ojeU mag

ii

With the proliferation of installed wind generators across the whole world, there has been a significant increase in the number of different types of wind generators schemes, due to the big investments made in this area. From all the generators there are three that are widely used: the squirrel cage induction generator, also known as fixed speed machine, the doubly fed induction generator, also known as variable speed controlled wind turbine and finally the direct driven wind generator, also known as the full variable speed controlled wind turbine.
It would be interesting to have a test platform to which different types of wind generators could be connected. The main goal of this master thesis is to create such a platform, using
Matlab/Simulink that provides a userfriendly environment to do so. With this platform we’ll be able to perform steady-state and transient analysis to an electrical grid with different types of wind generators connected and assess their impact on the whole system.
Several situations are studied along this thesis, such as the connection of the wind generators to the grid, the reaction of each wind generator when the nominal wind speed was reached to evaluate the pitch control system limiting the output power and the simulation of three-phase and phase-to-ground faults.
Finally, the fault ride through capability, which is a new feature of modern wind energy conversion systems required by government regulations, will be tested with the help from flexible AC transmission systems such as the static synchronous compensator.
Key words: wind generation, test platform, transient and steady-state analysis, fault ride through capability, flexible AC transmission systems, doubly fed induction generator, squirrel cage induction generator. iii

iv

Com a proliferação de geradores eólicos em todo o mundo, tem havido um aumento significativo do número de diferentes tipos de sistemas de geração de energia a partir do vento, devido aos grandes investimentos feitos nesta área. De todos os tipos de geradores eólicos, há três que são amplamente utilizados: a máquina de indução de rotor em gaiola, também conhecida como máquina de velocidade fixa, a máquina de indução duplamente alimentada, também conhecida como turbina eólica controlada com velocidade variável e, finalmente, a máquina síncrona de velocidade variável, também conhecida como turbina eólica controlada com velocidade totalmente variável.
Seria interessante ter uma plataforma de testes onde diferentes tipos de geradores eólicos pudessem ser ligados. O principal objetivo desta dissertação de mestrado passa por criar esta plataforma, usando o Matlab/Simulink que nos fornece um ambiente intuitivo para tal. Com esta plataforma, seremos capazes de realizar testes em regime permanente e transitório numa rede elétrica, com diferentes tipos de geradores eólicos, avaliando o seu impacto em todo o sistema.
Diversas situações são estudadas ao longo deste trabalho, a ligação de um gerador eólico à rede, a reacção de cada gerador quando a velocidade nominal do vento é atingida e também o estudo de diversos tipos de curto-circuitos na rede.
Será testada também a capacidade de Fault Ride Through dos geradores eólicos, uma nova capacidade que é exigida por regulamentos governamentais a este tipo de geradores. Para testar esta capacidade, usar-se-ão flexible AC transmission systems , nomeadamente o compensador estático de tensão.
Palavras chave: geração eólica, plataforma de testes, análise em regime permanente e transitório, capacidade fault ride through, flexible AC transmission systems, máquina duplamente alimentada, máquina de indução de rotor em gaiola. v

vi

This dissertation could not have been a reality without the help and support of a group of people to whom I want to leave my sincere thanks.
Firstly, I want to thank Professor Rui Castro, for giving me the opportunity to complete this final phase of the course under his guidance, for the promptitude and the time taken to help me, sometimes far beyond the available time. I also want to leave special thanks for being one of the teachers who most influenced me and motivated during my time at Instituto Superior
Técnico.
It is imperative to leave a special thanks to all my colleagues who accompanied me throughout these years, many of whom I am proud to be able to call friends and not just colleagues. There were people who not only helped me to acquire knowledge but also helped me to evolve as a person. I avoid discriminating their names with fear to forget someone however I want to thank everyone for helping making my academic experience very memorable.
In a non-academic context, I want to thank my family. To my parents who, besides giving me an education and the needed values to succeed in life, also worked hard so I could have a stable life and so I could have all I needed and more. To my brother, who was over 24 years not only a friend but also someone who I always looked up to.
Finally, I want to give a special thanks to all my friends. From those I have known for over twenty years to the ones I met just a few months ago, I feel very lucky to have them in my life since they always gave me the support, happiness and the motivation required to have stability and success in both my personal and academic life. They are a very significant part of my life.
To all, thank you. It would not have been possible without you. vii

viii

Esta dissertação de mestrado não poderia ter sido uma realidade sem a ajuda e apoio de um grupo de pessoas, ao qual eu quero deixar os meus mais sinceros agradecimentos.
Em primeiro lugar, quero agradecer ao professor Rui Castro, por me ter dado a oportunidade de completar esta fase final do curso sob a sua orientação, pela prontidão e tempo que disponibilizou para me ajudar, por vezes muito além do tempo que tinha disponível. Gostaria também de deixar um agradecimento por ter sido dos professores que mais me influenciou e motivou durante a minha passagem pelo Instituto Superior Técnico.
É imperativo deixar um agradecimento especial a todos os meus colegas que me acompanharam ao longo destes anos de curso, muitos dos quais eu me orgulho de poder chamar amigos e não apenas colegas. Foram pessoas que não só me ajudaram a adquirir conhecimentos mas também me ajudaram a evoluir enquanto pessoa. Evito descriminar os seus nomes, sob o medo de me esquecer de alguém, no entanto, quero agradecer a todos por terem ajudado a tornar a minha experiência académica muito memorável.
Num contexto não académico, quero agradecer à minha família. Aos meus pais que, para além de me terem dado uma educação e valores necessários para ter sucesso na vida, também se esforçaram muito durante toda a minha vida para que esta decorresse da maneira mais estável possível e sempre trabalharam arduamente para que eu pudesse ter tudo aquilo que precisaria e mais ainda. Ao meu irmão, que ao longo de 24 anos não foi só um amigo mas também alguém que sempre retive como um exemplo a seguir.
Finalmente, quero deixar um agradecimento especial a todos os meus amigos. Desde aqueles que conheço há mais de vinte anos aos que conheço há poucos meses, sinto-me com muita sorte de os ter na minha vida pois sempre me deram o apoio, a felicidade e a motivação necessários para ter estabilidade e sucesso a nível pessoal e a nível académico. São uma parte fulcral na minha vida.
A todos, muito obrigado. Sem vocês, não teria sido possível. ix

x

F IGURE 1.1
E VOLUTION OF THE WORLD CUMULATIVE WIND POWER INSTALLED CAPACITY [1]. ............. 1
F IGURE 2.1
E LECTRIC POWER CHARACTERISTIC FOR DIFFERENT ROTOR RESISTANCES [6]. ............... 5
F IGURE 2.2
B LOCK REPRESENTATION OF THE WTDFIG [6]. ............................................................. 6
F IGURE 2.3
E LECTRICAL SYSTEM OF THE DFIG [6]. ......................................................................... 7
F IGURE 2.4
V OLTAGE TIME CHARACTERISTIC ESTABLISHED BY REGULATIONS AS SEEN IN [3]. .......... 11
F IGURE 2.5
B ASIC PRINCIPLE OF SERIES COMPENSATION AS SEEN IN [4]. ........................................ 12
F IGURE 2.6
B ASIC PRINCIPLE OF SHUNT COMPENSATION AS SEEN IN [4]. ........................................ 12
F IGURE 2.7
P OWER FLOW IN FACTS DEVICES [6]. ........................................................................ 13
F IGURE 2.8
B LOCK DIAGRAM OF A STATCOM BASED ON [6]. ........................................................ 14
F IGURE 2.9
C ONNECTION BETWEEN THE STATCOM AND A NETWORK .
V
S
IS THE NETWORK VOLTAGE
AND V
I
THE
STATCOM’
S VOLTAGE [6]. .................................................................................... 14
F IGURE 2.10
V-I CHARACTERISTIC OF THE STATCOM [6]. ............................................................ 15
F IGURE 2.11
DVR' S CONTROL STRUCTURE [4]. ............................................................................. 16
F IGURE 3.1
T EST PLATFORM AS IT IS REPRESENTED IN M ATLAB /S IMULINK . ..................................... 17
F IGURE 4.1
S INGLE LINE REPRESENTATION OF THE TEST PLATFORM BASED ON [2]. ......................... 23
F IGURE 4.2
T URBINE POWER CHARACTERISTICS ............................................................................ 24
F IGURE 4.3
– W IND SPEED , ACTIVE AND REACTIVE POWER OF THE WTDFIG. ................................... 25
F IGURE 4.4
A CTIVE POWER GENERATION FROM EACH POWER PLANT AND FROM THE WTDFIG. ....... 26
F IGURE 4.5
V OLTAGE AT THE WTDFIG' S TERMINALS . ................................................................... 27
F IGURE 4.6
– W IND SPEED , ACTIVE AND REACTIVE POWER OF THE WTSCIG. ................................... 27
F IGURE 4.7
A CTIVE POWER GENERATION FROM EACH POWER PLANT AND FROM THE WTSCIG. ....... 28
F IGURE 4.8
V OLTAGE AT THE WTSCIG' S TERMINALS . ................................................................... 29
F IGURE 4.9
– W IND SPEED , ACTIVE AND REACTIVE POWER OF THE WTDFIG. ................................... 30
F IGURE 4.10
V OLTAGE AT THE WTDFIG TERMINALS
………………………………………...............31
F
IGURE
4.11
P
ITCH ANGLE OF THE
WTDFIG ………….. ................................................................ 31
F IGURE 4.12
W IND SPEED , ACTIVE AND REACTIVE POWER OF THE WTSCIG. .................................. 32
F IGURE 4.13
V OLTAGE AT THE WTSCIG TERMINALS
…………………………………………………32
F IGURE 4.14
P ITCH ANGLE OF THE WTSCIG …………… .............................................................. 32
F IGURE 4.15
A CTIVE POWER OF THE WTDFIG ………………………………………………………..33
F IGURE 4.16
R EACTIVE POWER OF THE WTDFIG. ........................................................................ 33
F IGURE 4.17
S LIP OF THE WTDFIG ……………………………………………………………………34
F IGURE 4.18
V OLTAGE AT THE WTDFIG TERMINALS . .................................................................... 34
F IGURE 4.19
V OLTAGE AT THE B5 BUS
………………………………………………………………..34
F
IGURE
4.20
V
OLTAGE AT THE
B6
BUS
…… .................................................................................. 34
F IGURE 4.21
A CTIVE POWER OF THE WTSCIG ……………………………………………………….35
F IGURE 4.22
R EACTIVE POWER OF THE WTSCIG. ........................................................................ 35
F IGURE 4.23
S LIP OF THE SCIG ……………………………………………………………………….35
xi

F IGURE 4.24
V OLTAGE AT THE WTSCIG TERMINALS . .................................................................... 35
F IGURE 4.25
V OLTAGE AT THE B5 BUS
………………………………………………………………...36
F IGURE 4.26
V OLTAGE AT THE B6 BUS
….. .................................................................................... 36
F IGURE 4.27
W IND SPEED , ACTIVE AND REACTIVE POWER OF THE WTDFIG. .................................. 37
F IGURE 4.28
V OLTAGE AT THE TERMINALS OF THE WTDFIG. ........................................................ 37
F IGURE 4.29
P OWER GENERATION OF THE POWER PLANTS AND THE WTDFIG. .............................. 38
F IGURE 4.30
W IND SPEED , ACTIVE AND REACTIVE POWER OF THE WTSCIG. .................................. 39
F IGURE 4.31
V OLTAGE AT THE TERMINALS OF THE WTSCIG. ........................................................ 39
F IGURE 4.32
P OWER GENERATION OF THE POWER PLANTS AND THE WTSCIG. .............................. 40
F IGURE 4.33
W IND SPEED , ACTIVE AND REACTIVE POWER OF THE WTDFIG. .................................. 41
F IGURE 4.34
V OLTAGE AT THE TERMINALS OF THE WTDFIG, DARK BLUE IS THE PHASE A, PINK IS THE
PHASE B AND LIGHT BLUE IS THE PHASE C. ............................................................................... 42
F IGURE 4.35
W IND SPEED , ACTIVE AND REACTIVE POWER OF THE WTSCIG. .................................. 43
F IGURE 4.36
V OLTAGE AT THE TERMINALS OF THE WTSCIG, DARK BLUE IS THE PHASE A, PINK IS THE
PHASE B AND LIGHT BLUE IS THE PHASE C. ............................................................................... 43
F
IGURE
4.37
– R
EACTIVE POWER FOR A
0 MVA STATCOM …………………………………………..45
F IGURE 4.38
V OLTAGE FOR A 0 MVA STATCOM ……………. ...................................................... 45
F IGURE 4.39
A CTIVE POWER GENERATED BY THE WTSCIG. ......................................................... 45
F IGURE 4.40
R EACTIVE POWER FOR A 30 MVA STATCOM …………………………………………46
F IGURE 4.41
V OLTAGE FOR A 30 MVA STATCOM. ...................................................................... 46
F IGURE A.1
P OSSIBLE APPEARANCES OF THE P OWERGUI BLOCK . .................................................. 50
F IGURE A.2
I NTERCONNECTION BETWEEN LINEAR AND NONLINEAR MODELS [8]. .............................. 51
F IGURE B.1
S IMULINK BLOCK FOR THE WTSCIG. .......................................................................... 53
F IGURE B.2
S IMULINK CIRCUIT OF THE WTSCIG BLOCK . ............................................................... 54
F
IGURE
B.3
W
IND TURBINE BLOCK
. ............................................................................................... 55
F IGURE B.4
A SYNCHRONOUS MACHINE BLOCK . ............................................................................. 56
F IGURE B.5
E LECTRICAL SYSTEM OF THE SQUIRREL CAGE MACHINE FOR THE D AXIS [8]. ................. 56
F IGURE B.6
E LECTRICAL SYSTEM OF THE SQUIRREL CAGE MACHINE FOR THE Q AXIS [8]. ................. 56
F IGURE B.7
S IMULINK BLOCK FOR THE WTSCIG. .......................................................................... 58
F IGURE B.8
S IMULINK CIRCUIT OF THE WTDFIG BLOCK . ............................................................... 60
F IGURE B.9
C ONSTITUTION OF THE G ENERATOR & C ONVERTERS BLOCK . ...................................... 61
F IGURE B.10
P OWER FLOW REPRESENTATION OF THE WTDFIG [8]. .............................................. 63
F
IGURE
B.11
T
RACKING
C
HARACTERISTIC
[8]. .............................................................................. 64
F IGURE B.12
R OTOR SIDE CONTROL SYSTEM [8]. .......................................................................... 65
F IGURE B.13
V-I CHARACTERISTIC [8]. ......................................................................................... 65
F IGURE B.14
G RID SIDE CONVERTER CONTROL SYSTEM [8]. .......................................................... 67
F IGURE B.15
P ITCH CONTROL SYSTEM [8]. ................................................................................... 67
F IGURE B.16
P OWER PLANT S IMULINK BLOCK . .............................................................................. 68
F IGURE B.17
C ONSTITUTION OF THE POWER PLANT BLOCK . ........................................................... 68
F IGURE B.18
S YNCHRONOUS MACHINE BLOCK . ............................................................................. 69
xii

