc /s
(4.5)
Thanks to the IMC theory, the parameters of Fc,exc (s) can now be written in terms
of the generator parameters, as
αc,exc 0−1
kic,exc
Gc,exc (s) = kpc,exc +
s
s
= αc,exc L003
Fc,exc (s) =
kpc,exc
kic,exc =
αc,exc (R300
+ Ra2 ).
(4.6a)
(4.6b)
(4.6c)
Choosing the active damping coefficient as [42, 43]
Ra2 = αc,exc L003 − R300 ,
(4.7)
makes the dynamics of G0c,exc (s) as fast as the closed-loop system bandwidth αc,exc .
Thus, the integral coefficient is modified to
2
kic,exc = αc,exc
L003 .
(4.8)
4.2. VECTOR CONTROL
35
Figure 4.3: Closed-loop current control and model of the DFIG.
4.2.2
DFIG Rotor Converter Control
The main purpose of the DFIG rotor converter is to control the active and reactive
power of the generator. Detailed derivation can be found in Publication I.
The DFIG rotor closed-loop current control is shown in Figure 4.3. Similar to the
exciter current controller, the DFIG current controller uses standard proportional
kpc and integral kic regulators, which are designed using IMC principles [42, 43].
The current controller is used in cascade configuration with the electrical transfer
0
function of the DFIG, Gc,DFIG (s), with rotor voltage reference, v2dq,ref
(s), as the
0
0
current controller’s output and rotor current error, i2dq,ref (s) − i2dq (s), as its input.
The Gc,DFIG (s) is based on the DFIG’s electrical dynamic model, as explained
in Publication I and Publication II.
It is also observed in Figure 4.3 that the cross-coupling coefficient jω2 (L1 + L02 )
in Gc,DFIG (s), which is the undesired result of the transformation from an αβ frame
to a dq frame, is cancelled by using jω2 (L1 + L02 ) in the positive closed-loop path
of Gc,DFIG (s) [42, 43]. Thus, the cross-coupling effects are cancelled provided that
the machine parameters are measured with considerable accuracy.
Moreover, as explained in Publication I, an active resistance coefficient [42,43],
Ra , is introduced in the closed-loop path of the Gc,DFIG (s), see Figure 4.3. As a
result, the dynamic performance of the DFIG model is set as desired with no impact
on the efficiency and losses of the generator.
4.2.3
Speed Controller
For optimum design of the closed speed-control loop, one must remember that the
RPE-BDFIG experiences additional torque disturbances from the rotating exciter—
not ignoring the fact that the rotating dc-link lies on the shaft—which needs to be
balanced at the same instant, without compromising the stability of the generator. Therefore, the speed/torque controller should be designed in a manner that
36
CHAPTER 4. CLOSED-LOOP CONTROL OF A RPE-BDFIG
Figure 4.4: Block diagram of a speed controller for a RPE-BDFIG.
the speed reference is followed, without a considerable overshoot in the speed and
torque—together with a good load-torque disturbance rejection. In the case of
RPE-BDFIG, choice of the degree-of-freedom (DOF) of the PI controller and its
parameter tuning is highly important, in order to minimize the steady-state error, introduced by the external disturbances, (i.e., torques of the turbine emulator
and rotating exciter). Moreover, as highlighted in [43], both good speed reference
tracking and load-torque disturbance rejection, cannot be realized through the use
of classical one-degree-of-freedom (1DOF) PI controller. It necessitates the use of
the two-degree-of-freedom (2DOF) PI controller [43, 44], in order to improve the
load-torque disturbance rejection. The modification in the speed-control design demands thorough understanding of the mechanical model of the RPE-BDFIG and
its speed controller. This is not as tedious as it may seem, in fact it is quite simple
to do—thanks to the IMC theory, used for the design of the closed speed-control
loop, as explained in Publication I, and summarized below.
As derived and explained in Publication I and seen in Figure 4.4, Gs (s) is the
transfer function representing the mechanical model of the RPE-BDFIG. Since the
friction coefficient is much smaller than the inertia of the generator, (resulting in a
poor load-torque disturbance rejection), an additional coefficient ba is introduced in
an inner feedback loop around the mechanical model [44]. As a result, the sensitivity
of G0s (s) to load disturbance rejection is made as fast as the bandwidth αs of the
closed speed-control loop. The speed controller also uses standard proportional kps
and integral kis regulators, with torque reference, Te,ref , as its output and speed
error, ωm,ref − ωm, , as its input. Tload is the external load torque and CT is a
machine dependent constant.
Note that, while designing the closed-loop speed control, the current dynamics are neglected. Therefore, αs must be at least a decade lower than the DFIG
closed current-control loop bandwidth, αc and the exciter closed current-control
loop bandwidth, αc,exc .
4.2. VECTOR CONTROL
1780
1780
Reference Speed
Measured Speed
1760
Speed [rpm]
1760
Speed [rpm]
37
1740
1720
1700
1740
1720
1700
1680
1680
1660
1660
−0.5
0
Time [sec]
0.5
(a) Step-up in speed.
Reference Speed
Measured Speed
−0.5
0
Time [sec]
0.5
(b) Step-down in speed.
Figure 4.5: Measurement results on an 11-kW RPE-BDFIG, when a step in speed
reference is applied.
Figure 4.5 show the measured response of a step in speed on an 11-kW prototype.
It is seen that the closed-loop speed control performs as expected in obtaining and
maintaining the reference speed of the generator.
4.2.4
DC-Link Voltage Controller
The task of dc-link voltage controller is to maintain a stable voltage across the
capacitor of the back-to-back converter, connected between the three-phase rotor
windings of the DFIG and the exciter. The dc-link closed-loop voltage control must
maintain constant voltage with out affecting the stable operation of the generator,
during transients in torque and speed. As shown in Publication I and simulation
results in Publication II, the dc-link voltage is vulnerable to torque and speed of
the generator because it is affected by the DFIG and exciter rotor powers. Moreover,
the reactive power control from the rotor of the generator also affects the dc-link
voltage, as explained in Publication V. In order to maintain a constant dclink voltage, the power entering/leaving the DFIG rotor must balance the power
leaving/enetering the exciter. The power balance between the DFIG rotor and
exciter rotor windings and the dc-link voltage dynamics are expressed [45] as
dv 2
1
Cdc dc = Pr,exciter − Pr,DFIG
2
dt
00 00
= 3v3q
i3q − Pr,DFIG ,
(4.9a)
(4.9b)
38
CHAPTER 4. CLOSED-LOOP CONTROL OF A RPE-BDFIG
Figure 4.6: Block diagram of a dc-link voltage model and its controller.
200
DC−Link Voltage [V]
DC−Link Voltage [V]
200
150
100
50
0
−0.5
0
Time [sec]
0.5
(a) DC-link voltage for a power step-up.
150
100
50
0
−0.5
0
Time [sec]
0.5
(b) DC-link voltage for a power step-down.
Figure 4.7: Measurement results on an 11-kW RPE-BDFIG for dc-link voltage
dynamics, when a step-up (2.7 kW to 6.6 kW) and step-down (6.6 kW to 2.7 kW)
in stator reference power is applied at t=0, respectively.
where Cdc is the capacitance and vdc is the dc-link voltage. Using Laplace transform, (4.9a)–(4.9b) are given in the frequency domain, as
1
2
00 00
Cdc svdc
(s) = 3v3q
i3q (s) − Pr,DFIG (s).
2
(4.10)
Accordingly, treating Pr,DFIG as an external disturbance, the transfer function of
the dc-link model is obtained as
Gv (s) =
2
vdc
(s)
6V3
=
,
00ref
sCdc
i3q (s)
(4.11)
where V3 is the nominal voltage of the exciter rotor windings.
It is observed that the pole of the dc-link model is at the origin, resulting in
a marginally stable system. However, as shown in Fig. 4.6, the problem can be
4.2. VECTOR CONTROL
39
Figure 4.8: Diagram of a phase-locked loop (PLL).
solved by introducing an inner feedback loop with a coefficient Ga referred to as
”active conductance” [45]. It moves the poles of the dc-link system to the left-half
plane. Ga acts on the output dc-link voltage, vdc , and modifies the input current
to the dc-link model, i003q [45], as shown in Fig. 4.6. i000
3q is the output current from
the dc-link voltage controller.
