copyright 2019, aashish pant
TRANSCRIPT
Modelling and Design of Grid Connected Doubly Fed Induction Generator
by
Aashish Pant, B.E.
A Thesis
In
Electrical and Computer Engineering
Submitted to the Graduate Faculty
of Texas Tech University in
Partial Fulfillment of
the Requirements for
the Degree of
MASTER OF SCIENCES
Approved
Dr. Miao He
Chair of Committee
Dr. Stephen Bayne
Mark Sheridan
Dean of the Graduate School
December, 2019
Copyright 2019, Aashish Pant
Texas Tech University, Aashish Pant, December 2019
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ACKNOWLEDGEMENTS
First of all, I would like to express my sincerest thanks to my thesis chairperson Dr. Miao
He for giving me the opportunity to work under him for the thesis. His continuous support,
encouragement and continuous guidance all this time has made the thesis possible.
I would also like to express my gratitude to my committee member Dr. Stephen Bayne for
his support and guidance through the completion of the thesis. Iβve learnt a lot from him in
the field of power electronics and semiconductor application.
Iβm very grateful to my colleague Mr. Saleh Dinkhah for his continued supervision for the
entirety of the thesis. Iβve learnt a great deal in the field of microgrid from him. I would
like to thank everyone who has directly or indirectly helped me for the completion of my
thesis.
At last, I would like to thank my parents back in Nepal for providing me the continuous
encouragement, support and persistent motivation throughout my years of study.
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TABLE OF CONTENTS
ACKNOWLEDGEMENTS ......................................................................... ii
ABSTRACT .................................................................................................. vi
LIST OF TABLES ...................................................................................... vii
LIST OF FIGURES ................................................................................... viii
CHAPTER 1 ................................................................................................... 1
INTRODUCTION ......................................................................................... 1
1.1 Wind Energy Conversion System (WECS) .............................................................. 1
1.2 Wind Turbines ........................................................................................................... 2
1.2.1 Horizontal Axis Wind Turbine (HAWT) ........................................................... 2
1.2.2 Vertical Axis Wind Turbine (VAWT) ................................................................ 3
1.3 Components of Wind Turbine ................................................................................... 3
1.4 Types of Wind Turbine Energy Conversion System ................................................ 5
1.4.1 Fixed Speed Wind Turbine (FSWT) .................................................................. 5
1.4.2 Variable Speed Wind Turbine (VSWT) ............................................................. 6
1.4.2.1 Partial Scale Frequency Converter Wind Turbine (PSFCWT) .................... 6
1.4.2.2 Full Scale Frequency Converter Wind Turbine (FSFCWT) ........................ 7
1.5 Advantages of DFIG Wind Turbine .......................................................................... 7
1.6 Disadvantages of DFIG Wind Turbine ..................................................................... 8
1.7 Power Electronic Converters ..................................................................................... 8
1.7.1 Back to Back PWM Converters.......................................................................... 8
1.8 The Operating Regions of the Wind Turbine ............................................................ 9
1.9 Vector Transformations........................................................................................... 10
1.9.1 Clarke Transformation ...................................................................................... 10
1.9.2 Park Transformation ......................................................................................... 11
CHAPTER 2 .................................................................................................13
OBJECTIVE OF THE RESEARCH .........................................................13
2.1 Thesis Organization................................................................................................. 14
CHAPTER 3 .................................................................................................15
LITERATURE REVIEW ...........................................................................15
CHAPTER 4 .................................................................................................17
MODELLING OF THE DFIG WECS ......................................................17
4.1 Aerodynamics of DFIG ........................................................................................... 17
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4.2 Betz Limit ................................................................................................................ 20
4.3 Maximum Power Point Tracking ............................................................................ 20
4.4 Modelling of Doubly Fed Induction Generator....................................................... 21
4.4.1 Modelling of the Electrical Induction Generator .............................................. 22
4.4.2 Dynamic Modelling of DFIG ........................................................................... 23
4.4.2.1 Space Vector Representation ..................................................................... 23
4.4.2.2 Ξ±Ξ² Modelling .............................................................................................. 26
4.4.2.3 dq Modelling of DFIG ............................................................................... 28
4.5 Design of the Control System for DFIG Wind Turbine .......................................... 30
4.5.1 Rotor side Converter (RSC) Controller ............................................................ 31
4.5.2 Grid Side Converter (GSC) Controller ............................................................. 33
4.6 Sinusoidal PWM with Third Harmonics Injection .................................................. 34
4.7 Angle Estimation ..................................................................................................... 36