F IGURE B.19
M ECHANICAL SYSTEM OF THE POWER PLANT [8]. ....................................................... 69
F IGURE B.20
E LECTRICAL MODEL OF THE MACHINE IN THE Q AND D AXIS [8]. ................................... 71
F IGURE B.21
D IESEL ENGINE SPEED AND VOLTAGE CONTROL BLOCK . ............................................. 72
F IGURE B.22
C ONSTITUTION OF THE D IESEL E NGINE S PEED & V OLTAGE C ONTROL BLOCK . ............ 72
F IGURE B.23
G OVERNOR & D IESEL E NGINE BLOCK . ...................................................................... 72
F IGURE B.24
B LOCK DIAGRAM OF THE GOVERNOR AND DIESEL ENGINE . ......................................... 73
F IGURE B.25
E XCITATION SYSTEM BLOCK . .................................................................................... 73
F IGURE B.26
P ROTECTION SYSTEM BLOCK . .................................................................................. 74
F IGURE B.27
C ONSTITUTION OF THE PROTECTION SYSTEM . ........................................................... 75
F IGURE B.28
T HREE PHASE ELECTRICAL BUS BLOCK . .................................................................... 76
F IGURE B.29
T HREE PHASE V-I MEASUREMENT BLOCK . ................................................................ 76
F IGURE B.30
A CTIVE AND REACTIVE POWER BLOCK . ...................................................................... 77
F IGURE B.31
STATCOM BLOCK . ................................................................................................. 78
F IGURE B.32
C ONSTITUTION OF THE STATCOM. ......................................................................... 79
F IGURE B.33
S INGLE LINE DIAGRAM OF THE STATCOM [8]. ......................................................... 80
F
IGURE
B.34
T
HREE
-
PHASE
P
I
S
ECTION
L
INE BLOCK
. ................................................................... 81
F IGURE B.35
E LECTRICAL REPRESENTATION OF THE PI SECTION LINE [8]. ....................................... 81
F IGURE B.36
T HREE PHASE P ARALLEL RLC L OAD BLOCK . ............................................................ 83
F IGURE B.37
T HREE PHASE TRANSFORMER BLOCK . ...................................................................... 84
F IGURE B.38
T RANSFORMER EQUIVALENT ELECTRICAL SCHEME [8]. .............................................. 85
F IGURE B.39
T HREE PHASE FAULT BLOCK . ................................................................................... 85
F IGURE B.40
E LECTRICAL SCHEME OF THE THREE PHASE FAULT [8]. .............................................. 86
F IGURE B.41
B REAKER BLOCK . .................................................................................................... 87
xiii

xiv

T ABLE 2.1
O PERATION MODES OF THE DFIG.
............................................................................................................... 9
T ABLE 2.2
O PERATION MODES OF THE SCIG.
............................................................................................................ 10
T ABLE 3.1
G ENERATOR DATA FOR THE WTDFIG . .................................................................................................... 18
T ABLE 3.2
G ENERATOR DATA FOR THE WTSCIG.
.................................................................................................... 19
T ABLE 3.3
T RANSFORMERS ' W INDING 1 PARAMETERS .
.......................................................................................... 20
T ABLE 3.4
T RANSFORMERS ' W INDING 2 PARAMETERS .
.......................................................................................... 20
T ABLE 3.5
L OADS OF THE TEST PLATFORM .
................................................................................................................. 21
T ABLE 3.6
– N OMINAL POWER OF EACH POWER PLANT .
............................................................................................ 21
T ABLE 3.7
P ARAMETERS OF THE POWER PLANT ' S SYNCHRONOUS GENERATOR .
......................................... 22
T ABLE B.1
M EASUREMENT LABELS .
................................................................................................................................ 84
xv

xvi

PWM
RLC
SCIG
STATCOM
VSC
WTDFIG
WTIG
WTSCIG
AC
DC
DDSG
DFIG
DVR
FACTS
GTO
IGBT
PLL
PMSG
Alternating Current
Direct Current
Direct Driven Synchronous Generator
Doubly Fed Induction Generator
Dynamic Voltage Restorer
Flexible AC Transmission Systems
Gate Turn Off
Insulated Gate Bipolar Transistor
Phase-Lock Loop
Permanent Magnet Synchronous Generator
Pulse Width Modulation
Resistor, Inductor and Capacitor
Squirrel Cage Induction Generator
Static Synchronous Compensator
Voltage-Sourced Converter
Wind Turbine Doubly Fed Induction Generator
Wind Turbine Induction Generator
Wind Turbine Squirrel Cage Induction Generator xvii

xviii

Abstract ......................................................................................................................................................................................... iii
Resumo ........................................................................................................................................................................................... v
Acknowledgments .................................................................................................................................................................. vii
Agradecimentos ........................................................................................................................................................................ ix
List of Figures ............................................................................................................................................................................. xi
List of Tables .............................................................................................................................................................................. xv
List of Abbreviations ............................................................................................................................................................ xvii
Contents ..................................................................................................................................................................................... xix
1.
Framework .................................................................................................................................................................... 1
1.1.
Introduction .............................................................................................................................................................. 1
1.2.
Objectives ................................................................................................................................................................ 2
1.3.
Main Contributions .............................................................................................................................................. 3
2.
1.4.
Thesis outline ......................................................................................................................................................... 4
Theoretical approach ............................................................................................................................................... 5
2.1.
Wind Generators .................................................................................................................................................. 5
2.1.1.
Doubly-Fed Induction Generator (DFIG) ............................................................................................ 5
2.1.2.
Squirrel Cage Induction Generator (SCIG) ....................................................................................... 9
2.2.
Fault Ride Through Capability ................................................................................................................... 10
2.2.1.
Basic principles ............................................................................................................................................. 10
2.2.2.
FACTS Devices ............................................................................................................................................ 11
2.2.2.1.
Static Synchronous Compensator ...................................................................................................... 13
2.2.2.2.
Dynamic Voltage Restorer ...................................................................................................................... 16
3.
4.
Parameters of the test platform ...................................................................................................................... 17
Tests and simulations .......................................................................................................................................... 23
4.1.
The test platform ............................................................................................................................................... 23
4.2.
Connection of the Wind Generators to the grid ................................................................................ 25
4.3.
Pitch control ......................................................................................................................................................... 30
4.4.
Three-phase short circuit at bus B6 ........................................................................................................ 33
4.5.
Three-phase short circuit at bus B13 ..................................................................................................... 36
xix

4.6.
Phase-to-ground short circuit at bus 13 ................................................................................................ 41
5.
4.7.
Fault Ride Through Capability ................................................................................................................... 44
Conclusion and future work .............................................................................................................................. 47
Appendix A ................................................................................................................................................................................. 49
Simulation Environment .................................................................................................................................................. 49
Appendix B ................................................................................................................................................................................. 53
Simulation Blocks ............................................................................................................................................................... 53
Wind Turbine Induction Generator ............................................................................................................................ 53
Wind Turbine Doubly-Fed Induction Generator ................................................................................................. 58
Power Plant ........................................................................................................................................................................... 68
Protection system .............................................................................................................................................................. 74
Three-phase electrical bus ............................................................................................................................................ 76
Static Synchronous Compensator (STATCOM) ................................................................................................ 78
Three-Phase PI Section Line ....................................................................................................................................... 81
Three-Phase Parallel RLC Load ................................................................................................................................ 83
Three-Phase Transformer ............................................................................................................................................. 84
Three-Phase Fault ............................................................................................................................................................. 85
References ................................................................................................................................................................................. 88
xx

To contradict the excessive use of fossil fuel in the 70’s wind energy appeared as a promising and reliable alternative. Since then great advances and great investments were made in the equipment to harvest this type of energy.
From 2005 to 2006 alone the global wind power generation capacity increased from 59 091 MW to 74 223 MW and it is estimated that by 2020 the capacity will exceed 1 260 000 MW according to [1]. In the next figure, it is represented the evolution of the world cumulative wind power installed capacity.
Figure 1.1 - Evolution of the world cumulative wind power installed capacity [1].
The development of modern and more efficient wind power conversion systems has begun in the 70’s but it was in the 90’s that a big evolution took place with the development of different wind turbine concepts and different wind generators too. It is crucial that the technology can keep up with the needs of the modern world, to guarantee better efficiency in the equipment and to guarantee also the credibility of this energy source.
There are three types of wind generators that are widely used nowadays: a fixed speed wind turbine system that has a squirrel cage induction generator (SCIG), directly connected to the grid, there’s a variable speed wind turbine system with a doubly fed induction generator (DFIG), with a wound rotor and a partial-rating power converter on the rotor circuit and, finally, there’s the full variable speed controlled with a wound rotor synchronous generator, connected to the grid through a full-rating power converter. This last wind generator is also known as direct driven synchronous generator (DDSG).
There are several other types of wind generators that are being studied and new grid connection schemes are being proposed. For example, since direct driven wind generators are
1

becoming larger with the increase of capacity and therefor are becoming more expensive, a permanent magnet synchronous generator (PMSG) is a valid alternative.
Hereupon it would be interesting to have an integrated test platform where the user could choose from different types of wind generators and perform tests and simulations of various situations so that the dynamic performance of each generator could be analyzed and compared with other types of generators. This platform should be also prepared to accept any type of wind generators that can be created and modeled in the future. Matlab/Simulink was the chosen software to create this test platform.
The objectives for this thesis are:

To use Matlab/Simulink to create a test platform for different types of wind generators.
The platform should be ready to be connected to any model of a generator, whether it’s a resident model in Matlab/Simulink’s library or a user-defined model.

To study the Simulink models that can be used to build our test platform, beginning with the most important ones: the resident models of wind generators, the Wind Turbine
Doubly Fed Induction Generator and the Wind Turbine Induction Generator, also known as the Wind Turbine Squirrel Cage Induction Generator. The equations that determine the behavior of the models, their inputs, outputs and how they can be connected to our test platform are going to be thoroughly researched.

To perform a series of tests and simulations with different types of wind generators connected to the test platform, such as: o Testing the normal performance of these generators and with irregular situations for different types of wind generators. The abnormalities in the electrical grid can be the wind speed exceeding the value that can still be availed by the wind turbine, a three-phase fault in two situations, when it happens in a bus near the wind generator and far too and a phase-to-ground fault. o Assessing the influence of Flexible AC Transmission Systems in the performance of the wind generators during a short circuit in the electrical grid.
With this test, the fault ride through capability of these types of generators will be studied and we’ll be able to know if the government’s established regulations regarding this matter can be fulfilled.
2

To achieve the objectives set for this master thesis, several resources were used. The models that were used to create the test platform and later to perform all the simulations are resident models in the SimPowerSystems library of Matlab/Simulink with the exception of the Threephase electrical bus and the Power Plant blocks.
The first one is a simple mask for the Three-phase V-I Measurement block, it was built to have resemblance to the common representation of an electrical bus.
The Power Plant block was based on a demo from Matlab/Simulink, which uses a diesel engine with a speed and voltage control system connected to a synchronous machine.
For the remainder of the models that were used on the test platform, such as the transformer block or electrical line, the Matlab offers a help section that contains articles on each of these models, how to use them and what are the mathematical equations behind them.
The test platform that was built in Matlab/Simulink was based on a 12 bus electrical grid that can be found in [2]. It was slightly changed to accommodate the integration of the wind generators.
This network will be thoroughly described later on this report, with all the parameters from all the elements being discriminated.
As mentioned before, the fault ride through capability is defined by a wind generator being able to stay connected to the electrical grid even in the event of a three-phase fault. There are certain voltage levels and reactive power flow limitations that are established by government regulations that must be met. To know what levels these regulations establish the document [3] was studied.
Moreover, to understand what kind of equipment is normally used to give a wind generator this capability, the following papers address this thematic, [4] and [5].
3

This master thesis is divided as it follows:

Chapter 1 – This present chapter presents a brief introduction to this master thesis;

Chapter 2 – The theoretical topics of this thesis are addressed;

Chapter 3 – All the Matlab/Simulink’s blocks are explained;

Chapter 4 – The test platform is described to its fullest and the results from the performed simulations are exposed and commented;

Chapter 5 – At this point, all the conclusions and acquired knowledge will be summarized and suggestions for future investigation under this subject will be given;

Appendix A – A brief explanation of the Simulink environment and how it computes the tests and simulations performed on the test platform;

Appendix B – The parameters of the test platform that is implemented on Simulink are thoroughly described.
4

In this chapter, a theoretical approach takes place to explain the most important topics and concepts that will be used throughout the creation of the test platform and later on, to perform an analysis on the results of the simulations. The first section describes the different types of wind generators that are used and the second addresses the fault ride through capability of these generators, when connected to the electrical grid. This study was based on [6].
The working principle of a DFIG is based on its capability to control its speed through rotor resistance variation. This is why the rotor can’t have a squirrel cage winding it has to be a wound rotor.
With different values for the rotor resistance, for the same electrical power, it is possible to have different values for the speed of the machine, as illustrated in the next figure.
Figure 2.1 - Electric power characteristic for different rotor resistances [6].
To control the output power, it’s placed an AC/DC/AC converter connected to the rotor replacing the variable rotor resistance. This way we can transfer electrical power through the machine’s rotor.
5