Using the internal model control principles, the dc-link voltage controller is
designed as a function of the dc-link model parameters [45]. The controller consists
of proportional kpv and integral kiv parameters.
The measurement results in Fig. 4.7, which are conducted on an 11-kW RPEBDFIG, show that the closed-loop dc-link control works well in maintaining the
reference voltage. At t=0, a step in power and torque is applied. It is seen that
the control is fast enough to maintain the dc-link reference voltage.
4.2.5
Phase-Locked Loop
In order to synchronize the generator to the grid, and keep its stable operation
during the steady- and transient conditions, it is necessary that the magnitude and
position of the grid voltage and flux vector is estimated with considerable accuracy.
In this thesis, this is achieved through the use of phase-locked loop (PLL), originally
proposed in [46]. The PLL is fast enough for dynamic and robust operation of the
generator. Detailed derivation can be found in Publication I.
The block diagram of the PLL is shown in Figure 4.8 [46]. The true grid flux
position θg and the estimated grid flux position θ̂ are fed to the phase-detector
(PD), which produces an error , on which the low-pass filter acts, in order to
generate the estimated grid frequency. The low-pass filter is composed of the ρ2 ,
2ρ, and the integrator [46]. The estimated frequency is integrated further to give
the estimated grid position θ̂. When θ̂ approximates θg , approaches zero, thereby
40
CHAPTER 4. CLOSED-LOOP CONTROL OF A RPE-BDFIG
(a) Power electronics, dSpace control, and power meter.
(b) Load machine, DFIG, and exciter.
Figure 4.9: Laboratory setup of an 11-kW RPE-BDFIG.
giving true estimates of the grid flux position and frequency.
ρ defines the disturbance rejection of the PLL [46]. Note that, ρ must be in the left
half plane of the frequency domain.
4.2.6
Control Performance
The experimental results in Publication I and simulation results in Publication
II indicate that the closed-loop current control functions well in maintaining the
desired torque, speed, and rotor converter dc-link voltage references.
Another prime focus of the findings in Publication I was also to study the
stability of the control when subjected to sudden large transients in torque or
power. The study was conducted on an 11-kW prototype in the laboratory shown
in Figure 4.9. Figure 4.10a and Figure 4.10b show measurement results of the
4.2. VECTOR CONTROL
41
8
10
Reference Power
Measured Power
Stator Power [kW]
Stator Power [kW]
10
6
4
2
0
−0.1
−0.05
0
0.05
Time [sec]
6
4
2
0
−0.1
0.1
50
50
40
40
30
20
0
−0.5
Reference Torque
Measured Torque
0
Time [sec]
(c) Torque dynamics.
−0.05
0
0.05
Time [sec]
0.1
(b) Power dynamics.
Torque [Nm]
Torque [Nm]
(a) Power dynamics.
10
Reference Power
Measured Power
8
30
20
10
0.5
0
−0.5
Reference Torque
Measured Torque
0
Time [sec]
0.5
(d) Torque dynamics.
Figure 4.10: Experimental results for the stability study conducted on an 11-kW
RPE-BDFIG at 1750 rpm, i.e., in the super-synchronous mode.
control performance of the generator when subjected to a step in power, in the
super-synchronous mode. It is seen that the dynamic response of the generator
is fast as the power reference set-point is achieved with considerable accuracy and
speed. Same trend is also seen in Figure 4.10c and Figure 4.10d, where the generator
follows a step in the torque. The results confirm that the closed-loop control has a
good dynamic performance, since it meets the desired changes in reference torque
and power set points. Similar conclusions can be drawn in the sub-synchronous
mode, as illustrated in Figure 4.11a to Figure 4.11d.
Besides, findings of the experimental results in Publication V indicate that
large amounts of reactive power, i.e., which result in the change in power factor
of the RPE-BDFIG from inductive to capacitive, as shown in Figure 4.12, can
be supplied to the grid. It is seen in Figure 4.12 that stator current is minimum
at unity power factor, due to zero magnitude of the reactive component of the
42
CHAPTER 4. CLOSED-LOOP CONTROL OF A RPE-BDFIG
8
10
Reference Power
Measured Power
Stator Power [kW]
Stator Power [kW]
10
6
4
2
0
−0.1
−0.05
0
0.05
Time [sec]
8
6
4
2
0
−0.1
0.1
(a) Power dynamics.
40
Torque [Nm]
Torque [Nm]
0
0.05
Time [sec]
0.1
50
Reference Torque
Measured Torque
30
20
10
0
−0.5
−0.05
(b) Power dynamics.
50
40
Reference Power
Measured Power
Reference Torque
Measured Torque
30
20
10
0
Time [sec]
(c) Torque dynamics.
0.5
0
−0.5
0
Time [sec]
0.5
(d) Torque dynamics.
Figure 4.11: Experimental results for the stability study conducted on an 11-kW
RPE-BDFIG at 1410 rpm, i.e., in the sub-synchronous mode.
current. Thus, the result in Figure 4.12 and in Publication V indicate that the
generator can be used to assist in maintaining the grid voltage stability. Besides,
stable operation of the RPE-BDFIG during variable reactive power generation also
confirms the validity of the implemented control.
4.2. VECTOR CONTROL
43
Stator Current (A)
15
10
5
0
0
Speed=1350 rpm
Speed=1400 rpm
Speed=1600 rpm
Speed=1700 rpm
0.5
1
Stator Power Factor
Figure 4.12: Measurement results of the 11-kW RPE-BDFIG’s stator current versus
stator power factor, at various speeds. In the power factor scale, capacitive power
factor operation is illustrated for values greater than 1.
Chapter 5
Low-Voltage Ride-Through of a
RPE-BDFIG
This chapter presents the low-voltage ride-through behaviour of the RPE-BDFIG.
It highlights different types of grid faults, which the generator must be capable of
riding through. Moreover, a suitable control strategy is introduced, in order to limit
oscillations during unsymmetrical faults.
This chapter is based on Publication VI, Publication VII, Publication
VIII, and the author’s licentiate thesis [3].
5.1
Introduction
The RPE-BDFIG also suffers from the same drawback as the slip-ring DFIG, with
regards to low-voltage ride-through (LVRT) of the generator. This is because the
RPE-BDFIG also consists of a partially-rated rotor mounted power electronic converter. Therefore, when the stator voltage drops at the stator terminals, the stator
current starts increasing. Since in an induction generator, the stator and rotor are
mutually coupled, scaled only by the number of winding turns, the rotor current
also starts increasing. For a deep voltage dip, the rotor current increases to such an
extent that, unless a suitable control measure is adopted, the rotor converter can be
severely damaged [47–51]. Moreover, large inrush rotor currents lead to over-voltage
in the dc-link and large transients in the torque. Thus, it is a major challenge for
generators operating with a partially-rated converter, which is unfortunately, also
the case with the RPE-BDFIG.
Besides, according to the European standard EN 50160 [52], one of the com45
46
CHAPTER 5. LOW-VOLTAGE RIDE-THROUGH OF A RPE-BDFIG
mon unsymmetrical voltage unbalances resulting in the power network are within
2–3% of the rated voltage. This is due to single-phase loads, unbalance loads, nonuniform impedances of the transmission lines and transformers, and non-uniform
compensation of the three-phases from the capacitor banks [53, 54]. Therefore, the
power plant components must comply and withstand these variations. As a result,
during the unsymmetrical grid faults, the generator is required to stay connected,
ride through voltage dips and, in fact supply reactive power in order to assist in reestablishing the nominal grid voltages. Hence, this motivates mitigation measures
such as elimination of negative-sequence current, in order to suppress oscillations
and protect the generator components. Due to the aforementioned reasons and
the fact that the unsymmetrical faults are one of the most common faults occurring in the power network, the wind generator must operate stably during such
faults. Therefore, depending on the voltage dip and grid code requirements, different strategies needs to be adopted for saving the converter from damage.