4.8 Current Loops .......................................................................................................... 37
4.8.1 Tuning of the Regulators .................................................................................. 37
4.8.1.1 Rotor Side Converter Controller Tuning ................................................... 37
4.8.1.2 Grid Side Converter Controller Tuning ..................................................... 38
CHAPTER 5 .................................................................................................41
SIMULATION .............................................................................................41
5.1 Model Description ................................................................................................... 41
5.2 Block Description .................................................................................................... 42
5.2.1 Wound Induction Generator ............................................................................. 42
5.2.2 Wind Turbine Aerodynamics Block ................................................................. 44
5.2.3 Controller Block ............................................................................................... 45
5.2.3.1 Rotor Side Controller ................................................................................. 45
5.2.3.2 Grid Side Controller ................................................................................... 46
5.2.4 Third Harmonics Injection ................................................................................ 47
5.3 Result/Validation ..................................................................................................... 47
5.3.1 Simulation at Rated Speed ................................................................................ 48
5.3.2 Operation of the Wind Turbine at the Sub Synchronous Speed ....................... 55
5.3.3 Variable Speed Operation of Wind Turbine ..................................................... 57
5.3.4 Reactive Power Control .................................................................................... 61
5.3.5 Third Harmonics Injection ................................................................................ 62
5.3.6 Symmetrical Voltage Dip Analysis .................................................................. 62
CHAPTER 6 .................................................................................................65
CONCLUSION AND FUTURE WORKS ................................................65
6.1 Conclusion ............................................................................................................... 65
6.2 Future Works ........................................................................................................... 65
BIBLIOGRAPHY ........................................................................................67
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APPENDIX I ................................................................................................70
APPENDIX II ...............................................................................................71
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ABSTRACT
This thesis focuses on the variable wind speed application of the Doubly Fed Induction
Generator (DFIG). The vector control scheme is applied to the DFIG for the control of the
torque, the dc bus voltage and the reactive power exchange with the grid. The grid
connected DFIG is simulated and with the controller blocks for the rotor side converter and
grid side converter control.
The vector control of the DFIG is performed by applying stator flux orientation control
scheme in synchronously rotating dq frame for the rotor side. The grid voltage orientation
vector control is implemented in the grid side converter. The torque of the induction
generator is controlled by the rotor side controller while the dc-link voltage and the
exchange of reactive power with the grid is controlled by the grid side converter.
The DFIG based WECS system due to variable speed application and low converter rating
makes it one of the most popular wind turbines used. The variable speed application of the
DFIG is conducted in this thesis. The vector control scheme is one of the most popular
control schemes. The robust control of the machine is possible with minimum harmonic
distortion. The current loops and the overall vector control scheme are studied in detail in
the thesis. The maximum power point tracker is also implemented to maximize the power
output of the wind turbine generator system. The injection of the third harmonics to the
reference signal to increase the output voltage still maintaining the power quality is also
implemented in the thesis. Furthermore, the analysis of the crowbar protection system to
protect the system under symmetrical voltage dips is also performed.
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LIST OF TABLES
Table 5. 1 Generator Parameters. ...................................................................................... 43
Table 5. 1 Continued. ........................................................................................................ 44
Table 5. 2 Aerodynamics Properties. ................................................................................ 45
Table 5. 3 Variation of wind velocity with time for simulation. ...................................... 57
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LIST OF FIGURES
Figure 1. 1 DFIG WECS System.. ...................................................................................... 2
Figure 1. 2 Wind Turbine with different components ........................................................ 4
Figure 1. 3 Schematic of FSWT. ........................................................................................ 5
Figure 1. 4 Schematic of Direct Drive PMSG with Full Scale Converter .......................... 7
Figure 1. 5 Back to Back PWM converter.. ........................................................................ 9
Figure 1. 6 The operation of Wind Turbine in different regions ........................................ 9
Figure 1. 7 Clarke Transformation. .................................................................................. 11
Figure 1. 8 Park Transformation. . .................................................................................... 12
Figure 4. 1 Power coefficient variation with tip to speed ratio for different pitch angles. 19
Figure 4. 2 Power curve for the Wind Turbine. ................................................................ 19