Until the nominal value of stator current is reached the output power is controlled in order to optimize the tip speed ratio of the rotor blade and to maximize the performance coefficient of the turbine. When the stator current reaches its nominal value we’ll have a constant output power.
The velocity control through the use of the slip energy gives us the possibility to have this machine working as a generator when the slip is positive. This is only possible if it is supplied active power to the rotor.
The induction generator’s stator is directly connected to the three-phase grid. The rotor is also connected to the grid through a AC/DC/AC converter and a step-up transformer.
The whole system is represented in the next figure.
Figure 2.2 - Block representation of the WTDFIG [6].
The AC/DC/AC converter consists of a three-phase six-arm bridge equipped with insulated gate bipolar transistors (IGBT) with a pulse width modulation (PWM). The basic principle of the PWM control system allows applying a sinus wave form with adjustable frequency, amplitude and phase to the converters’ terminals. A power factor between 0,9 inductive and 0,9 capacitive is usually guaranteed by the manufacturers.
The main responsibility of the converters’ control system is to assure the maximum power factor possible thusly maximizing the electrical power harvested from the wind.
6

In the next figure we can find a representation of the electrical system of the doubly-fed induction generator.
Figure 2.3 - Electrical system of the DFIG [6].
In the previous figure we have some parameters, R s
, X ls
, R’ r and X’ lr
that are, respectively, the resistances and leakage inductances of the stator and the rotor. X m
is the magnetizing inductance.
According to the electrical system representation the following relations are valid for the steady state:
V
S
V s
' r
 
( R
S
 jX ls
) I E
 
R r
 jX ' )

I ' r

E
(0.1)
The electromotive force (E) and the slip (s) are expressed by the following equations: s
E j X m


  s
 r
 s
I m
(0.2)
As far as the power flow is concerned, the following equations describe the active and reactive power flow in the stator and rotor:
P
S
Q
S


Re{ V I
S
*
} R I
S
2 
P ag
Im{ V I
S
*
}
 
X ls

I
S
2

Q ag
(0.3)
P ' r s
Q ' r s

Re{
V s
' r

Im{
V s
' r

I

I r r
 
R
 r
 s
' r I
2
P ag
 
X ' lr

I r
2 
X m

I m
2 
Q ag
(0.4)
7

where,

P
S
and Q
S
are the active and reactive power supplied to the network. If positive the power flows from the machine to the network;
 P’ r
/s and Q’ r
/s are the active and reactive power that flow in the rotor from the reference frame that rotates at the rate of the rotating magnetic field;

P ag
= Re[E∙I
S
*
] and Q ag
= Im[E∙I
S
*
] are the active and reactive power that flow in the machine’s air gap. If positive the power flows from the rotor to the stator.
The swing equation for active power of the machine’s rotor will be:
P ag

P ' r

R ' r

I ' r
2

P mec
(0.5)
In the previous equation P mec is the mechanical power that flows from the machine’s rotor. If positive the machine’s working as a generator and if negative the machine’s working as a motor.
We can also deduce the following expression: s P ag

P ' r

R ' r

I ' r
2
(0.6)
From the previous equation we can deduce that from the total active power that flow in the air gap, the portion s∙P ag
flows from the rotor after the losses being deduced. The other portion of
P ag
is the mechanical power, so the following equation is valid:
P mec
(1 s ) P ag
(0.7)
We can have two situations, power flowing to the machine through the rotor (P’ r
>0) or the reverse situation where the power is flowing from the machine (P’ r
<0).
The losses in the machine can be defined by the following set of equations:
P p

R I
S S
2

R ' r

I ' r
2
Q p

X ' lr

I ' r
2 
X m

I m
2 
X ls

I
S
2
(0.8)
Finally, we can have the following swing equations for this machine:
P ' r

R ' r

I ' r
2
P
S
R I
S
Q ' r

Q
S

Q p
2
P
S

P ' r

P mec

P p
(0.9)
If this machine is working, reactive power will be consumed. The reactive power that flows through the rotor will be Q’ r
/s, that when positive the power flow will be from the exterior of the
8

machine to the rotor. As an example, if the stator absorbs reactive power (Q
S
<0, stator power factor is capacitive) the reactive power in the rotor will flow from the rotor to the network
(Q’ r
/s<0) if |Qs|>Qp.
On the other hand, if the necessary reactive power for the functioning of the machine flows through the rotor, the stator power factor can be either inductive or capacitive.
With the doubly-fed induction generator, the following operations modes can occur: s > 0 s < 0
Table 2.1 - Operation modes of the DFIG.
P’r
>0
>0
<0
>0
>0
<0
Pag Pmec Mode
<0; P’r < R’ r∙
I’ r
2
<0
>0; P’r > R’ r∙
I’ r
2
>0
Motor
Generator
<0 <0
<0; P’r > R’ r∙
I’ r
2
<0
>0; P’r < R’ r∙
I’ r
2
>0
>0 >0
Motor
Motor
Generator
Generator
The SCIG has a working principle very similar to the DFIG. In terms of electrical system, it is the same as the DFIG with one change: we have to consider V’ r
= 0. The SCIG can’t work as a generator with positive slips because it has a short-circuited rotor therefor it will only work as a generator with negative slips.
The main disadvantage of the SCIG is that it will always consume reactive power whether it is working as a generator or a motor. This reactive power is proportional to the active power that flows from the machine to the network it is connected to.
To contradict this setback the SCIG are always equipped with a system that will compensate the reactive power consumption. This system is commonly composed by a series of capacitors that w ill decrease the machine’s consumption of reactive power.
9

With the squirrel cage induction generator, the following operations modes can occur: s > 0 s < 0
Table 2.2 - Operation modes of the SCIG.
P’ r
0
0
P ag
<0
>0
P mec
<0
>0
Mode
Motor
Generator
Since the use of the DFIG in the wind generators is generally preferred over the use of the
SCIG, due to some limitations of the SCIG, such as the lack of control of output power and the fact that the SCIG always consume reactive power, the association of the static synchronous compensator (STATCOM) with this machine has become popular to reverse this trend.
In the last years there has been a wide proliferation of wind generators, installed all over the world. Due to this significant increase in number certain regulations and policies in each country regarding this kind of energy generators had to be revised.
This great increase was also motivated by the Directive 2011/77/EC of the European Parliament and of the Council of 27 September 2001 on the promotion of electricity produced from renewable energy sources in the internal electricity market. This directive defined reference values to determine the goals of each country in this matter. Portugal had the reference value fixed on 39% of the produced energy being from a renewable source. Later on the government reviewed this established goals and defined a new percentage of 45%.
Nowadays, a significant percentage of the power generation is assured by wind power generation. According to [7], in Portugal 18% of the energy generation is harvested from the wind, which means that it’s crucial to be able to maintain the generation even in an event of a short-circuit in the electrical grid since this generators have a big contribution on the satisfaction of the demand.
10

According to the previously mentioned established regulations, during a short-circuit, whether it’s a three-phase, a phase-to-phase or a phase-to-ground fault, the wind generators must remain connected to the grid as long as the voltage across their terminals remains above the voltage-time characteristic that is represented in the following figure.
Figure 2.4 - Voltage-time characteristic established by regulations as seen in [3].
This imposition, also referred as the Fault Ride Through Capability , hopes to reduce the disturbances in the grid that could appear due to the grid faults. It can also prevent a grid wide blackout that could happen because of an unbalance between the demand and the generation of electrical energy. These are the two main reasons why it is so important for the wind generators to stay connected to the electrical grid and to be able to quickly resume its normal power generation.
When we have a WTDFIG, per example, connected to the grid its operation during a fault is complex due to the fact that the stator is directly connected to the grid while the rotor is connected via converter. To avoid destruction of the wind generator’s equipment what would normally happen is that it would be disconnected from the grid and later reconnected when the grid fault is cleared. As mentioned before this way of operation does not meet the new established regulations.
To help the wind generators to comply with these new regulations, fault mitigation equipment were projected which will be addressed in the next section.
Flexible AC Transmission Systems (FACTS) devices are a new type of power flow control system. Two examples of this type of equipment are the Dynamic Voltage Restorer (DVR) and the Static Synchronous Compensator (STATCOM), which are Flexible AC Transmission
11

Systems (FACTS). Both have the same main objective: to mitigate voltage swells at the wind generator’s terminals.
The DVR is a power electronics device which main objective is to protect a sensitive load from disturbances in the supply voltage. This will be achieved by injecting voltage in series with the load. The STATCOM, as it was explained before, will inject a reactive shunt current into the electrical grid.
The basic principle of operation of series and shunt compensation are represented in the next two figures, respectively.
Figure 2.5 - Basic principle of series compensation as seen in [4].
Figure 2.6 - Basic principle of shunt compensation as seen in [4].
This concept includes power electronics devices that allow the control of the electrical systems to be more flexible, namely in the ability to quickly and continuously change the parameters that control the dynamics of an electrical system.
The next figure should illustrate the working principle of the power flow control systems
(FACTS).
12

Figure 2.7 - Power flow in FACTS devices [6].
The power that flows between two systems through an inductive line can be influenced by three parameters: root mean squared value of the voltage (V
1
, V
2
), the line’s impedance (X
L
) and the l ag between the two voltages (δ = δ
1
- δ
2
). The FACTS will operate on one or more of these parameters. The choice of which parameters to control will depend on the objective that is to be met.
Although there are several FACTS devices available, the STATCOM is the one that better fits the needs of the SCIG. In steady state, it controls the voltage and also, during a short circuit in the network the STATCOM will react to it by injecting reactive power.
The STATCOM is an electronic device which main objective is to regulate the voltage in the connection point between the rest of the network and the device associated with it. The regulation is achieved through controlling the flow of reactive power.
Earlier versions of the STATCOM were based on thyristors that would control a group of capacitors or inductors installed in parallel. With some recent advances in power electronics, the STATCOM now uses DC/AC converters, also known as inverters, based on fully controlled semiconductors.
13

The STATCOM has also a coupling transformer, a control system and a direct current source, as shown in the next figure.
Figure 2.8 - Block diagram of a STATCOM based on [6].
The network and the STATCOM usually operate and different voltages, the coupling transformer will make possible for the connection between the two. The inverter in association with the control system and the direct current source will form a voltage source converter (VSC).
The inverter is based on a set of fully commanded semiconductors such as GTO (Gate Turn
Off) or IGBT. Its function is to generate an AC wave form from the voltage at the terminals of the direct current source. This voltage is achieved through a group of capacitors.
To better explain the working principle of the STATCOM, the next figure shows the equivalent scheme of the connection between the STATCOM to a network.
Figure 2.9 - Connection between the STATCOM and a network. V
S
is the network voltage and V
I the STATCOM’s voltage [6].
In the previous figure the STATCOM and electrical system are represented by the voltage sources V
I
and V
S
in series with a reactance X
L
which represents the equivalent reactance of the electrical system in series with the reactance of the coupling transformer of the STATCOM.
14

In this figure it is also represented the phasor diagram of the voltages where δ is the lag between the voltage of the electrical system and the STATCOM. There are five possible situations to be studied:
1. When V
S
is leading in relation to V
I
(0˚<δ<90˚) and V
S
=V
I
the active power flows from the network to the STATCOM;
2. When V
S
is lagging in relation to V
I
(90˚<δ<0˚) and V
S
=V
I
the active power flows from the STATCOM to the network;
3. When V
S
is in phase with V
I
(δ=0˚) and V
S
=V
I
the active or reactive power does not flow between the STATCOM and the network;
4. When V
S
is in phase with V
I
(δ=0˚) and V
S
>V
I
the STATCOM consumes reactive power and there is no active power flow;
5. When V
S
is in phase with V
I
(δ=0˚) and |V
S
|<|V
I
| the STATCOM supplies reactive power and there is no active power flow.
These situations describe how the STATCOM will work when connected to a network. Ideally the STATCOM is connected to an ideal voltage source since it would allow it to compensate both active and reactive power. In the real case the STATCOM only controls the reactive power since the voltage source is a set of capacitors.
The STATCOM has the ability to regulate the voltage in the connection bus (between the
STATCOM and the network) by alternating the injection of inductive or capacitive current.
Considering the voltage in the electrical system constant if the STATCOM’s voltage has lower amplitude than the network’s voltage, it absorbs reactive power generating currents that lag 90˚ in relation to the network’s voltage. If the opposite occurs, the STATCOM will supply the network with reactive power, generat ing currents that lead the network’s voltage by 90˚.
The next figure represents the VI characteristic of the STATCOM. If the network’s voltage diverts significantly from the reference value (which may happen during a short circuit) the
STATCOM can compensate the system by supplying a maximum constant current (inductive
[I max
] or capacitive [I min
]). If the network’s voltage is lower than the minimum working voltage of the STATCOM (V dcmin
) it will no longer have the ability to supply the maximum capacitive current
(I min
).
Figure 2.10 - V-I characteristic of the STATCOM [6].
15

To keep the voltage at the terminals of the wind generators constant, the DVR will inject dynamically the controlled inverse fault voltage. The Dynamic Voltage Restorer consists of a voltage source converter with an energy source at the DC side, an output filter, a coupling transformer and a bypass switch (composed by thyristors). A closed loop control was implemented using a rotating dq reference frame aligned to the grid voltage. This study was based on [4]. In the next figure we can find represented the DVR’s control structure.
Figure 2.11 - DVR's control structure [4].
The dynamics of this system allows to control (with and integral controller) the actual DVR voltage u p
to the reference voltage u
* p
that is computed by subtracting the actual grid voltage u g from the constant reference voltage u
* g
.
For the controller, the delay time (T
DVR
) of the voltage source converter caused by sampling and computation is modeled as a first order delay element and the gain (k
DVR
) are computed using the following relations:
T
DVR

1 f s k
DVR

1
2

T
DVR
(0.10)
The voltage source converter receives its pulses that are created by a PWM algorithm, after the transformation of the dq values into three phase coordinates occurs. The DVR can be synchronized to the grid voltage using a PLL. If the power factor of the wind turbine is equal to one, the complex power consumption of the DVR can be computed by the following expression:
S
DVR

U p

I
*
WT

( U g

U
WT
)

I
*
WT

( U
  
P
WT
(0.11) where U is the relative amplitude and δ is the phase angle jump of the voltage swell. The active and reactive power will correspond to the real and imaginary parts of the complex power, respectively. It is interesting to note that if there’s no phase angle jump of the voltage swell
(δ=0), the DVR will only compensate the active power in size of a fraction of the rated wind turbine power (P
WT
).
16

In this section of the report, each of the most significant Simulink blocks that will be used to create the test platform will be briefly explained and their parameters will be presented. To have a further insight into each of these blocks, the Appendix B should be consulted.
All the blocks that are explained in this chapter all belong to the SimPowerSystems library.
Other Simulink blocks, such as the Scope that’s used to observe the evolution over time of a certain measurement, are not explai ned since their working principle falls out of this thesis’ context. The next figure represents the test platform as it is simulated in Matlab/Simulink.
Figure 3.1 - Test platform as it is represented in Matlab/Simulink.
17