One of the commonly used measures for protection of the power electronic converter is through the use of rotor crow-bars [47–49, 51]. In this technique, the rotor
resistors with switches are connected to the rotor of the DFIG. Hence, when a grid
faults occurs, the crow-bar circuit is connected in series with the rotor resistance. A
large rotor resistance limits the rotor current, thereby saving the power electronics
from damage, and preventing acceleration of the wind turbine. However, for the
case, when the crow-bar resistances are connected and power electronic converter
is disconnected, the DFIG acts as a single-fed induction generator, consuming reactive power from the grid. This has negative impact on the voltage stability of the
electrical network, which means that the grid code requirements are not fulfilled.
In the past several studies have been conducted in order to prevent disconnection
of the converter during the crow bar operation, e.g., [48] presents a crowbar, which is
controlled via thyristor bridges, connected in parallel with the rotor-side converter,
whereby the rotor converter is still connected to the grid during the fault. One
major drawback of such control is that the controllability margin is low, since high
impedance in parallel to the converter reduces the rotor current, but at a cost of high
voltages across the rotor converter. To offset this effect, [55] proposes connection
of the crowbar in series with the rotor windings, in order to limit the rotor voltages
and currents, and maintain the connection of the rotor converter during the fault.
In such configuration, the rotor currents do not bypass the converter during the
fault, but flows into it. However, the device count increases as bypass switches
are required during normal operation. Nevertheless, using the modified crowbar
protection circuit, the generator is in a better position of fulfilling the grid codes,
but at an increased cost.
5.2. GRID CODES
47
Figure 5.1: E.oN grid code standard for a low-voltage ride-through of a wind turbine.
5.2
Grid Codes
The grid codes define the rules and requirements for a generating unit, in order to
set forth proper and stable operation of the electrical network. Nowadays, most of
the grid codes have been updated, including the codes for the wind turbine, which
put them in the same category as the conventional power units, such as steam, gas,
and hydro turbines. This implies that the wind generator shall support the grid
and supply reactive current during the fault. This is because in the last decade, the
percentage of power from wind has risen considerably, especially in Europe. Thus,
during a fault in the grid, the transmission system operators can not allow and
afford disconnection of the wind power plants from the grid. Doing so will cause
blackout and stability problems.
As an example, consider one of the established grid operator E.oN, who have
written grid codes, see Figure 5.1, which puts forth the requirements that the wind
turbine must supply reactive current and support the grid for 150 msec for a 100%
voltage dip, and for 325 msec for a 85% voltage dip [56]. As shown in Figure 5.1, the
wind turbine must stay connected over the limit line (solid blue line, region I) [56],
and must operate continuously for voltages down to 90% of its nominal value.
Moreover, the reactive power control must be activated within 20 msec, when the
48
CHAPTER 5. LOW-VOLTAGE RIDE-THROUGH OF A RPE-BDFIG
voltage drops below 90% [56]. It also states that the generated reactive current
must be at least 2% for each percentage of the voltage dip, when the voltage is
below 90% of its nominal value. After the voltage has recovered to its nominal
value [56], the reactive power control must continue to remain active for another
500 msec.
Besides, it is documented in standards like EN 50160 [52], that the unsymmetrical voltage variations of 2% are periodically and commonly present in the electrical
network during its normal operation. Therefore, these conditions demand that the
generator’s control is well adapted, in order to meet such requirements.
5.3
Voltage Dips and Types of Faults
A voltage dip is a temporary reduction (0.5–30 cycles) in the voltage due to faults
in the network or during starting of heavy loads [57–59]. The voltage dip can cause
serious problems in industry as this would lead to malfunctioning and tripping of
equipments and thereby loss of production. Therefore, the sensitivity of different
type of equipments, devices, and generation units to the various voltage dips, is an
important aspect which needs to be addressed. This will assist in developing means
to ride through such dips.
The most common types of faults occurring in the power network are the unsymmetrical faults, such as single-phase-to-ground faults (SPGF) and phase-to-phase
faults (PPF) [57–59]. In contrast, the occurrence of the symmetrical fault, i.e.,
three-phase fault is less frequent, but is more severe in terms of magnitude, than
its unsymmetrical counterpart. The three-phase faults occur due to starting of
large induction motors, energizing of transformers, short-circuit of electrical lines
due to lightning strike, wind, ice, tree or animal contact, and construction equipment [57–59]. At the transmission level, the most common cause of the SPGF is
due to a lightning strike [57, 59].
During a fault, the magnitude and phase-angle-jump of a voltage at a location,
depends on the impedance of the network, its distance from the fault location,
types of equipment connected in between and their connection types [57–59], e.g.,
transformers connected in delta or wye, and type of fault.
The phase-angle-jump is defined as a change in the angle of the voltage before
and during the fault [58, 60, 61].
5.3.1
ABC Classification
One common way of categorizing the faults in the three-phase system is using ABC
classification. It covers seven types of three-phase faults [62]; one symmetrical and
remaining six unsymmetrical faults, as shown in Figure 5.2. The classification is
5.4. BEHAVIOUR OF THE RPE-BDFIG DURING FAULTS
49
Figure 5.2: Classification of the voltage dips.
based on an assumption that the positive- and negative-sequence source impedances
are equal. Moreover, this classification takes into account the change in the fault
type during propagation through the transformer [62].
The type A fault is due to a three-phase (symmetrical fault), where the voltage
drops equally in the three-phases [62]. The type B fault is due to a single-phaseto-ground fault (SPGF), where the voltage drops in one phase only. The type
C fault is due to a phase-to-phase fault (PPF) or, SPGF fault which propagates
through the delta-wye transformer. The voltage drops in the two phases with an
associated phase-angle-jump [59, 62]. The type D fault is a PPF which propagates
through a delta-wye transformer or, SPGF which propagates through two deltawye transformers [59, 62]. The voltages in the three phases drop, whereas two of
the three phases also suffer from a phase-angle-jump [59, 62]. The type E fault is
due to a phase-to-phase-to-ground fault (PPGF), in which the voltage in the twophases drop in magnitude only, whereas the third phase remains unaffected [62].
The type F fault is also due to a PPGF, when it propagates through a delta-wye
transformer. Similarly, the type G fault is also a PPGF, when it propagates through
two delta-wye transformers.
5.4
Behaviour of the RPE-BDFIG during faults
The RPE-BDFIG behaviour during faults is directly dependent on stator flux oscillations, which are caused by the variations in the grid voltage. Therefore, control of
50
CHAPTER 5. LOW-VOLTAGE RIDE-THROUGH OF A RPE-BDFIG
the stator flux can limit the oscillations in the generator. However, this is challenging since the generator is directly connected to the grid, without external hardware
or control interface in between. This means that the rotor converter needs to act
through the agency of the rotor, in order to control the stator flux dynamics.
The mathematical treatment of the behavior of the RPE-BDFIG during faults
is given in Publication VII, whereas Publication VI presents the behaviour
of the RPE-BDFIG during symmetrical faults, when a passive resistive network
(PRN) is used, in order to protect the generator (see Section 5.4.1). The analysis
of the generator during successful ride through of unsymmetrical voltage dip, with
the help of dual vector control is presented in Publication VII, Publication
VIII, and Section 5.4.2.
5.4.1
Passive Resistive Network
Since the rotor winding terminals are not accessible in a RPE-BDFIG, an alternating technique needs to be implemented and investigated, in order to protect the
converter from damage and limit the acceleration of the turbine. In Publication
VI, a passive resistive network (PRN) proposed in [63], is adopted for the RPEBDFIG. This is because the PRN can be implemented at the stator terminals of
the RPE-BDFIG, which is of interest in our application.
The PRN is used as an external protection circuit, in order to protect the
generator and power electronic converter from damage, during deep voltage dips.
The PRN comprise of; a set of resistor Rs connected in parallel with the IGBT
switch SA , which are further connected in series with the generator stator windings,
and another set Rp and SB connected in parallel with the stator windings [63], as
shown in Figure 5.3. The combination of Rs and SA are used to dampen the stator
flux oscillations in the stator windings, which further dampen the rotor oscillations,
thereby protecting the converter from damage [63]. The combination of Rp and
SB consume part of the generated electrical power, in order to balance the input
mechanical power during the fault [63].