Figure 4. 3 DFIG connected to 50 Hz AC. ....................................................................... 21
Figure 4. 4 Equivalent circuit of the DFIG referred to stator. .......................................... 23
Figure 4. 5 The equivalent DFIG circuit in Ξ±Ξ² reference frame. ...................................... 27
Figure 4. 6 DFIG circuit in synchronous dq reference frame referred to stator. .............. 29
Figure 4. 7 Stator flux orientation vector control of RSC.. .............................................. 32
Figure 4. 8 Grid voltage orientation vector control block diagram. ................................. 34
Figure 4. 9 Fundamental, third harmonics and injection signal. ....................................... 35
Figure 4. 10 Third Harmonics Injector Block diagram. .................................................... 36
Figure 4. 11 Current control Loop for rotor side control. ................................................. 37
Figure 4. 12 Current control Loop for grid side converter.. ............................................. 39
Figure 5. 1 Modelling of vector control of DFIG using Matlab/Simulink. ...................... 41
Figure 5. 2 Wound Induction Generator Block from simulation. ..................................... 43
Figure 5. 3 Aerodynamics of wind turbine ....................................................................... 44
Figure 5. 4 Indirect Speed Controller MPPT in Simulink. ............................................... 46
Figure 5. 5 Third harmonics Injector implementation in Matlab/Simulink. ..................... 47
Figure 5. 6 Speed of the rotor in radians per second. ....................................................... 48
Figure 5. 7 Three phase stator voltage. ............................................................................. 48
Figure 5. 8 Three phase stator current. ............................................................................. 49
Figure 5. 9 Three phase rotor current. ............................................................................... 49
Figure 5. 10 The torque produced from the system. ......................................................... 50
Figure 5. 11 The mechanical power generated from the wind turbine. ............................ 50
Figure 5. 12 Stator Power produced in the DFIG. ............................................................ 51
Figure 5. 13 Rotor Power produced at the rated speed. .................................................... 51
Figure 5. 14 The direct axis component of the rotor current. ........................................... 52
Figure 5. 15 The quadrature axis component of the rotor current. ................................... 52
Figure 5. 16 The direct axis reference rotor voltage. ........................................................ 53
Figure 5. 17 The quadrature axis reference rotor voltage. ................................................ 53
Figure 5. 18 The DC-bus voltage. ..................................................................................... 54
Figure 5. 19 The direct axis current in grid side converter. .............................................. 54
Figure 5. 20 The quadrature axis current in the grid. ....................................................... 55
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Figure 5. 21 Speed, stator voltage, stator and rotor currents in sub synchronous speed .. 56
Figure 5. 22 Rotor speed, stator current and rotor current variation with wind speed ..... 58
Figure 5. 23 Variation of stator and rotor power with wind speed ................................... 60
Figure 5. 24 The reactive power exchange control with the grid ..................................... 61
Figure 5. 25 Reference signal without third harmonics and with third harmonics. .......... 62
Figure 5. 26 Crowbar Protection and voltage dip analysis. .............................................. 64
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CHAPTER 1
INTRODUCTION
1.1 Wind Energy Conversion System (WECS)
The system to convert the energy present in the wind to useful form of energy is known as
WECS. In the past, the power in the wind was harnessed to provide useful mechanical
power but in modern world WECS is mainly concentrated on conversion of energy to
electrical form. The conversion of the wind energy into the electrical energy depends on
several factors like angle of attack, tower height, wind speed, blade length, turbine type,
etc., [1]. The wind energy conversion system can be distinctly divided into three different
parts: aerodynamics, mechanical and the electrical component[2] as shown in figure below.
β’ Aerodynamics system: The aerodynamics of the WECS system consists of wind
blades, turbine hubs, turbine rotor. The kinetic energy present in the wind is
converted into the mechanical energy in this system.
β’ Mechanical System: The mechanical energy obtained from the kinetic energy is
processed in this system. It converts the obtained mechanical energy into
appropriate form to feed the electrical system. The mechanical system of the WECS
system consists of the low speed shaft, gear box, high speed shaft which is
connected to the induction generator.
β’ Electrical system: The mechanical energy is converted into the electrical energy in
this part. It consists of the electrical generator, electrical transformers, power
converters, grid connection [3].
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Figure 1. 1 DFIG WECS System [4].
1.2 Wind Turbines
WECS system is mainly divided based on the aerodynamic differences namely.,
aerodynamic drag and aerodynamic lift [5]. The modern wind turbines are based on the
principle of aerodynamic lift because of the low power coefficient of the aerodynamic drag
type.
The wind turbines convert kinetic energy present in the wind to the electrical energy. The
efficiency of the aerodynamic lift wind turbines is higher than that of aerodynamic drag
[6]. The wind turbines based on the aerodynamic lift can be further divided into two types.
1.2.1 Horizontal Axis Wind Turbine (HAWT)
HAWT rotates perpendicular to the direction of the wind flow, parallel to the ground in
horizontal direction. Almost all the wind turbines used today are HAWT type and wide
research is done in HAWT. It is immune to the backtracking effect. The wind turbine has
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to face the wind to extract the power so it requires additional mechanism to turn the turbine
towards the wind direction[7].