In the test platform developed during this thesis, several different electrical elements were used, such as, the models for the wind generators (the WTDFIG and the WTSCIG), the models for the
Power Plants, the protection system for the wind generators and the Power Plants, the threephase electrical bus, the STATCOM, the three-phase electrical line, the three-phase load and, finally, the three-phase transformer. There’s also an important block for the simulation of short circuits with this platform. It’s the model of a three-phase fault.
Both the model for the WTDFIG and the model for the WTSCIG use two very important models of electrical elements: the asynchronous machine and the wind turbine. For the first wind generator, the model of this machine has a wound rotor and for the latter it has a squirrel cage rotor connection. The wind turbine model that is present in both generators, receives as inputs the wind speed (which is a function defined externally by the user), the generator speed (which comes directly from the respective model of the asynchronous machine) and, finally, receives the pitch angle of the blades. As the output, this turbine has the electromagnetic torque, which will supply the previously mentioned asynchronous machine.
The control mode of the WTDFIG can be defined by the user: we can have either voltage control or reactive power control. For the simulations that will be presented in the next section, it was chosen the option of voltage control.
Regarding the parameters defined for each of these models, firstly, the model used for the
WTDFIG has the following parameters:
Table 3.1 - Generator data for the WTDFIG .
Stator
Rotor
Grid-side coupling inductor
Resistance Rs (pu)
Inductance Lls (pu)
Resistance Rr’
(pu)
Inductance Llr’
(pu)
Magnetizing inductance Lm
(pu)
Inertia constant H
(s)
Friction factor F
(pu)
Pair of poles p
Resistance R (pu)
Inductance L (pu)
Nominal DC bus voltage (V)
DC bus capacitor
(µF)
0.00706
0.171
0.005
0.156
2.9
5.04
0.01
3
0.0015
0.15
1200
60000
18

The next table shows the parameters that were defined for the WTSCIG model.
Table 3.2 - Generator data for the WTSCIG.
Stator
Rotor
Resistance Rs (pu)
Inductance Lls (pu)
Resistance Rr’ (pu)
Inductance Llr’ (pu)
Magnetizing inductance Lm (pu)
Inertia constant H (s)
Friction factor F (pu)
Pair of poles p
0.004843
0.1248
0.004377
0.1791
6.77
5.04
0.01
3
Line
1 - 4
4 - 5
4 - 9
8 - 9
5 - 6
7 - 8 r1 (Ω/km)
0
0.01732
0.008067
0.01056
0.06991
0.00715
2 - 8
3 - 6
0.006098
0.004068
6 - 7 0.019198
10 - 13 0.01
The three-phase lines have the following parameters that can be directly defined in the test platform: r0 (Ω/km)
0
0.22518
0.10487
0.13728
0.90884
0.09301
0.079279
0.052889
0.249583
0.13
Table 3.3 - Three-phase lines parameters. l1 (H/km) l0 (H/km) c1 (F/km) c0 (F/km) l (km)
3.55E-03 1.06E-02 1.20E-09 1.00E-12 210
5.56E-02 1.67E-01 1.13E-08 5.01E-09 190
5.24E-03 1.57E-02 1.13E-08 5.01E-09 240
9.92E-03 2.98E-02 1.13E-08 5.01E-09 220
1.75E-02 5.24E-02 1.13E-08 5.01E-09 180
4.44E-03 1.33E-02 1.13E-08 5.01E-09 230
3.85E-03 1.16E-02 1.13E-08 5.01E-09 200
3.01E-03 9.03E-03 1.13E-08 5.01E-09 230
1.04E-02 3.11E-02 1.13E-08 5.01E-09 200
4.00E-02 1.20E-01 1.13E-08 5.01E-09 30
19

As far as the transformers are concerned, the following table describes their parameters and the windings connections.
Table 3.3 - Transformers' Winding 1 parameters.
Transformers
9 - 11
10 - 5
Winding 1
Connection V
1
Ph-Ph (V rms
) R
1
(pu) L
1
(pu)
Yg 220 kV 0 0.08
Winding 1
7 - 12
13 - 14
Connection V
1
Ph-Ph (V rms
) R
1
(pu) L
1
(pu)
Delta 60 kV 0 0.08
Winding 1
Connection V
1
Ph-Ph (V rms
) R
1
(pu) L
1
(pu)
Yg 220 kV 0 0.08
Winding 1
Connection V
1
Ph-Ph (V rms
) R
1
(pu) L
1
(pu)
Delta 575 V 0 0.1
Table 3.4 - Transformers' Winding 2 parameters.
Transformers
9 - 11 Winding 2
Connection V
1
Ph-Ph (V rms
) R
1
(pu) L
1
(pu)
Delta 60 kV 0 0.08
10 - 5
7 - 12
13 - 14
Winding 2
Connection V
1
Ph-Ph (V rms
) R
1
(pu) L
1
(pu)
Yg 220 kV 0 0.08
Winding 2
Connection V
1
Ph-Ph (V rms
) R
1
(pu) L
1
(pu)
Delta 60 kV 0 0.08
Winding 2
Connection V
1
Ph-Ph (V rms
) R
1
(pu) L
1
(pu)
Yg 60 kV 0 0.1
20

The total active and reactive power consumption equals to 445.4 MW and 212 MVar, respectively. The loads are described in the following table, according to its respective bus.
Table 3.5 - Loads of the test platform.
10
10
11
11
12
12
14
Loads
Bus
6
8
V
N
(Vrms)
220 kV
220 kV
60 kV
60 kV
60 kV
60 kV
60 kV
60 kV
575 V
P (MW)
30
100
90
0
125
0
100
0
0.4
Q
L
(Positive MVar) Q
C
(Negative MVar)
12 0
40
40
0
65
0
15
0
0
0
0
10
0
15
0
15
0
There are three three-phase power plants in the test platform, with a total power generation of
520 MVA. The generation of each power plant is discriminated in the following table:
Table 3.6 – Nominal power of each power plant.
Generation
Bus
1
1
2
3
14
P (MW)
150
170
200
60
Q (MVar)
50
70
60
30
1
Swing bus.
21

The synchronous machine used in each of the power plants has a salient-pole rotor and has the following parameters:
Table 3.7 - Parameters of the power plant's synchronous generator.
Reactances (pu)
Xd
Xd’
Xd’’
Xq
Xq’’
Xl
Stator resistance Rs
(pu)
Inertia coefficient H
(s)
Friction factor F (pu)
Pair of poles
1.56
0.296
0.177
1.06
0.177
0.052
0.0036
1.07
0
2
22

In order to study the performance of different types of wind energy generators, a default network was created on Matlab/Simulink, based on the 12 bus network that is described in [2]. In the next figure this electrical grid is represented through a single line diagram.
Figure 4.1 - Single line representation of the test platform based on [2].
Although it is based on the 12 bus network mentioned before, to accommodate the wind energy generators two busses were added, B13 and B14, which are connected to the bus B10 through the 10-13 line and the 13-14 transformer. When the WTDFIG is used, a small resistive load is connected to its terminals, because of the limitations of the nonlinear elements in Simulink, as explained in Appendix A. The wind energy generator will be connected to the B14 bus.
This network has 10 three-phase lines, 4 three-phase transformers and 9 three-phase loads. As far as the generation is concerned, the electrical grid is fed through 3 power plants and the wind generator with a nominal power of 60 MW and the following power-wind speed characteristic.
23

Figure 4.2 - Turbine power characteristics.
When the WTSCIG is connected to the test platform, a capacitor bank of 400 kVar is connected at its terminals to compensate the reactive power consumption.
It is also important to refer that the rotor side controller of the WTDFIG is set to voltage regulation, for a reference voltage of 1 pu.
In Appendix B there ’s a representation of this test platform as it is simulated in the
Matlab/Simulink environment. In that section there are also all the parameters of these electrical grid elements.
With the test platform operational, which was described in its respective section, a series of tests and simulations were performed. The duration of each simulation was normally 60 seconds. To eliminate the initial transient, which is not relevant to this study, the system is set to have all the variables constant for the first 9 seconds. This transient occurs due to the solving method of Simulink. It’s an iterative method and since all the initial values are set to zero, the system will take some time to compute the steady state measurements.
The next list describes all the tests that will be performed:

Connection of the Wind Generators to the grid;

Pitch control;

Three-phase short circuit in bus B6;

Three-phase short circuit in bus B13;

Phase-to-ground short circuit in bus B13;

Fault Ride Through Capability.
In each of these simulations several variables will be observed and commented through their time characteristics.
24

In this section, a simple test was conducted just to study the behavior of different types of wind generators when connected to the test platform that was previously presented. In this test there are no faults in the grid, the wind generator is not initially connected but will be after 10 seconds of the simulation. The wind speed will be a function that increases its value and then it will decrease. This will allow us also to observe the active power harvested from the wind following the wind speed.
With a simulation time of 60 seconds, the next figures show the most relevant measurements for the purpose of this test. The first set of figures will be concerning the simulation using a
WTDFIG and the second set will be concerning the WTSCIG.
Figure 4.3
– Wind speed, active and reactive power of the WTDFIG.
As we can see from the previous figure, the generated active power follows the wind speed evolution with a small delay that can be explained by the machine’s dynamics. A different wind speed implies a different electromagnetic torque, which means a different output power.
25

However, due to the DFIG control system, a small delay is expected. The next figure will show the active power generation from all four production units in our test platform. A negative value means that there’s consumption of reactive power by the wind turbine.
Figure 4.4 - Active power generation from each power plant and from the WTDFIG.
The P1, P2 and P3 graphics correspond to the active power flowing out of the three power plants in the test platform and P14 is the active power flowing out of the wind generator.
As the active power harvested from the wind increases, the other three generators can see their generation attenuated. The electrical grid works as a whole. When the wind speed is higher (the power generated by the wind generator is higher) the use of power plants that do not work on renewable sources can be reduced.
When the wind generator is connected to the grid (at t = 10s) we can observe a strong transient that affects all the power plants in the electrical grid. The system can return to the normal operating state quickly due to the DFIG’s control system. However, there is a significant variation of the output active power which will force the non-renewable power plants to increase its generation.
Since the WTDFIG’s control system is set to voltage regulation, the voltage at its terminals shouldn’t have a significant variation from the reference value, which we can confirm in the next figure.
26

Figure 4.5 - Voltage at the WTDFIG's terminals.
As mentioned before, the next set of figures regards a test under normal conditions with a
WTSCIG connected to our test platform.
Figure 4.6
– Wind speed, active and reactive power of the WTSCIG.
27

Just like the WTDFIG, we can see the WTSCIG power generation following the wind speed evolution over time. However, due to the lack of control system of this generator (the stator is connected to directly to the grid and the rotor is short circuited) we can observe some fluctuations in the output power. Contrary to the WTDFIG there’s no significant delay between the change of the wind speed and the evolution of generated power over time. This can also be explained by the absence of the control system, connected between the rotor of the machine and the grid. The control system’s dynamics introduce a small delay to the wind generator’s system.
Figure 4.7 - Active power generation from each power plant and from the WTSCIG.
Just like with the WTDFIG, when the power generated by the WTSCIG increases the other three non-renewable power plants will reduce their generation in a way that the demand is satisfied.
When the wind generator is connected (at t = 10s) we can observe a transient that takes approximately 5 seconds to be extinguished, unlike when we have a WTDFIG. However, in this case, the peak values of the output power that result from this transient are considerably smaller in module than the peak values reached when the WTDFIG is connected to the grid.
28

The voltage at the WTSCIG terminals will not be constant during the connection to the grid due to the lack of the voltage regulation system that the WTDFIG has. In the next figure we can see the voltage at the WTSCIG’s terminals.
Figure 4.8 - Voltage at the WTSCIG's terminals.
29

In this section it was tested the situation where the wind reaches the wind generators maximum value and has to limit the power generation to its nominal value. The measurements observed were the wind speed, the active and reactive power of the generators, the voltage at its terminals and the pitch angle of the blades. The first three figures concern the simulation with a
WTDFIG and the other three concern the WTSCIG.
Figure 4.9 – Wind speed, active and reactive power of the WTDFIG.
As the wind speed increases, the active power generation follows its evolution until it reaches the nominal wind speed. The pitch control system starts do act and limits the output power to its nominal value, which is approximately 60 MW when the wind speed is approximately 20 m/s.
This limitation should occur when the wind speed was at 15 m/s but doesn’t due to the inertia of the wind turbine and the generator. When the wind speed reaches again values under 20 m/s, we can see that the power generation follows again the wind characteristic, which should occur for values less than 15 m/s.
30

Figure 4.10 - Voltage at the WTDFIG terminals. Figure 4.11 - Pitch angle of the WTDFIG.
Due to the control system of the WTDFIG that is connected to the AC/DC/AC converter, when the nominal speed is reached and the output power is limited to its nominal value a nd there’s no significant disturbance to the voltage at the wind generator’s terminals. The pitch angle value increases when the wind speed reaches the 20 m/s marker and thusly limiting the output active power of the generator as the wind speed increases.
The next set of figures will show the behavior of the WTSCIG when the wind speed reaches the nominal value. As we will observe, the lack of a control system within this generator will create a significant instability in the system.
31

Figure 4.12 - Wind speed, active and reactive power of the WTSCIG.
As the wind speed increases the system has a certain delay in controlling the generated active power. In this case, the power doesn’t stabilize in a fixed value, the lack of a control system that commands the pitch control results in an unstable limitation of the output power, contrary to what happens with the WTDFIG.
Figure 4.13 - Voltage at the WTSCIG terminals. Figure 4.14 - Pitch angle of the WTSCIG.
32

Unlike what happens with the WTDFIG, this generator has a small voltage swell at its terminals that seems to be aggravated when the nominal power has been reached. This voltage swell seems to be over when the output power is no longer limited by the pitch control.
The pitch angle in this type of generator does not have the same well-behaved evolution that can be observed in the simulation for the WTDFIG, where the pitch angle is computed with the help of the control system.
In this test, it is simulated a three-phase short circuit near the bus B6, 25 seconds after the simulation begins with the duration of 100 ms.
In this simulation the measurements taken were the active and reactive power of the WTDFIG and the WTSCIG, its slip and terminal voltage. To have a better look on what happens during the short circuit, the time evolution of these measurements was zoomed to a smaller time frame, around the time of the three-phase fault.
The first set of figures correspond to the simulation performed using the WTDFIG and then there are the figures that correspond to the simulation with the WTSCIG.
Figure 4.15 - Active power of the WTDFIG. Figure 4.16 - Reactive power of the WTDFIG.
33