The values of the resistances are chosen such that they decide the total generated
stator current i1 , as
i1 = kA
v1 − vg
v1
+ kB
Rs
Rp
= i1s + i1p ,
(5.1)
(5.2)
where kA and kB defines the control logics of the switches SA and SB [63], respectively. Their modulation is dependent on the magnitudes of the voltage dips
and the operating region of the generator with regards to power generation. The
desired current is the short-circuit current, which needs to be supplied to the grid
5.4. BEHAVIOUR OF THE RPE-BDFIG DURING FAULTS
51
Figure 5.3: Single-phase diagram of a passive resistive network.
according to the grid code requirements. In this way, the stator flux dynamics are
controlled, thereby avoiding fluctuations in the rotor currents and voltages. Thus,
the series resistance is calculated, as
Rs =
v1 − vg
.
i1s
(5.3)
The maximum value of the series resistance Rs occurs when the fault in the grid
causes the grid voltage to drop to zero. Thus, the modulation of switch SA should
occur in a manner, such that the series resistance Rs takes the difference between the
stator generated voltage v1 and the grid voltage vg during the fault and thereby,
counteracts voltage fluctuations across the stator terminals.
The value of the
parallel resistance Rp depends on the active power generated by the turbine. Immediately after the fault, it is obvious that the rated power cannot be delivered to
the grid. Since the mechanical power is the same, there is a need to maintain power
balance between the generated output power and the input mechanical power. This
is achieved by supplying part of the generated power to the grid, and the remaining
is dissipated into Rp as losses. The value of Rp depend on the operating power
region of the turbine and is selected by modulating the switch SB . The maximum
power limit of the resistance can be obtained for the scenario when the rated power
is wasted in Rp , i.e., no power is delivered to the grid. Thus, the parallel resistance
is calculated, as
v1
.
(5.4)
Rp =
i1p
The use of PRN offers the advantage that during the fault, the generator stays
connected to the grid, and supplies the reactive current, in order to improve the
voltage stability. As a result, the grid code requirements can be fulfilled. Furthermore, since the rotor converter is operating during the fault, therefore, when the
CHAPTER 5. LOW-VOLTAGE RIDE-THROUGH OF A RPE-BDFIG
100
0
−100
v
−200
vb
v
−300
130
130.1
a
130.2
Time (sec)
130.3
−1
7000
6000
130.2
Time (sec)
130.3
130.1
130.2
Time (sec)
130.4
130.4
d−axis current
q−axis current
−20
−40
−60
−80
−100
130
130.1
130.2
Time (sec)
−6000
−7000
−8000
−9000
130.3
130.4
130
130.1
130.2
130.3
Time (sec)
130.4
(c) DFIG rotor power
3.5
3
2.5
2
d−axis flux
q−axis flux
1.5
1
0.5
0
(e) DFIG rotor current
130
130.1
130.2
Time (sec)
130.3
130.4
(f) Exciter rotor flux
1840
Rotor Speed (rpm)
420
410
400
390
380
130.3
0
(d) Exciter rotor power
Capacitor Voltage (V)
130
−5000
(b) RPE-BDFIG stator flux
DFIG Rotor Current (A)
Exciter Rotor Power (W)
8000
130.1
−0.5
−1.5
130.4
9000
130
d−axis flux
q−axis flux
c
(a) Three phase grid voltages
5000
0
Exciter Rotor Flux (Wb)
200
DFIG Rotor Power (W)
0.5
300
Stator Flux (Wb)
Phase Voltages (V)
52
130
130.1
130.2
Time (sec)
130.3
130.4
(g) Rotor converter DC-link voltage
1820
1800
1780
1760
130
130.1
130.2
Time (sec)
130.3
130.4
(h) Shaft speed
Figure 5.4: Response of RPE-BDFIG at 37-kW operation and 85% voltage dip using
PRN protection scheme, (a) three-phase grid voltages, (b) RPE-BDFIG stator flux,
(c) DFIG rotor power, (d) exciter rotor power, (e) DFIG rotor current, (f) exciter
rotor flux, (g) rotor converter dc-link voltage, (h) shaft speed.
fault is cleared, synchronization of the converter to the grid is not required. This
leads to an immediate resumption of power to the grid.
The analysis conducted on the 37-kW RPE-BDFIG in Publication VI deals
with 85% voltage dip during symmetrical faults, based on E.oN grid code specifications. As explained in the publication and shown in Figure 5.4, it is seen that
PRN works well in reducing the amplitude of the rotor current during the 85%
voltage dip. Moreover, the magnitudes of oscillations in rotor power, speed, and
dc-link voltage, during the instant at which the fault begins at t=130 msec, are
5.4. BEHAVIOUR OF THE RPE-BDFIG DURING FAULTS
53
also reduced, thereby preventing adverse affects on the electrical and mechanical
components of the RPE-BDFIG.
5.4.2
Dual Vector Control
In order to deal with the negative-sequence currents, the dual vector control (DVC)
[also referred to as extended vector control (EVC)] is used, in order to control
the generator [51, 64, 65]. The DVC is implemented in the dq frame. As explained in Publication VII and Publication VIII, two dq frames are defined;
the positive-sequence dq + frame and the negative-sequence dq − frame [51, 64, 65].
The d-axes of the dq + frame is aligned with the positive-sequence grid flux vector.
Hence, it rotates with the positive-sequence grid-flux angular frequency. The d-axes
of the dq − frame is aligned with the negative-sequence grid flux vector, which rotates in the opposite direction to the positive-sequence grid flux, also with the grid
angular frequency. The negative-sequence components of the voltage and current
appear as 100 Hz oscillations in the positive-sequence frame, whereas the positivesequence components of the voltage and current appear as 100 Hz oscillations in
the negative-sequence frame. A lowpass Butterworth filter is designed and implemented, in order to filter 100 Hz oscillations in the two reference frames. Thereafter,
the positive-sequence and negative-sequence currents are controlled independently
in their respective dq frames [51, 64, 65].
As explained in Publication VII and Publication VIII, the prime focus of
the control has been to reduce the oscillation in the electrical and mechanical parts
of the generator, in order to prevent reduction in the lifetime of the generator’s
components. Figure 5.5 show the simulation results when the DVC is implemented
on a 2-MW RPE-BDFIG operating at 1800 rpm. The generator is subjected to
a single-phase-to-ground fault (SPGF). The fault causes a 100% voltage dip, and
a phase-angle jump of 45°in phase a. It is seen that the DVC works well, since
the negative-sequence currents are controlled in a manner which minimizes the
electrical and mechanical oscillations in the RPE-BDFIG. However, as seen in Figure 5.5(i) and Figure 5.5(j), the DFIG rotor current increases by 50% and the
exciter rotor current experiences a large current peak in the first 150 msec after the
fault. Consequently, either the size of the rotor converter needs to increase or, PRN
should be used in order to limit the increase in the rotor currents. To summarize,
DVC can be employed with a great deal of success in reducing the oscillations in
the RPE-BDFIG. A PRN might also be required to limit the increase in the rotor
currents.