1.2.2 Vertical Axis Wind Turbine (VAWT)
Vertical Axis Wind Turbine (VAWT) rotate perpendicular to the ground and is
omnidirectional i.e., it does not require to face the wind at any time. It can start to produce
power at very low wind speed. The gear boxes and other equipment can be combined and
installed near to the ground which makes it easier for maintenance. It is inefficient at higher
wind speeds and has very low starting torque. Relatively very low research is done in this
type of turbine than HAWT.
1.3 Components of Wind Turbine
The nacelle is the housing for all the electrical and the mechanical components. It contains
components like the gearbox, shaft, electrical generator. The main components of the wind
turbine are shown in the figure below and described below:
Rotor: The turbine rotor extracts the kinetic energy present in the wind. The wind strikes
the rotor blades and it starts to rotate which transfers the power to the rotor hub.
Shaft: The hub of the rotor is attached to the low speed shaft. The low speed shaft connects
the gear box and the hub of the rotor.
Gearbox: The gearbox changes the speed of rotation of the low shaft and connects to the
high-speed shaft. The electrical generator usually runs at the speed faster than the speed of
the low speed shaft, so the gearbox changes the speed to appropriate speed for the electrical
generator.
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Generator: The high-speed shaft provides the necessary mechanical energy for the
electrical generator. It than converts the energy into electrical form. The electrical
generator used for the DFIG is wound rotor induction generator.
Electronic controller: The controller employed to control various operational parameters
of the wind turbine. The direction of the wind turbine, yaw mechanism, voltage, speed
controllers are employed.
Figure 1. 2 Wind Turbine with different components [8].
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1.4 Types of Wind Turbine Energy Conversion System
The wind turbine energy conversion system can be divided into different types based on
the operating speed and the converters as described below:
1.4.1 Fixed Speed Wind Turbine (FSWT)
The fixed speed wind turbines are equipped with Squirrel Cage Induction Generator
(SCIG) which are connected directly to the grid [3]. This type of the turbine operates at the
fixed speed irrespective of the wind speed. The speed of the fixed speed wind turbine is
determined by the operating grid frequency the turbine is connected which cannot be
altered [9]. The FSWT are robust, simple in construction and cheaper in cost. The FSWT
suffer from the major drawback of the higher mechanical stresses, limited power quality
control and uncontrollable power consumption. Due to this the turbine is connected with
the shunt capacitors to compensate for the reactive power [10]. The soft starter is employed
to limit the large inrush current during the starting sequence.
Figure 1. 3 Schematic of FSWT [10].
.
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1.4.2 Variable Speed Wind Turbine (VSWT)
The variable speed wind turbine VSWT is designed to obtain the maximum efficiency over
the wide range of the wind speed[11]. The power electronics converters make the variable
speed operation possible by decoupling the rotor frequency. The rotation speed of the wind
turbine is adjusted to meet the maximum efficiency for the given wind speed. Due to this,
the tip to speed ratio can be kept at the constant value and thus the maximum power
coefficient [11]. The active and the reactive power control of the VSWT is easier and it
generates higher annual energy capture than the FSWT [9]. The have fewer mechanical
stresses, better power quality control. The drawbacks of the VSWT is it has complicated
system design and is comparatively higher in cost than the FSWT. The losses in the power
electronic converter is higher in this system.
1.4.2.1 Partial Scale Frequency Converter Wind Turbine (PSFCWT)
This configuration of the VSWT uses partial scale back to back power converter connected
to the rotor of the turbine. The stator of the machine is connected to the grid. The rotor of
the machine is connected to the grid via the power converter circuit. The power converters
in this configuration is rated at around Β±30% of the rated speed since the rotor only deals
with the slip power. The range of the speed control is around Β±30%. The decoupling of the
electrical and the mechanical frequency by the converter makes the variable speed
operation of the wind turbine possible [9], [12]. The protection of the converter is done
using the crowbar[12]. The converter also performs the reactive power compensation.
DFIG being one of the most popular wind turbines used today it suffers from several
drawbacks. The slip rings and the brushes used in the DFIG are prone to several electrical
and the mechanical failures.
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1.4.2.2 Full Scale Frequency Converter Wind Turbine (FSFCWT)
In this configuration of VSWT the rotor of the wind turbine is connected to the grid through
the full-scale converter. It allows control of the generator speed in the range up to 100%.
The configuration usually has the permanent magnet synchronous generator (PMSG).
Some of the configuration even runs without gearbox instead uses the multipole generator
system [9]. The figure below shows the PMSG with full scale converter. The system has
advantage of reduced noise since the gearbox is not present in the configuration of the
system.