Figure 4.17 - Slip of the WTDFIG. Figure 4.18 - Voltage at the WTDFIG terminals.
The WTDFIG has a similar behavior to the WTSCIG when a short circuit far from the generator occurs. There’s a significant variation of the reactive power, which can be explained by the oscillation observed in the machine’s slip.
The voltage at the wind generator’s terminals achieves a minimum of approximately 0.3 pu and the active power generated reaches a minimum of -40 MW.
Figure 4.19 - Voltage at the B5 bus. Figure 4.20 - Voltage at the B6 bus.
The voltage at the busses near the short circuit, B5 and B6, are significantly affected by it, in the first one we can observe a great voltage dip. The voltage in B6, naturally, is zero during the three-phase fault.
34

Figure 4.21 - Active power of the WTSCIG. Figure 4.22 - Reactive power of the WTSCIG.
Figure 4.23 - Slip of the SCIG. Figure 4.24 - Voltage at the WTSCIG terminals.
When a short circuit occurs far from the wind generator (in the B6 bus) we can observe some serious variation in the voltage at its terminals and in the active and reactive power generation.
At the time of the short circuit we can observe a voltage dip with the minimum value of approximately 0.3 pu. The active power suffers also a great reduction in value, with a minimum value of -80 MW which will provoke an increase in module of the slip of the SCIG.
During the fault, the electromotive force of the rotor will be higher than the voltage at the SC IG’s terminals which can explain the variation of the reactive power. It will have a great increase at first and before it stabilizes it will have a decrease in value.
All the measurements tend to stabilize in their prefault values which mean that there’s no loss of synchrony in the electrical grid.
35

Figure 4.25 - Voltage at the B5 bus. Figure 4.26 - Voltage at the B6 bus.
The voltage in B6 will be zero during the fault, returning then quickly to its steady-state value, which can be expected for the bus where the short circuit happens. In the bus B5, the voltage suffers a significant dip, the value decreases to approximately 0.2 pu.
The great difference between the results we get with the WTSCIG and the WTDFIG is that with the latter can reach the steady-state much quicker after a three-phase fault in the grid, however the transients can be more aggressive. Per example, with the generated active power of both wind generators, with the WTSCIG we take approximately 5 seconds to stabilize the generation unlike the WTDFIG that takes approximately half a second to stabilize and to resume the steady-state situation. This can be explained by the control system of the AC/DC/AC converter that connects the rotor of the machine to the grid.
The WTDFIG reacts better to a grid fault and that’s one of the reasons why nowadays this type of wind generators is more popular than the WTSCIG.
A three-phase short circuit was simulated in a bus near the wind generator (bus B13). To have a better look on what happens during the short circuit the time evolution of the observed measurements was zoomed to a smaller time frame, around the time of the three-phase fault.
The following figures show the results from this simulation, first for the WTDFIG and then for the
WTSCIG.
36

Figure 4.27 - Wind speed, active and reactive power of the WTDFIG.
When a short circuit occurs near a WTDFIG, as we can see the active power generation also goes to zero, such as the WTSCIG. The main difference is the time the system takes to return to its normal operating state. In this case the system will recover from the fault in a matter of 200 ms, due to the control system connected to the AC/DC/AC converter.
Figure 4.28 - Voltage at the terminals of the WTDFIG.
37

The voltage at the WTDFIG terminals also suffers a great dip, reaching a minimum value very close to zero. This means that this type of generator doesn’t have also a fault ride through capability on its own.
Figure 4.29 - Power generation of the power plants and the WTDFIG.
Until the wind generator resumes its normal active power generation, the other three generation units will compensate. Since the WTDFIG recovers from the fault very quickly, this compensation is barely visible in the graphic above.
38

Figure 4.30 - Wind speed, active and reactive power of the WTSCIG.
When the three-phase fault occurs in bus B13, the wind generator becomes temporarily isolated from the grid. The active power generation is nullified and a significant amount of reactive power is generated. With a WTSCIG connected to the grid, it takes approximately 2 seconds to have all the measurements returning to its steady-state evolution.
Figure 4.31 - Voltage at the terminals of the WTSCIG.
39

The voltage at the terminals has a minimum value of approximately 0.1 pu. This can be critical due to the regulations specifications established for wind generators, if the voltage at its terminals is lower than 0.2 pu it is mandatory to shut down the generator from the grid. This generator alone does not have the fault ride through capability that is required.
Figure 4.32 - Power generation of the power plants and the WTSCIG.
As mentioned before, when the short circuit occurs the power generation of the wind generator becomes null.
During the fault the required active power to satisfy the demand will be supplied by the nonrenewable power plants. When the fault is cleared the wind generator will not instantaneously be able to supply its share of the load, so we can observe the other generation units of the test platform compensating this deficit created by the WTSCIG, just like when the WTDFIG is connected.
40

In this section a phase-to-ground short circuit will take place, 25 seconds after the beginning of the simulation, near the wind generator (bus 13). The short circuited phase will be the phase A.
The first set of figures will concern the WTDFIG, followed by the measurements taken from the simulation using a WTSCIG.
Figure 4.33 - Wind speed, active and reactive power of the WTDFIG.
Unlike what happens with the three-phase short circuit at bus 13, the active power generation isn’t null during the fault. The time that the generator takes to return to its steady-state is similar in both cases, for the WTDFIG.
41

Figure 4.34 - Voltage at the terminals of the WTDFIG, dark blue is the phase A, pink is the phase B and light blue is the phase C.
The voltage of each phase at the terminals of the WTDFIG will not be the same, as it happened with the threephase fault. In this case, we’re able to discern, during the fault, each of the voltage components, as seen in the previous figure. Comparing to the three-phase fault, we can observe a smaller voltage dip at the terminals of the wind generator.
42

Figure 4.35 - Wind speed, active and reactive power of the WTSCIG.
Figure 4.36 - Voltage at the terminals of the WTSCIG, dark blue is the phase A, pink is the phase B and light blue is the phase C.
43

Just like with the WTDFIG, when a short circuit occurs near the terminals of the WTSCIG the active power generation won’t be zero during the fault. The two great differences between these two situations is that with the WTSCIG we’ll experience a bigger time gap until the system reaches its steady-state and a smaller variation of active and reactive power generation during the transient.
With the WTSCIG we have a bigger voltage dip for at least one of the phases of the electrical grid near its terminals.
Looking at this results, the main difference between the three-phase and the phase-to-ground short circuit is the voltage dip that occurs at the terminals of each of the wind generators, in the first situation the electrical grid experiences a bigger voltage dip near them. This fact can result in the protection systems disconnecting these generators from the network.
In this section, the test platform will have a STATCOM connected to the wind generator with the main purpose of giving it the fault ride through capability required by government regulations.
Two situations will be studied, the one with a STATCOM of 0 MVA and other with 30 MVA.
When we have a STATCOM of 0 MVA is the same as if it wasn’t connected in parallel to the wind generator.
The Protection System block will be connected to perform these tests. The most important limit to set is the minimum voltage at the terminals of the wind generator. According to [3] the minimum value is 0.2 pu.
The WTDFIG has already the rotor-side control system that is able to inject reactive power into the electrical grid during a fault so the use of a STATCOM with this type of wind generator is redundant. Therefor the next set of figures will only concern the simulation of the STATCOM connected to the WTSCIG. The short circuit will be in the B13 bus and it’s going to be a threephase fault with the duration of 100 ms.
44

Figure 4.37
– Reactive power for a 0 MVA STATCOM.
STATCOM.
Figure 4.38 - Voltage for a 0 MVA
The output reactive power of the WTSCIG reaches about -70 MVar after the short circuit happens and the voltage at the terminals reaches a minimum value of 0.15 pu, which triggered the protection system that will disconnect the wind generator from the rest of the grid, as the next figure shows:
Figure 4.39 - Active power generated by the WTSCIG.
45

Figure 4.40 - Reactive power for a 30 MVA STATCOM. Figure 4.41 - Voltage for a 30 MVA STATCOM.
As the nominal power of the STATCOM device increases to 30 MVA we can see that when the short circuit occurs, the new maximum value of reactive power flowing out of the WTSCIG is approximately 100 MVar. The STATCOM injects reactive power so the voltage dip at the terminals of the wind generator will be smoother. In fact, as we can see from figure 4.41, the new voltage minimum is approximately 0.35 pu, which is perfectly within the limits imposed by the regulations.
46

The main objective of this thesis was achieved. A test platform was created in the
Matlab/Simulink environment and it is ready to be tested with the WTDFIG and the WTSCIG.
Several simulations were conducted that can lead us to several important conclusions about the performance of different types of wind generators connected to an electrical grid.
The great difference that separates the WTDFIG from the WTSCIG is the control system the first one has, that controls the AC/DC/AC converter that connects its rotor to the grid. This system will allow a better performance of the generator when facing any kind of disturbances.
When the wind nominal speed is reached, the WTDFIG’s pitch angle control will control smoothly the output power which will be equal to its nominal power. The WTSCIG does not have this control system so the pitch control system will be faulty, the limitation of the output power will not be ideal which will result in an abnormal variation of it. When the nominal speed is reached, since the power generation is not properly controlled, we can observe the voltage at the WTSCIG’s terminals to have a small swell. In these simulations there was no loss of synchrony when this happened, but in certain conditions that occurrence may happen.
When a three-phase fault occurs in the network, these two types of wind generators have different reactions. The WTDFIG’s can present higher variations of the voltage and power generation than the WTSCIG after a fault in the grid, due to a large stator current that leads to large rotor currents that can damage the AC/DC/AC converter. However the WTDFIG can return to the operation in the steady-state significantly quicker than the WTSCIG, due to its control system and converter that connects the rotor to the grid.
The use of WTDFIG over the WTSCIG has been a trend for the past years. The great advantages of the WTSCIG are its robustness, the ease and affordable price to massively produce them. However, this type of generator does not support grid voltage control due to its necessity to obtain the excitation current from the stator terminal.
As far as the Fault Ride Through Capability that the regulations require from the wind generators, this can be achieved through FACTS devices. One of these devices was tested and it was the STATCOM so we could observe its influence in the WTSCIG ’s performance when a three-phase fault occurred. With the STATCOM, a great amount of reactive power was injected into the grid so that the voltage dip that resulted from the fault could be softened. With this, the generator no longer had to be disconnected from the grid. The WTDFIG wasn’t tested with the
STATCOM because it has already the rotor-side control system that is able to inject reactive power into the electrical grid during a fault which is the purpose of the STATCOM.
47

There are a few subjects that can be addressed to continue this work. Other models of wind generators can be created to test its performance when connected to an electrical grid and facing any kind of adversities. The direct drive wind turbine could be a first choice to further this investigation.
There are other aspects that could be studied, such as the use of other FACTS devices to give the wind generators the fault ride through capability. Devices that are connected in series with the generator like the Dynamic Voltage Restorer or the Static Synchronous Series Compensator could be simulated and later on compared to the results obtained with the STATCOM.
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To perform all the simulations it was used the Matlab/Simulink software. From all the libraries available in Simulink the one that was used was the Simscape library, more precisely, the
SimPowerSystems library.
The SimPowerSystems library is an electrical toolbox accessible from Simulink. It provides us with tools for modeling and simulating both basic electrical circuits and more complex electrical power systems. With this library we can model the distribution, transmission, generation and consumption of electrical power and its conversion into mechanical power as well.
The SimPowerSystems library allows us to quickly build models to simulate power systems with numerous and varied elements, from a simple electrical circuit with a resistor and a DC voltage source to a more complex power system with several elements such as transformers, lines, machines, power electronic devices, etc.
This library also includes a set of wind generation blocks that will be explained later on.
To perform the simulations in Simulink using elements from the SimPowerSystems library, the
Powergui block must be present. This block will store the equivalent Simulink circuit that represents the state-space equations of the model.
The Powergui allows us to choose different methods to solve the circuit that we want to simulate:

Continuous method, which uses a variable step Simulink solver;

Ideal Switching continuous method;

Discretization of the electrical system for a solution at fixed time steps;

Phasor solution method.
The simulations included in this thesis use the phasor solution method for the Wind Turbine
Doubly-Fed Induction Generator and for the Wind Turbine Induction Generator. When
49

simulating the Direct Drive Synchronous Machines, due to the power electronics devices it is necessary to use the Discretization of the electrical system.
The graphical representation of this block in Simulink may vary from the different methods to solve the circuit:
Figure A.1 - Possible appearances of the Powergui block.
The Powergui block also offers us several analysis tools such as:

Steady-State Voltages and Currents Displays the steady-state voltages and currents of the model;

Initial States Setting Allows to display and modify initial capacitor voltages and inductor currents of the model;

Load Flow - Allows us to perform load flow and initialize three-phase networks and machines so that the simulation starts in steady state. It uses Newton-Raphson method to provide robust and fast convergence solution;

Machine Initialization Allows us to initialize three-phase networks containing threephase machines so that the simulation starts in steady state;

LTI Viewer Generates the state-space model of our system;

Impedance vs Frequency Measurement Displays the impedance versus frequency defined by the Impedance Measurement blocks;

FFT Analysis - Allows us to perform a Fourier analysis of signals stored in a Structure with time format;

Generate Report Generates a report of steady state variables, initial states and machine load flow for our model;

Hysteresis Design Tool Designs a hysteresis characteristic for the saturable core of the Saturable Transformer block and the Three-Phase Transformer blocks;

Compute RLC Line Parameters This feature allows us to compute the RLC parameters of overhead transmission line from its conductor characteristics and tower geometry.
50