400
200
0
va
vb
vc
−600
429.9 429.95 430 430.05 430.1
−6
−8
−10
−12
−14
430
Time (sec)
5
0
−5
−10
430.5
431
Time (sec)
10000
6000
4000
2000
0
431.5
430
1000
0
430.5
431
Time (sec)
10
5
0
0
I3d
−50
I3q
430
430.5
431
Time (sec)
431.5
(j) exciter rotor current
430
430.5
431
Time (sec)
430.5
431
Time (sec)
431.5
1000
0
−1000
−2000
−3000
−4000
430
430.5
431
Time (sec)
431.5
(f) DFIG rotor power
5
0
−5
431.5
(h) stator current
DC−Link Voltage (V)
50
431.5
d−axis current
q−axis current
15
−5
431.5
100
431
Time (sec)
DFIG rotor I , I
Stator I1d, I1q (kA)
Exciter Rotor Power(kW)
2000
(g) exciter rotor power
Exciter Rotor Current(A)
430.5
20
430
430
(e) stator power
3000
−100
Active power
Reactive power
8000
(d) exciter torque
−1000
−60
(c) RPE-BDFIG torque
DFIG Rotor Power (kW)
10
430
Time (sec)
431.5
−40
(kA)
15
−15
431
−20
(b) turbine torque
Stator Power (kW,kVAr)
Exciter Torque (kNm)
(a) grid voltages
430.5
0
2q
−400
−4
2d
−200
−2
−10
DFIG rotor d−current
DFIG rotor q−current
−15
−20
430
430.5
431
Time (sec)
431.5
(i) DFIG rotor current
2200
1200
Speed (rpm)
Grid Voltage (V)
600
RPE−BDFIG Torque(kNm)
CHAPTER 5. LOW-VOLTAGE RIDE-THROUGH OF A RPE-BDFIG
Turbine Torque (kNm)
54
1100
1000
900
2000
1800
800
430
430.5
431
Time (sec)
431.5
(k) dc-link voltage
1600
430
430.5
431
Time (sec)
431.5
(l) mechanical speed
Figure 5.5: Behavior of the RPE-BDFIG during the SPGF, for a 100% voltage dip,
and phase-angle jump of 45°in phase a: (a) grid voltages, (b) turbine torque, (c)
RPE-BDFIG torque, (d) exciter torque, (e) stator power, (f) DFIG rotor power,
(g) exciter rotor power, (h) stator current, (i) DFIG rotor current, (j) exciter rotor
current, (k) dc-link voltage, and (l) mechanical speed.
Chapter 6
Design and Thermal Aspects of a
Rotating Power Electronic
Converter (RPEC)
This chapter presents a preliminary design and 3-D thermal analysis of a rotating
power electronic converter for an 11-kW generator.
This chapter is based on Publication IX and Publication X.
6.1
Rotating Electronics
Power electronics on the rotor of electrical machines has been used since 1960s,
especially in brushless synchronous generators [66, 67]. The diode rectifier with
a rotating exciter are commonly used, in order to supply the dc field current to
the rotor windings of the synchronous generator, without slip rings and carbon
brushes [66,67]. Synchronous generators are used for large-scale electric power production, such as in hydro generators. These type of brushless generators are currently produced by ABB, Westinghouse Electric Corporation [66], WEG group [67],
etc.
In a brushless synchronous generator, the brushless rotating exciter and its
diodes take care of reactive power. In contrast, in the RPE-BDFIG, the rotating
exciter and the converters take care of both the active power, i.e, slip power of
the DFIG, and the reactive power of the generator. Thus, requirements from the
RPE-BDFIG exciter and its converter are more demanding than its synchronous
generator counterpart. Since, the converters and exciter of the RPE-BDFIG also
55
56
CHAPTER 6. DESIGN AND THERMAL ASPECTS OF A ROTATING
POWER ELECTRONIC CONVERTER (RPEC)
handle active power, greater demands are placed on their size optimization and
cooling. A preliminary finite element analysis of the thermal modeling of the RPEC
for the RPE-BDFIG is given in Publication IX and Publication X, where a
3-D study has been conducted for a converter suitable to be mounted on an 11kW generator. In this publication, the thermal footprint on different parts of an
IGBT, rotating shaft, and its heatsink are analysed using the finite element method
(FEM). Furthermore, the dimensions of the heatsink, and the shaft fan which cools
the rotating converter and the generator, are also investigated in Publication IX
and Publication X.
A conceptual design of the converter is shown in Figure 6.1 and explained
in Publication IX. The outer radius of the converter is 160 mm, which can be
mounted on an 11-kW RPE-BDFIG, whose shaft height is 180 mm. The rotating
converter is composed of two wheels. The outer wheel is made of aluminium and
holds the components of the converter against the centrifugal forces. The outer
wheel is connected to the internal wheel through the thin rods (not shown in the
figure). The internal wheel is screwed to the shaft and thereby holds the whole
converter on to the shaft.
Figure 6.2 summarizes the maximum junction temperatures of the IGBT switch
obtained from the FEA. The IGBT is switched at 5 kHz and operated at the rated
rotor current of the 11-kW RPE-BDFIG, i.e., 43 A. The FEA is conducted for the
IGBT when it is cooled by the heatsink and forced convection through the shaft
mounted fan. The study is performed for two heatsinks. Heatsink 2 is one-third
the size of Heatsink 1. It is seen that the Heatsink 2 is sufficient to cool the IGBT
(as the maximum junction temperature is around 123° C, which is below the rated
junction temperature of 125° C), when the inlet velocity of air blown by the shaft
fan is more than 3 m/s. As seen in Figure 6.3, this velocity of air can be easily
obtained from the shaft mounted fan of the generator with 180 mm shaft height.
Hence, it can be concluded that the size of the heatsink and the cooling offered by
the shaft fan are sufficient, in order to mount the converter on the limited space
offered by the generator.
6.1. ROTATING ELECTRONICS
57
Figure 6.1: The rotating power electronic converter (RPEC).
Max. Temp. ( °C)
150
100
50
Heatsink 1
Heatsink 2
0
0
10
20
Air Velocity (m/s)
30
Figure 6.2: Maximum steady-state junction temperatures of the IGBT versus air
velocities, when cooled by Heatsink 1 and Heatsink 2 through forced convection.
CHAPTER 6. DESIGN AND THERMAL ASPECTS OF A ROTATING
POWER ELECTRONIC CONVERTER (RPEC)
Inlet air velocity (m/s)
30
20
Fan radius 30 mm
Fan radius 140 mm
10
0
1200
1400
1600
Rotor speed (rpm)
1800
(a) Velocity of air as a function of rotor speed for
two different radius of the fan.
150
Fan radius (mm)
58
100
50
0
2000
1500
Rotor speed (rpm) 1000 0
10
20
30
Inlet air velocity (m/s)
(b) 3-D diagram of the air velocity versus fan radius versus rotor
speed.
Figure 6.3: Size of the shaft mounted fan.
Chapter 7
Unity Power Factor Operation of a
Single-fed Induction Machine using
the Lindmark Concept
This chapter gives an overview of a single-fed induction machine with the rotating
electronics.
This work was performed in the beginning of the author’s Ph.D project and is
included because this concept is also based on the rotating power electronics.
This chapter is based on Publication XI, Publication XII, and the author’s
licentiate thesis [3].
7.1
Rotating Power Electronic Induction Drive
This chapter summarizes an invention by Magnus Lindmark [68], which utilizes
a single-fed induction machine with two rotating power electronic converters connected to its rotor, as shown in Figure 7.1. The generator uses three-phase windings
in the stator, which is directly connected to the grid, whereas the rotor uses threephase windings in an open-end configuration. This means that both terminals of
the rotor windings are available for connection. One of the terminals of the threephase windings are connected to one of the three-phase converter, whereas the other
corresponding terminals of the rotor windings are connected to the second threephase converter, as shown in Figure 7.2. The two converters are connected to each
other in a back-to-back configuration, with a dc-link in between.
59
60
CHAPTER 7. UNITY POWER FACTOR OPERATION OF A SINGLE-FED
INDUCTION MACHINE USING THE LINDMARK CONCEPT
Lindmark phase-shifted the voltages produced by the two converters with respect to each other by an angle θps , in order to generate another voltage vector
referred to as vps . This voltage vector is applied to the terminals of the rotor windings, which thereby changes the angle of the rotor current. Since the stator and
rotor currents are mutually coupled, therefore, the angle of the stator current also
changes. Through proper control strategy, the angle of the stator current is made
to change in a manner so as to improve the power factor. Hence, the rotor of the
converter is used to inject reactive power, thereby improving the power factor of
the machine, as explained in detail in Publication XI and Publication XII.
In Publication XI, the steady-state model is developed and verified through
experiments on an 11-kw prototype machine. It is seen in Figure 7.3, that the
unity power factor of the machine is obtained over a wide power range, i.e., from
3-kW to its rated 11-kW power. In addition, it is also explained in Publication
XI and shown in Figure 7.4 that the power factor characteristics of the induction
machine can be manipulated by varying the rotor resistance. Moreover, as shown
in Figure 7.5, the efficiency of the induction machine can also be adjusted with
the rotor resistance, in conjunction with the variable power factor operation of the
machine.