Figure 1. 4 Schematic of Direct Drive PMSG with Full Scale Converter [12].
The direct drive system becomes very larger and expensive for higher power generation
for this purpose single stage gearbox and medium-speed PMSG with full scale power
converter is used [12].
1.5 Advantages of DFIG Wind Turbine
β’ The DFIG based power converters are rated at the Β±30% of the rated power so this
allows the speed control range of Β±30%.
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β’ The decoupling of the rotor frequency and the grid frequency makes the systems
variable speed operation possible.
β’ The wound rotor induction generator is used which is simple, robust and cheaper
than Permanent Magnet Synchronous Generator (PMSG).
1.6 Disadvantages of DFIG Wind Turbine
β’ The control scheme for DFIG based wind turbine is complex in nature.
β’ The need for slip rings and the gearbox makes the system vulnerable to fault.
β’ The fault ride through (FRT) capability of the DFIG is relatively weak since the
grid is directly connected to the stator of the generator [12].
1.7 Power Electronic Converters
The power converters connect the wind turbineβs rotor side to the grid. The flow of the
power in the converter is bi-directional based on the application [6]. The turbine
characteristics with that of the grid is matched by the power electronic converters.
1.7.1 Back to Back PWM Converters
The figure below shows the configuration of the back to back converter. The converter has
two converters and a dc link or decoupling capacitor in between them. The decoupling or
dc link capacitor offers the separate control of the two converters [13]. The dc-link
capacitor also imposes the drawback on the configuration by reducing the overall lifetime
of the system. The other drawback of the back to back PWM converter is the switching
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loss. The switching losses in the configuration are high since it uses two converters [6],
[13].
Figure 1. 5 Back to Back PWM converter [13].
1.8 The Operating Regions of the Wind Turbine
The operating region of the wind turbine is based on the wind speed, generator speed and
the power generated by the generator [14]. The operating regions are illustrated in the
figure below:
Figure 1. 6 The operation of wind turbines in different regions [14].
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β’ Minimum Speed Operating Region
The minimum speed of operation of the wind turbine is defined in order to avoid
the resonant frequency of the tower. The resonant frequency of the tower is around
0.5 Hz [8]. The generator speed is kept at its minimum speed which is usually 30%
below the synchronous speed. The minimum speed at which the turbine starts to
work is known as the cut in speed.
β’ Optimum Speed operating region
This is also called the maximum power tracking region. The wind turbine is
adjusted to maximize the power at the given wind speed. In this region, the power
output from the wind turbine increases as the wind speed increases.
β’ Pitch Controlled Region
Beyond the rated speed of the wind turbine, the blades of the turbine can be
adjusted so that the power output from the turbine during higher wind speed
remains constant. The pitch angle is varied and thus the angle of attack of the wind
on the blade. This changes the value of the power coefficient and the control of the
power even at higher speed is made possible.
1.9 Vector Transformations
1.9.1 Clarke Transformation
The Clarke transformation transforms the 3-phase system a,b,c to the two orthogonal
coordinate system (Ξ±,Ξ²). This transformation transforms the three phase reference frame to
the two phase stationary reference frame [15].
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ππ πΌ =2
3(ππ π) β
1
3(ππ π β ππ π)
ππ π½ =2
β3(ππ π β ππ π)
Figure 1. 7 Vector transformation using Clarke Transformation [15].
The voltage equations can be transformed by above equation in stationary reference frame
and is written in matrix form as given by following equation:
[ππΌππ½
] =2
3[ 1 β
1
2β
1
2
0β3
2β
β3
2 ]
β [π£πππ£πππ£ππ
]
1.9.2 Park Transformation
Park Transformation is done in the next step to transform the orthogonal stator components
to the d-q coordinate system. The two components are in stationary reference frame and is
converted to the rotating. reference frame using park transformation.
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ππ π = ππ πΌ β πΆππ (π) + ππ π½ β πππ(π)
ππ π = ππ π½ β πΆππ (π) β ππ πΌ β πππ(π)
Figure 1. 8 Vectors transformation using Park Transformation [15].
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CHAPTER 2
OBJECTIVE OF THE RESEARCH
The main objective of this research is to implement the vector control method for the
performance control of the doubly fed induction generator. The modelling and design of
the wind turbine and the performance analysis when the system is connected to the grid.
The research also studies the variable speed operation of the doubly fed induction
generator-based wind turbine. The thesis aims for complete understanding of the current
loops for the vector control of the grid connected DFIG WECS. The thesis also aims to
inject the third harmonics signal to the reference voltage signal for pulse width modulation.