When a simulation starts and there’s a Powergui block present, an initialization mechanism is called that computes the state-space model of out electric circuit and builds the equivalent system that can actually be simulated by Simulink.
This procedure follows three steps:
1. All the SimPowerSystems blocks are sorted followed by an evaluation of the entire block’s parameters and the network topology. Then the blocks are separated into two groups: linear and nonlinear blocks. Every electrical node is automatically given a node number;
2. As the network’s topology is obtained the state-space 2 model of the linear part of the circuit is computed. All of the steady-state calculation and initializations are performed at this point.
If the solving method chosen was to discretize the circuit, the discrete state-space model is computed from the continuous state-space model, using the Tustin
3
method.
With the phasor solution method, the state-space model is replaced with the complex transfer matrix H(j) that relates inputs and outputs at the specified frequency. This matrix is the one that defines the network algebraic equations.
3. Finally the Simulink model of our circuit is built and it’s stored inside the Powergui block.
An S-Function block is used to model the linear part of the circuit as well as the switches and power electronic devices. The nonlinear elements are simulated by predefined Simulink models that can be found in the SimPowerSystems library. The electrical sources blocks are simulated using the Simulink Source block. The interconnection between the linear circuit and the nonlinear models can be better understood through the following block diagram:
Figure A.2 - Interconnection between linear and nonlinear models [8].
There are several limitations of the nonlinear models. Since they are simulated as current sources, they cannot be connected in series with inductors and can’t have open terminals. It is
2
The state-space model corresponds to the A, B, C and D matrices.
3
Also known as the bilinear transformed, is used to transform continuous-time system representations to discrete-time and vice versa.
51

impossible also to feed a machine through and inductive source. This limitation can be avoided by connecting a large resistance in parallel with the source inductances or across the machine terminals.
52

In this section, the most important blocks that were used to assemble the wind energy generator test platform and thoroughly described based on the Matlab help files [8].
Figure B.1 - Simulink block for the WTSCIG.
Inputs:
 wind (m/s) - Input of the wind speed, can be either a function or a constant. One can use an interpolation of several wind velocities to simulate the wind evolution over time.
If the option External mechanical torque is selected, the wind velocity input will not be visible;

Tm (pu) - This input will only be visible if the External mechanical torque option is selected. The mechanical torque must be negative for power generation. This input should be used with an external turbine model;
 trip - Command signal of the wind turbine protection system. When the value of the trip is zero (LOW) the protection system isn’t active. The protection system will be activated when the trip value is equal to one (HIGH), which will happen when any of the generator’s measurements exceeds the reference values that were established. When the system is activated, the wind turbine is turned off which means that the generation of active and reactive power is equal to zero.
53

Outputs:
 m - Output vector which contains 8 signals from the Wind Turbine Induction Generator
(WTIG). Each signal can be accessed individually using a Bus Selector . The signals are:
1. Vabc (complex) (pu) - Phase to ground voltages Va, Vb e Vc at the WTIG terminals;
2. Iabc (complex) (pu) - Phasor currents Ia, Ib e Ic, that flow in the WTIG terminals;
3. P (pu) - Output active power of the WTIG in pu. If this value is greater than zero in means that there is generation of active power;
4. Q (pu) - Output reactive power of the WTIG in pu. If this value is greater than zero in means that there is generation of reactive power;
5. wr (pu) - Generator rotor speed in pu;
6. Tm (pu) - Mechanical torque applied to the generator in pu;
7. Te (pu) - Electromagnetic torque in pu;
8. Pitch_angle (deg) - Pitch angle of the blades of the WTIG in degrees.

A, B and C - The three terminals of the WTIG.
Figure B.2 - Simulink circuit of the WTSCIG block.
The WTIG, which models a WTSCIG, is formed by a model of a Wind Turbine, a model of an asynchronous machine, both residents in the Simulink library, a block of Data acquisition, which has the function of acquiring certain measurements and to compile them in an output variable m . Each variable can be later accessed through a Bus Selector . There is also a set of blocks that will break the connection of the WTIG to the rest of the network if the Trip system is activated. We have also the bus B1 that measures the phasor voltage and current at the asynchronous machine terminals.
54

Figure B.3 - Wind turbine block.
The block that simulates the wind turbine has for inputs the generator speed, which in the WTIG is the rotor speed of the asynchronous machine. The other two inputs are the angle of the wind turbine’s blades (pitch angle β) and the wind speed, which can be defined by the user.
To compute the pitch angle of the wind turbine’s blades it’s used a proportional integrator derivative controller, which limits the electric output power to the nominal power. This action only occurs when the electric output power exceeds the nominal power. Until that point the pitch angle is equal to zero. When the nominal power is reached the controller acts by increasing the pitch angle until the nominal and electric output power are equal.
The wind turbine has for an output the mechanical torque. The mechanical torque of this turbine will be the input for the induction generator of the WTIG. We can compute the mechanical output power of this turbine (P m
) using the following expression:
P m
 c p
 
A u
3
2
(0.12) where,
 c p
is the performance coefficient of the turbine;
 λ is the tip speed ratio of the rotor blade tip speed to wind speed;
 β is the pitch angle of the wind generator’s blades;
 ρ is the air density [kg/m 3
];

A is the area swept by the turbine’s blades;
 u is the wind velocity.
To have as the output of the wind turbine the mechanical torque, the following expression is applied:
Tm

P m
 r
(0.13)
55

where,

P m
is the mechanical output power computed using the expression (3.1);
 ω r
is the rotor speed of the induction machine.
Figure B.4 - Asynchronous machine block.
This block models a three-phase asynchronous machine with the possibility to choose the type of machine from wound rotor, single squirrel-cage or double squirrel-cage. We can also define the dq reference frame between the rotor, stator or synchronous. The stator and rotor are both
Y connected with and internal neutral point. For the WTIG the rotor is connected as single squirrel-cage and has the rotor as the reference frame.
The electrical system of the squirrel-cage machine is represented in the next two figures for the d axis and q axis, respectively.
Figure B.5 - Electrical system of the squirrel-cage machine for the d axis [8].
Figure B.6 - Electrical system of the squirrel-cage machine for the q axis [8].
56

The electrical system dynamics can be described with the following equations:
V qs

R i d
 qs
  ds
V ds

R i
V
V
T e d dt
 ds
  qs
' qr

R ' r
 i ' qr
 dt d

' qr 
(
  
' dr
' dr


1,5
R ' r

  i '
( dr

 ds d i dt
 qs dt
' dr

 qs
(

   i ds

) r
)

' qr
(0.14) where,
 qs
 ds

' qr
L i qs
L i ' qr
L i ds
L i ' dr

L ' r
 i ' qr
 m
 qs

' dr

L ' r
 i ' dr
 m
 ds
L s

L ls

L m
L ' r

L ' lr

L m
(0.15)
As for the mechanical system of the asynchronous machine we have the following equations: d
 m d dt
 dt m

2

1
H
( T e
F
 m

T m
)
  m
(0.16)
These are the variables in the previous equations:

R s
, R’ r
are the stator and rotor resistances;

L ls
, L’ lr
are the stator and rotor leakage inductances;

L m
, L s and L’ r
are the magnetizing stator and total rotor inductances;

V qs
, i qs
, V’ qr and i’ qr
are the stator and rotor voltages and currents in the q axis reference frame;

V ds
, i ds
, V’ dr and i’ dr
are the stator and rotor voltages and currents in the d axis reference frame;
 φ qs
, φ ds
, φ’
 ω m
, ω, ω qr
, φ’ dr
are the stator and rotor, q and d axis fluxes; r
and p are the angular velocity of the rotor, the synchronous angular velocity, the electrical rotor angular velo city (ω m
∙p) and the number of pole pairs;
 θ m
, θ r
, T e
e T m are the rotor angular position, the electrical rotor angular position (θ m
∙p), the electromagnetic torque and the shaft mechanical torque;

J, H e F are the combined rotor and load inertia coefficient, the combined rotor and load inertia constant and the combined rotor and load viscous friction coefficient.
57

Figure B.7 - Simulink block for the WTSCIG.
This block has the same inputs and outputs of the WTIG block previously described. However, the output vector m has several more variables that are available do the user.
Inputs:
 wind (m/s) - Input of the wind speed, can be either a function or a constant. One can use an interpolation of several wind velocities to simulate the wind evolution over time.
If the option External mechanical torque is selected, the wind velocity input will not be visible;
 trip - Command signal of the wind turbine protection system. When the value of the trip is zero (LOW) the protection system isn’t active. The protection system will be activated when the trip value is equal to one (HIGH), which will happen when any of the gene rator’s measurements exceeds the reference values that were established. When the system is activated, the wind turbine is turned off which means that the generation of active and reactive power is equal to zero;

Tm - This input will only be visible if the External mechanical torque option is selected. The mechanical torque must be negative for power generation. This input should be used with an external turbine model;

Vref - This input is only visible when the Mode of operation parameter is set to
Voltage regulation or when the External grid voltage reference is selected. We can define this reference value;

Qref - This input is only visible when the Mode of operation parameter is set to Var regulation or when the External generated reactive power reference is selected. We can define this reference value;

Iq_ref - This input is only visible when the parameter External reactive current Iq_ref for grid-side converter is selected. We can define this reference value.
58

Outputs:
 m - Output vector which contains 8 signals from the Wind Turbine Doubly-Fed Induction
Generator (WTDFIG). Each signal can be accessed individually using a Bus Selector .
The signals are:
1. Iabc (complex) (pu) - Phasor currents Ia, Ib e Ic, that flow in the WTDFIG terminals;
2. Vabc (complex) (pu) - Phase to ground voltages Va, Vb e Vc at the
WTDFIG terminals;
3. Vdq_stator (pu) - d and q components of the stator voltage. Vd_stator and
Vq_stator are respectively the real and imaginary components of the positive sequence voltage of the stator;
4. Iabc_stator (complex) (pu) - Phasor currents Ia, Ib e Ic that flow in the stator;
5. Idq_stator (pu) - d and q components of the stator current. Id_stator and
Iq_stator are respectively the real and imaginary components of the positive sequence current in the stator;
6. Vdq_rotor (pu) - d and q components of the rotor voltage. Vd_rotor and
Vq_rotor are respectively the real and imaginary components of the positive sequence voltage of the rotor;
7. Idq_rotor (pu) - d and q components of the rotor current. Id_rotor and
Iq_rotor are respectively the real and imaginary components of the positive sequence current in the rotor;
8. wr (pu) - Generator rotor speed in pu;
9. Tm (pu) - Mechanical torque applied to the generator in pu;
10. Te (pu) - Electromagnetic torque in pu;
11. Vdq_grid_conv (pu) - d and q components of the grid side converter voltage. Vd_grid_conv e Vq_grid_conv are respectively the real and imaginary components of the positive sequence voltage of the grid side converter;
12. Iabc_grid_conv (complex) (pu) - Phasor currents Ia, Ib e Ic that flow in the grid side converter;
13. P (pu) - Output active power of the WTDFIG in pu. If this value is greater than zero in means that there is generation of active power;
14. Q (pu) - Output reactive power of the WTDFIG in pu. If this value is greater than zero in means that there is generation of reactive power;
15. Vdc (V) - DC voltage in the WTDFIG;
16. Pitch_angle (deg) - Pitch angle of the blades o the WTDFIG in degrees.

A, B and C - The three terminals of the WTDFIG.
59

Figure B.8 - Simulink circuit of the WTDFIG block.
Just as the WTIG, the model for the WTDFIG has the same Matlab resident model of a Wind
Turbine. The same equations that were described in the previous section for this turbine are valid for the model used in the WTDFIG. In this model we have also a bus (B1) which is responsible for the measuring of the three-phase voltage and current.
Besides the two blocks previously described we have also the block that includes the generator, all the converters that are necessary for this type of wind generator and includes also the control system. These converters are responsible for the AC/DC/AC conversion. They are divided as the rotor side converters (C rotor
) and the grid side converters (C grid
). This converters use IGBTs
4
, which are forced-commutated power electronics that are responsible for the conversion from AC to DC voltage. On the DC side of the converter there is a capacitor that acts as the DC voltage source for the grid-side converter, C grid
. To connect this converter to the grid, a coupling inductor L is used.
The previously mentioned control system is the one which creates the pitch angle command and the voltage command signals V r
e V gc
that command respectively the converters C rotor
and
C grid
, thus controlling the active and reactive power generation by the wind turbine and controlling the DC voltage as well. These three parts of the control system will be described later on.
4
Insulated Gate Bipolar Transistor.
60

Inside this block we will find the model for the asynchronous machine (Asynchronous machine -
Positive sequence phasor model), the control block, the block which contains the current gridside converters and the power converters and finally we have the block responsible for the data acquisition.
Figure B.9 - Constitution of the Generator & Converters block.
The asynchronous model used in this WTDFIG has a wound rotor and is modeled in the stator dq reference frame. Both windings, the stator and rotor, are Y connected with an internal neutral point. The negative sequence of this model was eliminated.
The electrical and mechanical system for this type of induction machine is described in section
2.1.1, where the WTDFIG is described.
61

As far as the power generation is concerned we have the following equations to describe the mechanical power that flows from the wind turbine to the rotor of the induction machine (P m
) and to describe the output power in the machine’s stator (P
S
):
P m

T m
  r
P s

T em
  s
(0.17)
Assuming we have a lossless system, we have the following equation to describe the mechanical dynamic of this system:
J
 d
 r dt

T m

T em
(0.18)
In the equation (3.7) J is the combined rotor and wind turbine inertia coefficient, T m
is the mechanical torque that is applied to the rotor, T em
is the electromagnetic torque applied to the rotor by the generator and ω r
is the angular velocity of the rotor.
Finally we have to consider the output rotor power of the machine (P r
). We consider the induction machine to be in a permanent state and with fixed velocity in a lossless system:
T m

T em
P m
P P r
P r

P m
P s
T m
  r

T em
  s
T m

 s r
  s s T m
 s s P s
(0.19)
In the previous equation we have the variables ω s
, which is the synchronous angular velocity and s , which is the slip of the induction machine and is computed using the following equation: s


 s r
(0.20)
The slip value is usually considerably smaller than 1 which means that P r
is very small when compared to P s
. Since T m is positive when there is generation of active power and since ω s
is also positive and constant, P r
depends only of the polarity of the slip. If the slip is negative (the machine’s speed is higher than the synchronous speed) we’ll have a positive P r
positive and if the slip is positive (the machine’s speed is smaller than the synchronous speed) we’ll have a negative P r
.
For the first case (s<0), P r
is transmitted to the capacitor on the DC side of the converters, which reduces the DC voltage. For the second situation (s>0), P r
is transmitted from the DC side of the converters which translates in an increase of the DC voltage.
62