In Publication XII, an experimental analysis of the machine is performed
at various speed. It is shown that for operation close to the synchronous speed,
the capacitor size and the converter size is only a fraction of the power rating of
the machine. This is because as indicated in Publication XII, the capacitance
is normalized by slip squared, implying its small size. Thus, unity power factor
is obtained when the rotor capacitance is equal to the magnetization and leakage
inductance of the machine.
7.1.1
Advantage of the Lindmark Concept
The concept is useful for self-excitation of an induction machine due to small sizes
of the capacitors and electronics. Moreover, the concept can be utilized for the
manufacture of induction machines with high number of pole-pairs. It is well known
that the power factor deteriorates as the pole-pair numbers of an induction machine
increase. Consequently, using the Lindmark concept, in which small size capacitors
are utilized, direct-drive induction generators can be feasible.
7.1. ROTATING POWER ELECTRONIC INDUCTION DRIVE
Figure 7.1: Configuration of a rotating power electronic induction drive [3].
Figure 7.2: Connection of converters to the rotor windings [69].
61
CHAPTER 7. UNITY POWER FACTOR OPERATION OF A SINGLE-FED
INDUCTION MACHINE USING THE LINDMARK CONCEPT
Stator Power Factor
62
1
0.8
0.6
0.4
0
Theoretical Values
Experimental Values
5
10
Mechanical Power (kW)
Figure 7.3: Stator power factor versus mechanical power, using the Lindmark concept.
−ve sign shows capacitive value
Stator Power Factor
1
0.5
0
Rotor Resistance=0.618Ω
Rotor Resistance=0.468Ω
Rotor Resistance=0.318Ω
−0.5
−1
0
5
10
Mechanical Power (kW)
Figure 7.4: Variation of the stator power factor with the changes in rotor resistance
versus mechanical power, using the Lindmark concept.
0.95
Efficiency
0.9
0.85
0.8
0.75
0.7
0
Rotor Resistance=0.618Ω
Rotor Resistance=0.468Ω
Rotor Resistance=0.318Ω
5
10
Mechanical Power (kW)
15
Figure 7.5: Variation of the efficiency with the changes in rotor resistance versus
mechanical power, using the Lindmark concept.
Chapter 8
Conclusions
This chapter presents the summary of the project and recommendations for future
research work.
8.1
Summary
In this thesis, a novel configuration of the BDFIG with rotating power electronics
has been investigated. The derivation and analysis of the dynamic and steadystate model of the RPE-BDFIG is presented. It is shown that through the use of
an on-board rotating exciter and power converter, the slip power can be successfully recovered and delivered to the grid. Moreover, it is demonstrated, that the
exciter and electronics can be used to magnetize the DFIG from its rotor, thereby
improving the grid voltage stability and power factor of the generator.
In addition, to the author’s knowledge, first-time evaluation of the DFIG with
the power electronics and the rotating exciter has been conducted in this thesis.
The closed-loop control of the generator is implemented on an 11-kW test bench
in the laboratory. Note that the generator still uses slip rings and brushes for
the connection of the power electronic converter. The main focus of this work is
to analyze and understand the working principle of the topology, and to confirm
recovery of slip power. The experimental results indicate stable operation of the
generator. It is shown that the closed-loop control is good enough in order to handle
torque disturbances from the exciter. Furthermore, the dc-link voltage of the rotor
converter is also maintained without sacrificing the stability of the generator. The
reactive power control and variable power factor operation of the generator is also
demonstrated through experiments. It is shown that with the help of the rotating
exciter and converter, the generator’s power factor can be varied over a wide range,
without affecting its stability. Therefore, the generator can also be used to support
63
64
CHAPTER 8. CONCLUSIONS
the grid during faults.
Furthermore, low-voltage ride-through behaviour of the 37-kW and 2-MW RPEBDFIG is analyzed. The results indicated that if a suitable control strategy is
used, the generator can ride through deep voltage dips and meet the requirements
of the grid codes. The results also highlight that no matter how good the control
is, nevertheless an external protection circuit such as PRN (which is used in this
thesis) is still required for the protection of the converter during deep voltage dips.
In addition, it is demonstrated, that the DVC works well for the RPE-BDFIG, as
it reduces the electrical and mechanical oscillations to a large extent. The results
shown are promising since the generator shows stable operation during faults and,
above all, the rotor converter maintains its connection during faults.
Besides, a preliminary design and thermal FEA of the rotating converter is
performed, and the sizes of the heatsink and shaft fan are roughly dimensioned.
8.2
Future Work
The study of the generator needs to be extended using the power electronics
mounted on the rotor, and controlling it by the reference commands sent through
wireless communication. The practical aspects related to the construction of the
rotating power electronics, and challenges with regards to the mounting of the electronics on the generator shaft, needs to be investigated. However, it is believed
that since the controller is also mounted on the electronic board and rotating with
the shaft, the performance of the generator will not be affected. The biggest issue
would probably be the mechanical strength of the rotating converter as it would
be subjected to high centrifugal forces. Moreover, the inertia of the generator will
change once the power electronic converter is mounted on the shaft. However, it
is expected that this will not be an issue with regard to the control of the system, because the closed-loop controls designed in this thesis uses the IMC method.
Therefore, the increase in inertia can easily be accounted for.
The next challenge is to integrate the two machines into one, similar to what
has been done for the conventional BDFIG. Design of a single-frame RPE-BDFIG
which includes the exciter, power electronics, and wireless module is an interesting
aspect for future research. Thereafter, optimization analysis of the single-frame
RPE-BDFIG can be performed, in order to reduce the losses and achieve maximum
power density.
Finally, further investigations on low-voltage ride-through of the generator should
be conducted.
List of Figures
1.1
2.1
2.2
2.3
3.1
3.2
3.3
3.4
3.5
Doubly-fed induction generator (DFIG) with zoomed-in view of its slip
rings [3, 4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Maximum power point tracking (MPPT) curve, showing wind generator
power versus rotational speed [26]. . . . . . . . . . . . . . . . . . . . . .
Generator and its drive-train. . . . . . . . . . . . . . . . . . . . . . . . .
(a) Direct-drive generator. . . . . . . . . . . . . . . . . . . . . . . .
(b) Indirect-drive generator. . . . . . . . . . . . . . . . . . . . . . .
Configuration of the BDFIM. . . . . . . . . . . . . . . . . . . . . . . . .
10
11
11
11
14
Configuration of the rotating power electronic converter brushless doublyfed induction generator (RPE-BDFIG). . . . . . . . . . . . . . . . . . . 20
Active power flow in the the RPE-BDFIG. . . . . . . . . . . . . . . . . 21
(a) Super-synchronous mode. . . . . . . . . . . . . . . . . . . . . . 21
(b) Sub-synchronous mode. . . . . . . . . . . . . . . . . . . . . . . 21
Modes of operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
(a) Direction of rotation of the magnetic field in the super-synchronous
mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
(b) Direction of rotation of the magnetic field in the sub-synchronous
mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Simulation results for a step load response of a 37-kW RPE-BDFIG, in
the super-synchronous mode. . . . . . . . . . . . . . . . . . . . . . . . . 23
(a) Shaft speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
(b) Turbine torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
(c) RPE-BDFIG torque. . . . . . . . . . . . . . . . . . . . . . . . . 23
(d) Exciter torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Simulation results for a step load response of a 37-kW RPE-BDFIG, in
the sub-synchronous mode. . . . . . . . . . . . . . . . . . . . . . . . . . 25
(a) Shaft speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
65
66
List of Figures
(b) Turbine torque. . . . . . . . . . . . . . . . . . . . . . . . . . . .
(c) RPE-BDFIG torque. . . . . . . . . . . . . . . . . . . . . . . . .
(d) Exciter torque. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Measurements results of the operation of an 11-kW RPE-BDFIG during
the synchronous mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(a) Generated power. . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Frequency of currents in the three windings. . . . . . . . . . .