The areas of investigation of the thesis are summarized below:
β’ Implementation of the stator flux orientation vector control for rotor side converter.
β’ Implementation of the grid voltage orientation vector control for the rotor side
controller
β’ Implementation of the maximum power point tracker (MPPT).
β’ Implementing the third harmonics injection to the reference voltage signal.
Besides, the thesis also studies the aerodynamics of the wind energy conversion system.
The working of the back to back power electronic converter. The operation of the wind
turbine at sub-synchronous, synchronous and the super synchronous speed.
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2.1 Thesis Organization
The chapter 3 of the thesis presents the literature review. Several relevant papers and the
research works done in the field are presented in the chapter.
The fourth chapter of the thesis presents the modelling and design of the doubly fed
induction generator. Also, the relevant theory and the equations from the aerodynamics to
the electrical modelling of the system is presented in this chapter. This chapter also presents
the vector control scheme for the induction generator, the current loops and the tuning of
the PI controllers. The chapter concludes by presenting relevant theory on the third
harmonics signal injection.
The fifth chapters deal with the simulation and validation of the result. The wind turbine
performance is observed. It demonstrates the results from Matlab/Simulink and discussion.
The sixth chapter of the thesis concludes the research. It also points out the future works
on the system.
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CHAPTER 3
LITERATURE REVIEW
Energy is the most essential factor in the social and economic growth of the modern world.
The environmental hazards and the scarcity of the nonrenewable source of energy has
created a global concern on the existing energy sources. The lack long term replacement
for the fossil fuels has enriched the interest in the renewable energy sources. The wind
energy is one the most favorable long-term solution for the energy concern over the fossil
fuel. The concern The wind energy is one of the most competitive and viable energy
sources due to several advancement in the wind turbine system [16]. The review paper
[17], historical development of the wind energy is presented. In [18] the current scenario
of the wind energy in the world, and the advancement in the wind turbine design is
discussed. The inclusion of the wind power in the grid increases the fluctuation and
randomness in the power. The high penetration of the wind farm can lead to the power
system oscillation [19].
DFIG is one of the most popular wind turbine models widely used today. The small sizing
of the converters, cheaper cost, variable wind speed operation are the regions are the
reasons that makes DFIG one of the most popular research areas. One of the most important
requirement of the energy resource is that it should be grid friendly [19]. The critical issues
associated of connecting the DFIG wind turbines with the grid is presented in reference
[20]. The paper elaborates the frequency regulation, fault ride through capability, reactive
power support of the DFIG is studied.
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The vector control of the DFIG in the stator reference frame is performed in reference [21].
Several configuration of the wind turbine for the variable speed application is presented in
reference [22]. The dynamic modelling of the wind turbine based on doubly fed induction
generator (DFIG) is also presented in the literature. The variable speed application of the
wind turbine using back to back PWM converters is presented in reference [23]. The
detailed mathematical derivation and the block diagram for the vector control is presented.
The design of the controllers from the current loops is also presented in reference [23]. The
vector control of the doubly fed induction generator for the isolated load using PWM
converter is performed in reference [24]. The decouple orthogonal component is used to
control the stator flux since the stator flux is no longer determined by the grid [24].
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CHAPTER 4
MODELLING OF THE DFIG WECS
The modelling of the DFIG WECS can be divided in the following sections as aerodynamic
modelling, mechanical modelling and electrical modelling.
4.1 Aerodynamics of DFIG
The aerodynamics system converts the kinetic energy present in the wind to the mechanical
energy. The generated mechanical energy is in the form of torque and speed [14]. The
mechanical power produced has the cubic power relation with the wind velocity so
fluctuations in the wind speed creates the variation in the generated power. The total energy
present in the wind is given by:
ππ =
1
2ππ΄ππ€
3 (1)
The mechanical power and the torque of the wind turbine is given by:
ππ =
1
2πππ 2ππ€
3πΆπ (2)
ππ‘ =
1
2πππ 3ππ€
2πΆπ‘ (3)
Where,
Ο = Density of the air = 1.23 Kg/m3
A = Ο R2 = Cross sectional area of the blade.
R= Radius of the wind turbine.
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Cp=Power coefficient.
Ct= Torque Coefficient = Cp/Ξ»
Ξ» = Tip Speed Ratio = π Ξ©π‘
ππ€
In the above equation the power and the torque coefficients are used since only the fraction
of the total kinetic energy present in the wind is converted into the mechanical energy at
the wind turbine.