This block contains the two power converters that were previously described, the C rotor
and the
C grid
. As far as the power flow is concerned each of the converters plays a very important part, the C grid
is used to generate or to consume P gc
(the output power of this converter) so that the
DC voltage stays constant over time. In a permanent state and considering the AC/DC/AC converter to be lossless, the power P gc
is equal to P r and the wind turbine’s speed is computed using P r
, which is consumed or generated by the C rotor
.
About the power control, the AC voltage generated by the C rotor
is positive when the generator speed is smaller than the synchronous speed and negative when the generator speed is higher than the synchronous speed. The frequency of this AC voltage is equal to the product of the grid frequency by the absolute value of the machine’s slip.
We can assume that both C rotor
and C grid
have the ability to generate or to consume reactive power and can be used to control the voltage and reactive power at the grid-side terminals of the wind generator.
The power flow of the WTDFIG system is represented in the following figure:
Figure B.10 - Power flow representation of the WTDFIG [8].
63

The Control block includes the control system of the converters C rotor
e C grid
, and the pitch angle control system too. a) C rotor
control system
The rotor-side converter is used to control the output power and voltage (or reactive power) of the wind turbine. The output power is controlled in such a way that a pre-defined power-velocity characteristic is followed. This characteristic is called Tracking Characteristic and it’s represented in the next figure:
Figure B.11 - Tracking Characteristic [8].
The wind turbine speed, ω r
, is measured and every correspondent value of the mechanical power in the characteristic is used as the power reference value for the power control cycle. For different wind velocities we have different power characteristics for the turbine.
The Tracking Characteristic is defined by four points marked in the previous figure as A, B, C and D. Until the velocity of the point A the output is zero. Between the points A and B the characteristic is linear which means that the velocity of the point B is higher than in the point A.
We’ll find the maximum output power between the points B and C (it’s the maximum output power of the turbine vs the speed of the turbine). From the point C until point D the characteristic is linear again and from the point D the output power is equal to 1 pu.
In the next figure there’s a representation of the rotor-side control system:
64

Figure B.12 - Rotor-side control system [8].
The electrical output power, measured at the grid-side terminals of the wind turbine, will add with the total of the power losses (mechanical and electrical). Later on this sum is compared with the reference value that was obtained through the Tracking Characteristic . To reduce the output power error to zero, it’s used a regulator that resorts to a proportional integrator. The output of this regulator is the reference current of the rotor I qr_ref
, that has to be injected in the rotor through the converter C rotor
. This current component is the one that creates the electromagnetic torque (T em
). The positive sequence of I qr
is compared to I qr_ref
and the error is reduced to zero through the action of the current regulator. At the output of this current regulator we have the voltage V qr
, generated by the converter C rotor
.
As far as the voltage and reactive power control is concerned, it’s used the value of the current that flows in the converter C rotor
. This control system is also represented in the previous figure.
If the wind turbine works under Voltage Regulation, the following V-I characteristic is used:
Figure B.13 - V-I characteristic [8].
65

As long as the current in this converter doesn’t exceed the limits that are shown in the V-I characteristic, the voltage is regulated to the reference value, V ref
. However, there could be a slight variation of this value. This effect is represented by the slope in the V-I characteristic.
If the voltage regulation is selected, the V-I characteristic can be described by the following equation:
V

V ref

X
S

I (0.21) where,

V is the positive sequence voltage (pu);

I is the current in this converter (pu/Pnom) (If I > 0, the current is inductive);

X
S
is the slope or the reactance slope (pu/Pnom);

P nom
is the nominal three-phase power for the converter that is defined by the user.
When the reactive power regulation is activated in the wind turbine ( var regulation ), the reactive power at the grid-side terminal is constant due to the actions of the reactive power regulator.
At the output of the voltage regulator (that is inside the reactive power regulator) is the d axis reference current, I dr_ref
, which will be injected in the rotor by the converter C rotor
. The same current regulator that was used in the output power control is used to regulate the positive sequence value of the current I dr
. The output of this regulator is the d axis voltage V dr
generated by the converter C rotor
.
V dr
and V qr
are, respectively, the d and q axis components of the voltage V r
.
Finally, there is a limitation that is imposed to the reference current of the rotor, I r_ref
, that should be always limited to 1 pu. Its value is √ , which means that if this limit is reached the component I qr_ref
is reduced until the current I r_ref
is equal to 1 pu again. b) C grid
control system
The converter C grid
is used to regulate the capacitor voltage, which will be used as a DC voltage source. This model will allow us to use the converter to generate or to consume reactive power.
In the next figure it’s represented the control system of the converter C grid
, which consists of:

Measurement systems, that measures the d and q axis components of the positive sequence of the AC currents that will be controlled and measures the DC voltage, V dc
, as well;

One external regulation cycle that consists of a DC voltage regulator. At the output of this regulator we have the reference current I dgc_ref
for the current regulator. I dgc
is the current in phase with the grid voltage that controls the flow of active power;
66


One internal regulation cycle that consists of a current regulator. This regulator controls the amplitude and phase of the voltage created by the converter C grid
(V gc
) from the current I dgc_ref
, that was created by the DC voltage regulator and by the reference current I q_ref
.
Figure B.14 - Grid-side converter control system [8].
The amplitude of the reference current of the grid-side converter, I gc_ref
, is equal to
√ , which maximum value is limited to a value that’s defined by the maximum output power at the nominal voltage. When this amplitude is higher than the maximum value, the value of I q_ref
is reduced so that the limitations are met. c) Pitch angle control system
The pitch angle is equal to zero as long as the wind velocity does not reach the point D of the
Tracking Characteristic . From that value on, the pitch angle is proportional to the difference between the wind speed value and the speed value of the point D of the characteristic.
The next figure will show a simplified diagram of this control system:
Figure B.15 - Pitch control system [8].
67

Figure B.16 - Power plant Simulink block.
This block that represents a power plant has no inputs. The only outputs are the three-phase terminals of the plant that can be connected to the grid.
Figure B.17 - Constitution of the power plant block.
The power plant block is not a resident model in the Simulink library but it was present in a
Matlab example of the use of the Emergency Diesel-Generator and Asynchronous Motor
5
.
Inside the power plant block we have the block for the synchronous machine, a three-phase resistive load and a power factor correction capacitor. We also have a three-phase breaker, a three-phase transformer with an external neutral point connected to a small resistance that will elevate the voltage rating to the one of the grid where the plant is connected. We have also a bus (B100) that will measure the voltage and current at the terminals of the machine. To control
5
This example can be accessed by typing power_machines in the Matlab terminal.
68

the three-phase circuit breaker we have the Plant & Motor Protection system and finally we have the Diesel Engine Speed & Voltage Control block that controls the synchronous machines.
This block will provide the excitation voltage V f
, the mechanical power to the machine and will also control the speed and voltage.
Figure B.18 - Synchronous machine block.
The synchronous machine that was used has a salient-pole rotor and has as the mechanical input the mechanical power (P m
).
The mechanical system of this machine is described by:


 
 
2


1
H


0 t

( T m
 e
)

K d

0

(0.22) where,
 Δω is the speed variation with respect to speed of operation;

H is the constant of inertia;

T m
is the mechanical torque;

T e
is the electromagnetic torque;

K d
is the damping factor representing the effect of damper windings;
 ω(t) is the mechanical speed of the rotor;
 ω
0
is the speed of operation (1 pu).
The following block diagram describes how the mechanical part of the model is implemented.
The model computes a deviation with respect to the speed of the operation, and not the absolute speed itself.
Figure B.19 - Mechanical system of the power plant [8].
69

The damping factor, K d
, simulates the effect of damper windings normally used in synchronous machines. If we connect this synchronous machine to an infinite network, the variation of the machine’s power angle delta (δ), which results from a variation of the mechanical power (P m
), can be approximated by the following second-order transfer function:


P m s
2
2
2

  
 s
H
  n
   n
2
(0.23) where,
 δ is the power angle, which is the angle of the internal voltage E with respect to the terminal voltage, in radians;

P m
is the mechanical power, in pu;
 ω n
is the frequency of electromechanical oscillations =
 s
P max
, in rad/s;
 ζ is the damping ratio

( K d
/ 4) 2 / (
 s
HP max
) ;
 ω s
is the electrical frequency in rad/s;

P max
is the maximum power transmitted through reactance X at terminal voltage V t
and internal voltage E. P max
 t
/ , in pu;

H is the inertia constant;

K d
is the damping factor (torque/speed, both in pu).
As far as the electrical part of the machine is concerned, it is represented by a sixth-order statespace model, and its input is the excitation voltage V f
. This model includes the dynamics of the stator, field and damper windings.
For this model, the rotor reference frame (dq frame) is used to represent the equivalent circuit.
The rotor parameters and electrical quantities are considered from the stator and are identified by primed variables. The d and q axis quantities will have the indexes d and q , respectively. The same happens for the rotor (R), stator (s), leakage inductance (l), magnetizing inductances (m), field (f) and damper (k) winding quantities.
The electric model of this machine is represented in the next figure, for each of the reference axis:
70

Figure B.20 - Electrical model of the machine in the q and d axis [8].
This model is governed by the following equations:
V d

R i d dt
V q

R i d dt

R


R

V ' fd
V ' kd

R ' fd
 i ' fd
 d dt

' fd

R ' kd
 i ' kd
 d dt

' kd
V ' kq 1

R ' kq 1
 i ' kq 1
 d dt

' kq 1 d
V ' kq 2

R ' kq 2
 i ' kq 2
 d dt

' kq 2 q where,
 d
 q

' fd
   d
L md
( ' fd
 i ' )
   mq
' kq

L ' fd
 i ' fd

L md
( i d
 i ' )

' kd

L '
 i ' kd kd

L ( i md d
 i ' ) fd

' kq 1

' kq 2

L ' kq 1
 i ' kq 1

L mq
 i q

L ' kq 2
 i ' kq 2

L mq
 i q
71
(0.24)
(0.25)

Figure B.21 - Diesel engine speed and voltage control block.
This block models the diesel engine that will be connected to the synchronous machine. It will provide the mechanical power and the excitation voltage that the machine requires. Besides the diesel engine, this block contains also a governor and excitation systems and has as inputs the reference speed (wref), reference voltage (Vtref) and also the synchronous machine’s measurement vector (m). As outputs this block has the mechanical power (Pm), the excitation and terminal voltage (Vf and Vt) and the angular speed (w). The next figure shows the inside of the Diesel Engine Speed & Voltage Control block:
Figure B.22 - Constitution of the Diesel Engine Speed & Voltage Control block. a) Governor & Diesel Engine system
Figure B.23 - Governor & Diesel Engine block.
72

These two models can be described by the following block diagram:
Figure B.24 - Block diagram of the governor and diesel engine.
This block diagram implements a diesel engine and governor system. It has as inputs the desired speed (wref) and the actual speed (w), both in pu. The output is the diesel engine mechanical power (Pm).
The controller in this system has the following transfer function:
H c
 
(1
(1
 
3
)
     2 )
(0.26)
Finally, the actuator has the following transfer function:
H a
 s (1
(1
 
 
4
)
T s
5
)(1 T s
6
)
In this model it’s also considered a certain time delay (Td) in the motor. b) Excitation system
(0.27)
Figure B.25 - Excitation system block.
This block includes not only the excitation system for the synchronous machine but also its voltage regulator.
This system uses the dq components of the terminal voltage of the synchronous machine to compute the excitation voltage (Vf). As inputs, this block has the desired stator terminal voltage
(vref), the vd and vq components of the terminal voltage (vd and vq) and the stabilization voltage from the user-supplied power system stabilizer (vstab), all in pu. As the output we have the field voltage vfd (Vf) that will be applied to the synchronous machine.
73

This block is responsible for the opening of the three-ph ase breaker at the generator’s terminals. It has as inputs the three-phase voltage and current in the bus (B2300) and the rotor speed of the synchronous machine. The protection system is thoroughly explained in the next section.
If one of these situations occurs, the value of Trip_Plant will be equal to 1 which will open the three-phase breaker.
Figure B.26 - Protection system block.
Inputs:

Vabc (pu) - Phase to ground voltage measured at the terminals of the system that is to be protected;

Iabc (pu) - Phase currents (Ia, Ib and Ic) that flow at the terminals of the system that is to be protected;

Vdc (V) - DC voltage of the system;

Reset - This input will reset the whole protection system if it’s HIGH (equal to 1). If one of the imposed limits are reached and the protection system is activated, we can deactivate it using this input;

Speed (pu) - The generator rotor speed.
Outputs:

Trip - This output value is the result of the comparison of the input values with the limits defined by the user. The Trip value is equal to 1 if one of the limits is breached, otherwise it is equal to 0 ;

TripTime - This output value will tell us at what time the protection system was activated;

TripStatus - The TripStatus is a vector that can take the value of 1 or 0 that will indicate which of the limits was breached.
74

Figure B.27 - Constitution of the protection system.
This protection system will be activated if one of the following situations occurs:

Instantaneous AC Overcurrent;

AC Overcurrent (positive-sequence);

AC Current Unbalanced;

AC Undervoltage (positive-sequence);

AC Overvoltage (positive-sequence);

AC Voltage Unbalanced (Negative-sequence);

AC Voltage Unbalanced (Zero-sequence);

DC Overvoltage;

Under speed;

Over speed.
Each of these situations occurs if the input values don’t meet the user defined intervals in which they should be included. For the DC voltage it’s only defined the maximum value permitted, but for the phase-to-ground voltage Vabc we have several conditions that need to be met: a
75

maximum and minimum value and a maximum voltage ratio. The protection system will only be activated after a user defined time delay.
Figure B.28 - Three-phase electrical bus block.
This Simulink block is a mask to the three-phase V-I measurement block that can be found in the SimPowerSystems library, that is represented in the next figure.
Figure B.29 - Three-phase V-I measurement block.
The Three-Phase V-I Measurement block can be used in an electrical system to measure the instantaneous three-phase voltages and currents. It is meant to be connected in series with other three-phase elements of an electrical system. The outputs of this block can be chosen between the three phase-to-ground or phase-to-phase peak voltages and currents. These outputs’ units can be either per unit (pu) values or volts and amperes.
If the measurement chosen is the phase-to-ground voltages in pu, the block converts the measured voltages based on the peak value of the nominal phase-to-ground voltage:
V abc
( pu )

V
_ _
V base
( )
(0.28) where,
V base

V nom
( V rms
)