3.7 dq dynamic model of the RPE-BDFIG. . . . . . . . . . . . . . . . . . .
(a) d-axis equivalent circuit. . . . . . . . . . . . . . . . . . . . . . .
(b) q-axis equivalent circuit. . . . . . . . . . . . . . . . . . . . . . .
3.8 Turbine and REP-BDFIG stator power in the super-synchronous mode,
at 1800 rpm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(a) Mechanical power supplied by the turbine. . . . . . . . . . . .
(b) RPE-BDFIG’s generated power delivered to the grid. . . . . .
3.9 DFIG rotor and exciter power at 1800 rpm. . . . . . . . . . . . . . . . .
(a) DFIG rotor power. . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Exciter rotor power. . . . . . . . . . . . . . . . . . . . . . . . .
3.10 Power factor at the RPE-BDFIG stator terminals at 1800 rpm. . . . . .
4.1
4.2
4.3
4.4
4.5
Reference frames for the control of the RPE-BDFIG. . . . . . . . . . . .
Closed-loop current control and model of the exciter. . . . . . . . . . . .
Closed-loop current control and model of the DFIG. . . . . . . . . . . .
Block diagram of a speed controller for a RPE-BDFIG. . . . . . . . . .
Measurement results on an 11-kW RPE-BDFIG, when a step in speed
reference is applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(a) Step-up in speed. . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Step-down in speed. . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Block diagram of a dc-link voltage model and its controller. . . . . . . .
4.7 Measurement results on an 11-kW RPE-BDFIG for dc-link voltage dynamics, when (a): step-up (2.7 kW to 6.6 kW) and (b): step-down
(6.6 kW to 2.7 kW), in stator reference power is applied at t=0, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(a) DC-link voltage for a power step-up. . . . . . . . . . . . . . . .
(b) DC-link voltage for a power step-down. . . . . . . . . . . . . .
4.8 Diagram of a phase-locked loop (PLL). . . . . . . . . . . . . . . . . . . .
4.9 Laboratory setup of an 11-kW RPE-BDFIG. . . . . . . . . . . . . . . .
(a) Power electronics, dSpace control, and power meter. . . . . . .
(b) Load machine, DFIG, and exciter. . . . . . . . . . . . . . . . .
4.10 Experimental results for the stability study conducted on an 11-kW
RPE-BDFIG at 1750 rpm, i.e., in the super-synchronous mode. . . . . .
25
25
25
26
26
26
27
27
27
28
28
28
29
29
29
29
32
33
35
36
37
37
37
38
38
38
38
39
40
40
40
41
List of Figures
67
(a) Power dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Power dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . .
(c) Torque dynamics. . . . . . . . . . . . . . . . . . . . . . . . . .
(d) Torque dynamics. . . . . . . . . . . . . . . . . . . . . . . . . .
4.11 Experimental results for the stability study conducted on an 11-kW
RPE-BDFIG at 1410 rpm, i.e., in the sub-synchronous mode. . . . . . .
(a) Power dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) Power dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . .
(c) Torque dynamics. . . . . . . . . . . . . . . . . . . . . . . . . .
(d) Torque dynamics. . . . . . . . . . . . . . . . . . . . . . . . . .
4.12 Measurement results of the 11-kW RPE-BDFIG’s stator current versus stator power factor, at various speeds. In the power factor scale,
capacitive power factor operation is illustrated for values greater than 1.
41
41
41
41
5.1
5.2
5.3
5.4
5.5
E.oN grid code standard for a low-voltage ride-through of a wind turbine.
Classification of the voltage dips. . . . . . . . . . . . . . . . . . . . . . .
Single-phase diagram of a passive resistive network. . . . . . . . . . . .
Response of RPE-BDFIG at 85% voltage dip using PRN . . . . . . . . .
(a) Three phase grid voltages . . . . . . . . . . . . . . . . . . . . .
(b) RPE-BDFIG stator flux . . . . . . . . . . . . . . . . . . . . . .
(c) DFIG rotor power . . . . . . . . . . . . . . . . . . . . . . . . .
(d) Exciter rotor power . . . . . . . . . . . . . . . . . . . . . . . .
(e) DFIG rotor current . . . . . . . . . . . . . . . . . . . . . . . .
(f) Exciter rotor flux . . . . . . . . . . . . . . . . . . . . . . . . . .
(g) Rotor converter DC-link voltage . . . . . . . . . . . . . . . . .
(h) Shaft speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Behavior of the RPE-BDFIG during the SPGF . . . . . . . . . . . . . .
(a) grid voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) turbine torque . . . . . . . . . . . . . . . . . . . . . . . . . . .
(c) RPE-BDFIG torque . . . . . . . . . . . . . . . . . . . . . . . .
(d) exciter torque . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(e) stator power . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(f) DFIG rotor power . . . . . . . . . . . . . . . . . . . . . . . . .
(g) exciter rotor power . . . . . . . . . . . . . . . . . . . . . . . . .
(h) stator current . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(i) DFIG rotor current . . . . . . . . . . . . . . . . . . . . . . . .
(j) exciter rotor current . . . . . . . . . . . . . . . . . . . . . . . .
(k) dc-link voltage . . . . . . . . . . . . . . . . . . . . . . . . . . .
(l) mechanical speed . . . . . . . . . . . . . . . . . . . . . . . . . .
42
42
42
42
42
43
47
49
51
52
52
52
52
52
52
52
52
52
54
54
54
54
54
54
54
54
54
54
54
54
54
68
6.1
6.2
6.3
7.1
7.2
7.3
7.4
7.5
List of Figures
The rotating power electronic converter (RPEC). . . . . . . . . . . . . .
Maximum steady-state junction temperatures of the IGBT versus air
velocities, when cooled by Heatsink 1 and Heatsink 2 through forced
convection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fan size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(a) Velocity of air as a function of rotor speed for two different
radius of the fan. . . . . . . . . . . . . . . . . . . . . . . . . . .
(b) 3-D diagram of the air velocity versus fan radius versus rotor
speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Configuration of a rotating power electronic induction drive [3]. . . . . .
Connection of converters to the rotor windings [69]. . . . . . . . . . . .
Stator power factor versus mechanical power, using the Lindmark concept.
Variation of the stator power factor with the changes in rotor resistance
versus mechanical power, using the Lindmark concept. . . . . . . . . . .
Variation of the efficiency with the changes in rotor resistance versus
mechanical power, using the Lindmark concept. . . . . . . . . . . . . . .
57
57
58
58
58
61
61
62
62
62
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Appendix A
Glossary of Symbols and
Abbreviations
Symbols
α
αc
αc,exc
αs
αv
ψ
ω
θ
b1
b2
Cdc , C
CT
Cp
Dwt
i
Iˆ
J1
J2
R
L
Lm1
Lm2
P
Bandwidth of the closed-loop control
Bandwidth of the DFIG closed-loop current control
Bandwidth of the exciter closed-loop current control
Bandwidth of the closed-loop speed control
Bandwidth of the closed-loop voltage control
Flux
Electrical speed in radians per second
Electrical position in radians
Friction coefficient of the DFIG or induction machine
Friction coefficient of the exciter
Capacitance of the rotating capacitor
Flux-dependent constant
Wind turbine power coefficient
Wind turbine rotor diameter
Current
Current magnitude
Inertia of the DFIG or induction machine
Inertia of the exciter
Resistance
Inductance
DFIG or induction machine magnetization inductance
Exciter magnetization inductance
Power
77
78
pp1
pp2
s1
s
Te
Texciter
Tturbine
v
vdc
V̄
V̂
vwind
Appendix A. Glossary of Symbols and Abbreviations
Pole-pairs of the DFIG or induction machine
Pole-pairs of the exciter
Slip
Laplace variable
Electromagnetic torque of the RPE-BDFIG
Electromagnetic torque of the exciter
Torque provided by the turbine
Voltage
DC-link voltage
Voltage complex vector
Voltage magnitude
Wind speed
Subscripts
1
2
3
4
exc
d
q
D
Q
r
p
n
ps
N
wt
Stator of the DFIG or induction machine or RPE-BDFIG, grid
Rotor of the DFIG or induction machine
Rotor of the exciter
DC field winding (second stator) of the exciter
Exciter
d-axis
q-axis
Damper winding in the d-axis
Damper winding in the q-axis
Rotor
Positive
Negative
phase shift
Number of winding turns
Wind turbine
Abbreviations
BDFIG
DFIG
DVC
EVC
ERSC
IMRSC
LVRT
PLL
PWM
Brushless Doubly-Fed Induction Generator
Doubly-Fed Induction Generator
Dual Vector Control
Extended Vector Control
Exciter Rotor Side Converter
Induction Machine Rotor Side Converter
Low Voltage Ride Through
Phase-Locked Loop
Pulse Width Modulation
Appendix A. Glossary of Symbols and Abbreviations
PIR
PR
PRN
RPE-BDFIG
Proportional Integral Resonance
Proportional Resonance
Passive Resistive Network
Rotating Power Electronic Brushless Doubly-Fed
Induction Generator
79
Appendix B
Summary of Publications
This chapter presents the abstracts of the appended papers. The papers and their
abstracts are copyright of the respective conferences and IEEE.