The power conversion coefficient is the function of the blade pitch angle (Ξ²) and the tip to
speed ratio (Ξ»). The tip to speed ratio is the speed of the tip of the turbine blade relative to
the speed of the wind. The generated power depends on the relative velocity of the rotor
tip and the wind speed. Several numerical approximations have been suggested for Cp(.)
[25]. The numerical approximation for the Cp(.) in this thesis is used as described in [26].
πΆπ = 0.5176(
116
ππβ 0.4π½ β 5)π
β21ππ + 0.0068π (4)
ππ =1
π + 0.08π½β
0.035
π½3 + 1 (5)
The extracted power from the wind turbine can be controlled by controlling the Cp value.
During the higher winds, the generator and the converter can be overloaded. At these
conditions the rotor speed must be controlled. This is done by rotating the pitch of the
blade. The graph below shows the relationship between the power conversion coefficient
and tip to speed ratio for different values of the pitch angle.
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Figure 4. 1 Power coefficient variation with tip to speed ratio for different pitch angles.
The power curve for the 1.5 MW wind turbine is shown in the figure below:
Figure 4. 2 Power curve for the wind turbine.
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4.2 Betz Limit
The wind passing through the wind turbine still possess some velocity and thus the kinetic
energy. Due to this fact, the entire energy present in the wind cannot be theoretically
converted into the mechanical energy. The theoretical maximum limit given by the Betz
limit is 0.593 or 59.3%.
4.3 Maximum Power Point Tracking
The maximum power point tracker is used in the wind turbine to maximize the power
output of the turbine. The employed maximum power point tracker will follow the wind
speed and adjust accordingly to maximize the power from the turbine. For the operation of
the wind turbine on maximum power point, we have following optimum values for the tip
to speed ratio, Power conversion and torque coefficient as below. To ensure maximum
aerodynamic efficiency the power coefficient should be kept at the optimum value so that
the turbine can extract maximum power [27].
ππππ‘ =π π
ππ€ πΆπ = πΆπ_πππ₯ πΆπ‘ = πΆπ‘_πππ₯
The aerodynamic torque extracted by the wind turbine during the maximum power point
is given in [8] is.
ππ‘ =1
2ππ
π 5π2
ππππ‘2 πΆπ‘πππ₯
= πΎπππ‘_π‘π2 (6)
πΎπππ‘_π‘ =1
2ππ
π 5
ππππ‘2 πΆπ‘πππ₯
(7)
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4.4 Modelling of Doubly Fed Induction Generator
The doubly fed induction generator (DFIG) based wind energy conversion system is the
widely popular variable speed wind generation system. It offers the advantage of the
control of the active and the reactive power independently [28]. DFIG WECS has following
major components. It consists of generator, turbine, Rotor side Controller (RSC), Grid side
Controller (GSC), Coupling transformer, DC link as shown in the figure below.
Figure 4. 3 DFIG connected to 50 Hz AC [29].
The DFIG based WECS incorporates wound induction generator as an electrical generator.
The stator of the generator is connected to directly to the grid. The rotor of the induction
machine is connected to the AC grid network by slip rings through back to back converter
and the transformer. The βinverter Iβ in the above figure is called the Rotor side Converter
(RSC) and the one in the right is called the Grid Side Converter (GSC). The two converters
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are connected back to back through the DC link. The grid side converter controls the
variation in the DC-link voltage. The Rotor Side converter is employed to control the
torque and the speed of the induction machine. The power converter operates in bi-
directional mode hence the induction machine can operate in sub-synchronous,
synchronous and also in hyper-synchronous mode [23].
4.4.1 Modelling of the Electrical Induction Generator
In the Doubly Fed Induction Generator (DFIG) WECS the wound rotor induction generator
is used. The generator has slip rings. This configuration of the DFIG enables the sizing of
the converter to be around 33% of the rated power. The three-phase induction generator
has the stator flux rotating at the synchronous speed and the rotor rotating at the speed less
than the synchronous stator due to slip.
The synchronous speed at which the stator flux rotates is given by the following equation:
ππ =120 β π
π (8)
Where,
f is the frequency and P is the number of poles of the generator.
The slip of the generator is defined as below:
π =(ππ β ππ)
ππ (9)
Here, ππ and ππ are the angular frequency of the stator and the rotor.
The use of the cascaded converter at the rotor side enables the control of the slip ring
induction motor at the sub-synchronous and super synchronous speed. The power
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reversibility is possible in the rotor side of the converter which enables the control of the
induction machine in the sub-synchronous and super-synchronous speed [30].
4.4.2 Dynamic Modelling of DFIG
4.4.2.1 Space Vector Representation
The steady state equivalent electric circuit of the DFIG referred to the stator can is shown
in the figure below:
Figure 4. 4 Equivalent circuit of the DFIG referred to stator [31].