2
3
(0.29)
76

If the measurement chosen is the phase-to-phase voltages in pu, the block converts the measured voltages based on the peak value of the nominal phase-to-phase voltage:
V abc
( pu )

V
_ _
V base
( )
(0.30) where,
V base

V nom
( V rms
)

2
(0.31)
As far as current measurement is concerned, if it is measured in pu, the block converts the measured currents based on the peak value of the nominal current:
I ( pu ) abc

I ( ) abc
I ( ) base
(0.32) where,
I base

P base
( VA )
V nom
( V rms
)

3
2
(0.33)
The values of V nom
and P base
are specified in the Three-Phase V-I Measurement block dialog box.
This mask that represents the electrical bus, suppresses the outputs of the V-I Measurement block. The two outputs (three-phase voltage and current) can be accessed through labels that can be named by the user.
The voltages and currents that are measured with this block will be posteriorly processed by another measurement block, the 3-Phase Active & Reactive Power block, which has the following Simulink block:
Figure B.30 - Active and reactive power block.
77

First, to know the active and reactive power of a certain bus, this block will compute the total power with the following equation:
S

1
2

V abc

I abc
*
(0.34)
Both active and reactive power can be accessed for measurement purposes by separating the real and imaginary components of the total power, which will respectively be the active and reactive power.
Figure B.31 - STATCOM block.
Inputs:

Trip - This input can be a logical signal (0 or 1). When the input is HIGH, the STATCOM is disconnected and its control system is disabled. This input can be used as a simplified version of the protection system;

Vref - This input will only be visible if the option External control of reference voltage
Vref is checked.
Outputs:
 m - Output vector containing 16 STATCOM internal signals. Each of these signals can be accessed individually using a Bus Selector. The signals are:
1.
2.
3. Va_prim (pu), Vb_prim (pu) and Vc_prim (pu) - The first three signals of the output vector contain the phasor voltages (phase to ground) Va, Vb and Vc at
4. the STATCOM primary terminals;
5.
6. Ia_prim (pu), Ib_prim (pu), Ic_prim (pu) - These three signals contain the phase currents Ia, Ib and Ic flowing into the STATCOM;
78

7. Vdc (V) - DC voltage;
8. Vm (pu) - Positive-sequence value of the measured voltage (pu);
9. Vref (pu) - Reference voltage;
10. Qm (pu) - STATCOM reactive power. A positive value indicates inductive operation;
11. Qref (pu) - Reference reactive power;
12. Id (pu) - Direct-axis component of current (active current) flowing into
STATCOM. A positive value indicates active power flowing into the STATCOM;
13. Iq (pu) - Quadrature-axis component of current (reactive current) flowing into
STATCOM. A positive value indicates capacitive operation;
14. Idref (pu) - Reference value of direct-axis component of current flowing into the
STATCOM;
15. Iqref (pu) - Reference value of quadrature-axis component of current flowing into the STATCOM;
16. modindex - The modulation index m of the PWM modulator. A positive number
(m) between 0 and 1. When m equals to 1 it means that the VSC (Voltage-
Sourced Converter) is generating the maximum voltage without over modulation;

A, B and C - The three terminals of the STATCOM.
Figure B.32 - Constitution of the STATCOM.
The Static Synchronous Compensator (STATCOM) is a shunt device of the Flexible AC
Transmission Systems (FACTS) family. Its main function is to control power flow and improve
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transient stability on power grids. The STATCOM is able to regulate the voltage at its terminals by controlling the amount of reactive power injected or absorbed from the power system. This system is usually associated with a Wind Turbine Squirrel Cage Induction Generator to improve its performance.
The reactive power is controlled by a Voltage-Sourced Converter (VSC) that is connected to the secondary side of a coupling transformer. The VSC uses forced-commutated power electronics devices that in this particular case are IGBTs that use Pulse-Width Modulation to ensure a sinusoidal waveform from a DC voltage source.
To understand the way the STATCOM operates we can study the following single-line diagram of this STATCOM, with a simplified block diagram of its control system.
Figure B.33 - Single-line diagram of the STATCOM [8].
This STATCOM has not only the previously mentioned VSC but also a Control System. This system consists of:

A phase-lock loop (PLL) which synchronizes on the positive-sequence component of the three-phase primary voltage (V1). With the output of the PLL the direct-axis and quadrature-axis components of the AC three-phase voltage and currents can be computed. This voltages and currents are labeled as Vd, Vq, Id and Iq on the diagram;

Measurement systems responsible for the acquisition of the d and q components of the
AC positive-sequence voltage and currents to be controlled and the DC voltage (Vdc) as well.

An outer regulation loop with two regulators, one for the AC voltage and one for the DC voltage. The output of the AC voltage regulator is the reference current Iqref that will be used as a reference for the current regulator. The output of the DC voltage regulator is the reference current Idref that will be used in the current regulator as well;
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
An inner current regulation loop that consists only of a current regulator which controls the magnitude and phase of the voltage generated by the PWM converter (V2d and
V2q) from the previously mentioned reference currents produce by the DC voltage regulator (Idref) and by the AC voltage regulator (Iqref). This regulator is complemented by a feed forward type regulator that predicts the V2 voltage output from the V1 measurement and the transformer leakage reactance.
Figure B.34 - Three-phase Pi Section Line block.
This block models a balanced three-phase transmission line model with parameters lumped in a
PI section. Its inputs and output are the ABC terminals that can be connected to any threephase element in a network.
Unlike the Distributed Parameter Line model, where the resistance, inductance and capacitance are uniformly distributed along the line, the PI Section Line block lumps the line parameters in a single PI section as shown in the next figure.
Figure B.35 - Electrical representation of the pi section line [8].
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Assuming the three phases are balanced, the line parameters R, L and C are specified as positive and zero-sequence parameters that take into account the inductive and capacitive couplings between the three-phase conductors and the ground parameters as well.
The self and mutual resistances (R s
and R m
), self and mutual inductances (L s
and L m
) of the three coupled inductors, the phase capacitances C p
and ground capacitances C g
as well are all deduced from the positive and zero-sequence RLC parameters as follows.
Considering the following line parameters:
 r1, r0 - Positive and zero-sequence res istances per unit length (Ω/km);
 l1, l0 - Positive and zero-sequence inductances per unit length (H/km);
 c1, c0 - Positive and zero-sequence capacitances per unit length (F/km);
 f - Frequency (Hz);
 lsec - Line section length (km).
We can then evaluate the total positive and zero-sequence RLC parameters including hyperbolic corrections as follows:
R
1 r l sec

L
1 l l sec


 l 1 r 1
C
1 c l sec
  c 1
R
0 r l sec

L
0 l l sec


 l r
0
0
C
0 c l sec
  c 0
(0.35) where k r1
, k l1
, k c1
, k r0
, k l0
and k c0
are the positive and zero-sequence hyperbolic correction factors.
If the line section is short, approximately smaller than 50 km, the correction factors are negligible. However for long lines these hyperbolic corrections must be taken into account to have an exact line model at the specified frequency.
Finally, the RLC line section parameters are computed with the following expressions:
R s
R
1
R
0
) / 3
L s
L
1
L
0
) / 3
R m

( R
0

R
1
) / 3
L m

( L
0

L
1
) / 3
C p

C
1
C g
C C
0
/ ( C
1

C
0
)
(0.36)
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Figure B.36 - Three-phase Parallel RLC Load block.
The three-phase parallel RLC load block models a three-phase balanced load as a parallel combination of RLC elements. Its inputs and outputs are the three-phase terminals A, B and C.
This load absorbs active and reactive power proportionally to the square of the applied voltage to its terminals. The impedance value is constant for a specified frequency.
The user can define the nominal phase-to-phase voltage, the nominal frequency, the active power of the load and the inductive and capacitive reactive power, positive and negative var, respectively.
The connection of the three phases of the load can also be defined with the following options:

Y ( grounded) - Neutral is grounded;

Y (floating) - Neutral is not accessible;

Y (neutral) - Neutral is made accessible through a fourth connector;

Delta - Three phases connected in delta.
This block also gives the possibility to measure the three voltages across each phase of the
Three-Phase Parallel RLC Load block terminals. The measurements can be accessed through a Multimeter block.
If the Branch voltages option is selected, the three voltages across each phase of the block are measured. For a Y connection, these voltages are the phase-to-ground or phase-to-neutral voltages and for a delta connection, these voltages are all phase-to-phase voltages.
If the Branch currents option is selected, the three total currents (sum of R, L and C currents) that flow through each phase of the load are measured. For a delta connection, these currents are the currents flowing in each branch of the delta.
Finally, if the Branch voltages and currents option is selected, the three voltages and three currents of the load are measured.
The next table describes the labels given to each voltage or current measurement.
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Table B.1 - Measurement labels.
Measurement Label
Branch voltages Y (grounded): Uag, Ubg, Ucg
Y (floating): Uan, Ubn, Ucn
Y (neutral): Uan, Ubn, Ucn
Delta: Uab, Ubc, Uca
Branch currents Y (grounded): Ia, Ib, Ic
Y (floating): Ia, Ib, Ic
Y (neutral): Ia, Ib, Ic
Delta: Iab, Ibc, Ica
Figure B.37 - Three-phase transformer block.
This block implements a mode of a three-phase transformer using three single-phase transformers. It has as inputs and outputs the three-phase terminals (A, B, C, a, b and c).
The transformer is based on three single-phase transformers that can be either linear transformers or saturable transformers. T his option can be made in the transformer’s parameter menu. In this test platform, linear transformers were used for the simulations.
The two windings of the three-phase transformer can have one of the following connections:

Y;

Y with accessible neutral;

Grounded Y;

Delta (D1), delta lagging Y by 30 degrees;

Delta (D11), delta leading Y by 30 degrees;
If the Y with accessible neutral option is selected, a new output will appear with the label N .
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The parameters that can be defined are the nominal power, the frequency, the magnetization resistance and inductance and, for each winding, the phase-to-phase voltage, the winding resistance and the leakage inductance.
The linear transformer model that’s in the library SimPowerSystems has the following equivalent electrical scheme:
Figure B.38 - Transformer equivalent electrical scheme [8].
As shown in the previous figure, this model takes into account the winding resistances (R1 and
R2) and the leakage inductances (L1 and L2). The magnetizing characteristics of the core are also taken into consideration, which are modeled by a linear branch (Rm and Lm).
This block has some limitations, although the windings can be left floating, an internal resistance is then connected to the floating windings and to the main circuit. This connection will not affect the voltage and current measurements.
Figure B.39 - Three-phase fault block.
This block can simulate a three-phase fault in a network. It implements a three-phase circuit breaker where the opening and closing times can be controlled either from an external Simulink signal (if the external control mode is selected) or from an internal control timer (if the intern
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control mode is selected). If the intern control mode is selected, the user can define the transition times in the parameter menu.
As inputs and outputs this block has the three-phase terminals that can be connected to the network and has as a possible input, the external control signal as mentioned before.
The Three-Phase Fault block uses three Breaker blocks that can be controlled individually, depending on the kind of fault that the user wants to simulate. The faults can be phase-tophase, phase-to-ground or a combination of phase-to-phase and ground faults.
The next figure shows an equivalent electrical scheme for this block.
Figure B.40 - Electrical scheme of the three-phase fault [8].
The ground resistance R g
is automatically set to 10
6
ohms, if the type of fault selected is the ground fault. If the fault selected to be simulated is a phase-to-phase fault between A and B, the options Phase A Fault and Phase B Fault options need to be selected from the parameter menu. If the user wants to simulate a phase-to-ground fault for the phase A, the Phase A Fault and Ground Fault parameters need to be selected and a small value for the ground selected needs to be defined.
When the external control mode is selected, a control input appears in the block icon. This input must be a logical sign, equal to zero or one. If the input value is zero, the breakers will open and they’ll close when the value is equal to one.
Series R p
-C p
snubber circuits are included in the model. They can be optionally connected to the fault breakers. When connected in series with an inductive circuit, an open circuit or a current source, the snubbers of the Three-Phase Fault block must be used.
In the parameter menu, the user can define which of the three phases will have the fault. The fault resistances, ground resistance (R g
), the transition status, the transition times, the snubbers resistance (R p
) and the snubbers capacitance (C p
) can also be defined by the user.
In the transition status we can specify the vector of switching status when the Three-Phase
Fault block is in internal control mode.
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As mentioned, the Three-Phase block uses three Breaker blocks. These blocks implement circuit breakers with internal resistances R on
, which will be the three-phase fault resistance defined in the parameter menu. The Breaker closes when the control signal goes to 1 (HIGH) and opens when the control signal goes to 0 (LOW).
The Breaker has the following Simulink block:
Figure B.41 - Breaker block.
It has its terminals ( 1 and 2 ) that will be connected to each phase and has an input ( c ) where the control signal is connected.
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[1] Global Wind Energy Council, “Global Wind 2009 Report,” 2010.
[2] J. P. S. Paiva, Redes de Energia Eléctrica: uma análise sistémica, Lisboa: IST Press,
2005.
[3] G. Marcelino e S. Ludovino, “Crescimento da geração distribuída em Portugal e alterações a nível regulamentar induzidas por este crescimento,” em XIII Encuentro Regional
Iberoamericano de Cigré , Puerto Iguazú, 2009.
[4] C. Wessels e F. Fuchs, “High Voltage Ride Through with FACTS for DFIG Based Wind
Turbines,” Institute of Power Electronics and Electrical Drives, Kiel, 2009.
[5] A. Adamczyk, R. Teodorescu, R. Mukerjee e P. Rodriguez, “FACTS Devices for Large
Wind Power Plants,” Department of Energy Technology, Aalborg University, Denmark,
2010.
[6] R. Castro, Uma Introdução às Energias Renováveis: Eólica, Fotovoltaica e Mini-hídrica,
Lisboa: IST Press, 2011.
[7] REN, “Technical Data 2011,” REN, Lisboa, 2012.
[8] Mathworks, “Matlab Help Files,” Mathworks, Cambridge MA, 2012.
[9] H. Li e Z. Chen, “Overview of different wind generator systems and their comparisons,” IET
Renewable Power Generation, Vol. 2, No. 2, pp. pp. 123-138, 2008.
[10] A. Oppenheim, Discrete Time Signal Processing Third Edition, 2010.
[11] N. J. P. O. Barros, “Análise do Impacto da Integração de Energias Renováveis em Redes
Distribuição,” FEUP, Porto, 2011.
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