Publication I: Experimental Validation of a Rotating Power Electronic
Brushless Doubly-Fed Induction Generator for Variable-Speed Operation
This paper is the core of the thesis, as it presents the mathematics, control
aspects, experimental results, and stability study of the rotating power electronic
brushless doubly-fed induction generator (RPE-BDFIG), operated with variable
speed and torque. The theory behind the operation of the generator is explained,
its dynamic model and control aspects are discussed, and closed-loop control of the
generator is implemented and verified through experiments on an 11-kW prototype.
The measurement results show stable operation for variable speed and torque regions. Moreover, it is shown that the integrated rotating exciter is sufficient to
recover and deliver slip power to the grid, hence, verifying successful brushless operation. Besides, it is verified that the generator operates well in both regions of
operation, i.e., the sub-synchronous and super-synchronous modes, and is stable
under torque transients added by the rotating exciter.
Publication II: Dynamic Modeling and Control of a Brushless DoublyFed Induction Generator with a Rotating Power Electronic Converter
The dynamic model of the 37-kW brushless doubly-fed induction generator with
a rotating power electronic converter is derived and analyzed through simulations.
Furthermore, feedback control of the topology is also implemented and analyzed.
It is shown that the generator shows stable operation in steady state as well as in
dynamic state, at variable speeds. Using the closed-loop control, the generator is
81
82
Appendix B. Summary of Publications
able to maintain desired speed, torque, and dc-link voltage set-points.
Publication III: Synchronous Operation of a Rotating Power Electronic
Brushless Doubly-Fed Generator
This paper presents through experiments the synchronous operation of the 11kW RPE-BDFIG. It is shown that the generator operates well at the synchronous
speed of the main machine, delivering the desired power to the grid. Furthermore,
it is illustrated that the RPE-BDFIG behaves similar to a synchronous generator
in the synchronous mode. The closed-loop control of the generator is implemented
in real-time, and the current and voltage waveforms of the stator and rotor of the
RPE-BDFIG are experimentally analyzed.
Publication IV: Brushless Doubly-fed Induction Machine with Rotating Power Electronic Converter for Wind Power Applications
This paper presents the simulation study of the 4-kW RPE-BDFIG in motor
mode and during steady-state conditions. The steady state equivalent circuit of
the machine is derived and analyzed. It is shown through simulations that the slip
power is recovered and stator terminals of the machine can be operated at a unity
power factor for ±20% speed range around the synchronous speed. Furthermore, it
is shown that the presented system operates at a high efficiency at rated load and
unity power factor, due to successful slip power recovery.
Publication V: Variable Reactive Power Control of a Rotating Power
Electronic Brushless Doubly-Fed Generator
This paper presents an in-depth mathematical treatment and experimental analysis of the reactive power control of the 11-kW RPE-BDFIG. The rotating exciter
and power electronic converters supply reactive power from the rotor of the DFIG,
thus manipulating the power factor at the stator terminals. Theory for variablereactive-power operation is developed and verified through experiments on an 11kW prototype. The measurements results for the variable reactive power operation
are shown for the generator’s power factor ranging from inductive to unity to capacitive.
Publication VI: Behavior of a Brushless Doubly-Fed Induction Generator with a Rotating Power Electronic Converter during Symmetrical
Voltage Sags
Impact of the different magnitudes of symmetrical voltage dip on the performance of the 37-kW RPE-BDFIG are presented. The transient simulation study
is carried out in order to investigate the magnitude of the voltage dip the rotor
converters can withstand, before a protection scheme is needed for the low-voltage
Appendix B. Summary of Publications
83
ride-through (LVRT) of the generator. Furthermore, successful LVRT under severe
voltage dips is also performed using passive resistive network strategy.
Publication VII: Low-Voltage Ride-Through of a 2-MW Rotating Power
Electronic Brushless Doubly-Fed Generator
This paper presents results for unsymmetrical LVRT of a 2-MW RPE-BDFIG.
The phenomenon behind the behavior of the generator during various voltage dips
is examined and explained. The dual vector control (DVC) of the generator, which
assists the generator in riding-through unsymmetrical faults, and minimizes electrical and mechanical oscillations, is presented. Furthermore, studies of the impact of
phase-angle jumps and various magnitudes of voltage dips (including 100% voltage
dip) on the operation of the generator, are presented.
Publication VIII: Extended Vector Control of a Rotating Power Electronic Brushless Doubly-Fed Induction Generator under Unsymmetrical
Voltage Sags
This paper also presents the implementation of the DVC on a 37-kW RPEBDFIG, when subjected to unsymmetrical voltage dips. The impact of phase-angle
jumps is neglected and faults causing magnitudes of voltage dips of 50%, are considered. Two separate synchronous reference frames are defined and standard PI
controllers are implemented in the reference frames in order to control the positive
and negative sequence currents independently. Through these means the effect of
the negative sequence currents is mitigated and it is shown that the oscillations in
the behavior of this new type of generator are considerably reduced.
Publication IX and X: Dynamic and Steady-State 3-D Thermal Design
and Investigation of the Rotating Power Electronic IGBT Converter
These papers deal with a 3-dimensional development of a thermal model of a
power electronic converter mounted on the generator shaft and rotating with it.
The dimensions of the heat sink are determined and the temperature gradients of
the converter, its heat sink, and shaft during natural and forced convection are
analyzed for variable rotor speeds. It is shown that the chosen sizes of the IGBT
and heat sink offer compact design of the rotating converter, which is sufficient
for its mounting in the limited space, offered by the generator shaft. Furthermore,
transient temperature profile is also presented. Additionally, transient thermal profile of the converter and dimensions of the cooling fan are also calculated. Besides
analysis of the cooling requirements of the converter during over-currents due to
grid faults is also investigated.
Publication XI: Theoretical and Experimental Investigation of the Self-
84
Appendix B. Summary of Publications
Excited Rotating Power Electronic Induction Machine
This paper presents the theoretical model and experimental analysis of a novel
topology of the self-excited induction machine using rotating power electronic converters, invented by Magnus Lindmark is presented. The power electronic converters are connected to the rotor of the induction machine and it is shown that the
machine operates at unity power factor at variable load conditions including rated
load. Special control strategy of the two converters helps in magnetization of the
induction machine from the rotor. The experimental analysis is conducted in the
industry using an 11-kW induction machine, and close agreement is found between
the theoretical model and the experimental results. Besides, the rotor resistance is
varied and its effect on the power factor and performance of the machine is studied
and analyzed.
Publication XII: Induction Machine at Unity Power Factor with Rotating Power Electronic Converter
A configuration for the self-excitation of the induction machine invented by
Magnus Lindmark, is presented. The power electronic converter using solid state
switches is connected to the rotor, whereas the stator is directly connected to the
grid. Using appropriate control, the reactive power consumed by the motor can
be generated in the rotor resulting in unity power factor operation. The rotor
connected power electronic converter is also used for constant speed operation of
the induction machine at variable torque. The operation of the machine at variable
speeds is presented, and mathematical treatment of the rotor capacitor size is given.