The equations of the voltages and the fluxes in the stator and the rotor referred to stator
are given below:
ππ = π π πΌπ + πππ πΏππ πΌπ + πππ πΏπ(πΌπ + πΌπ) (10)
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ππ
π =
π π
π πΌπ + πππ πΏπππΌπ + πππ πΏπ(πΌπ + πΌπ) (11)
Ξ¨π = πΏπ πΌπ + πΏππΌπ (12)
Ξ¨π = πΏππΌπ + πΏππΌπ (13)
Where,
Vs = Stator Voltage.
Is = Current flowing through Stator.
Rs = Stator resistance.
LΟs = Stator self-inductance.
Lm = mutual inductance.
Vr = Voltage across the rotor circuit.
S = Slip of the system.
Ir = Current flowing through the rotor circuit.
Ls= LΟs + Lm = Total stator inductance.
LΟr = Rotor side self-inductance.
Lr= LΟr + Lm = Total rotor inductance.
Ξ¨s = Stator flux.
Ξ¨r = Rotor flux.
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The equations for the active and the reactive power can be obtained as following:
ππ = 3π π |πΌπ |2 + 3ππ πΏππΌπ{πΌπ πΌπ
β} (14)
ππ = 3ππ πΏπ |πΌπ |2 + 3ππ πΏππ π{πΌππΌπ
β} (15)
The rotor active and the reactive power are obtained as:
ππ = 3π π|πΌπ|2 β 3π ππ πΏππΌπ{πΌπ πΌπ
β} (16)
ππ = 3π ππ πΏπ|πΌπ|2 + 3π ππ πΏππ π{πΌπ πΌπ
β} (17)
The expression for the torque is given by the following equation.
πππ = 3πΏπ
ππΏππΏπ π. πΌπ{Ξ¨π Ξ¨π
β} (18)
Where,
π = (1 βπΏπ2
πΏπ πΏπ)
The equation for the mechanical power of the DFIG can be written as:
ππ = ππ + ππ (19)
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4.4.2.2 Ξ±Ξ² Modelling
The stator voltage, rotor voltage and the fluxes are transformed into the stationary reference
also known as the (Ξ±-Ξ²) reference frame as below:
ππΌπ = π π ππΌπ +π
ππ‘ππΌπ (20)
ππ½π = π π ππ½π +π
ππ‘ππ½π (21)
The rotor voltages can be transformed as follows:
ππΌπ = π πππΌπ +π
ππ‘ππΌπ + ππππ½π (22)
ππ½π = π πππ½π +π
ππ‘ππ½π β ππππΌπ (23)
Similarly, the fluxes in the stator and the rotor can be represented in the stationary reference
frame as follows:
ππΌπ = πΏπ ππΌπ + πΏπππΌπ (24)
ππ½π = πΏπ ππ½π + πΏπππ½π (25)
ππΌπ = πΏπππΌπ + πΏπππΌπ (26)
ππ½π = πΏπππ½π + πΏπππ½π (27)
The equivalent circuit of the machine in the Ξ±Ξ² reference frame is shown below:
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Figure 4. 5 The equivalent DFIG circuit in Ξ±Ξ² reference frame [31].
The equation of the active and the reactive power can be calculated in the stationary
reference frame as below:
ππ =3
2(π£πΌπ ππΌπ + π£π½π ππ½π ) (28)
ππ =
3
2(π£π½π ππΌπ β π£πΌπ ππ½π ) (29)
Similarly, the active and the reactive power in the rotor side can be calculated as follows:
ππ =
3
2(π£πΌπππΌπ + π£π½πππ½π) (30)
ππ =
3
2(π£π½πππΌπ β π£πΌπππ½π) (31)
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The equation for the electromagnetic torque in stationary reference frame is given by:
πππ =
3
2π(ππ½πππΌπ β ππΌπππ½π) (32)
4.4.2.3 dq Modelling of DFIG
The voltage and the flux equations in the space vector model of DFIG in the synchronously
rotating frame are defined as below:
π£ππ = π π πππ +ππππ
ππ‘β ππ πππ (33)
π£ππ = π π πππ +ππππ
ππ‘+ ππ πππ (34)
Similarly, the rotor voltages in synchronously rotating dq reference frame can be written
as follows:
π£ππ = π ππππ +ππππ
ππ‘β πππππ (35)
π£ππ = π ππππ +ππππ
ππ‘+ ππ πππ (36)
The fluxes in the stator can be written as follows:
πππ = πΏπ πππ + πΏππππ (37)
πππ = πΏπ πππ + πΏππππ (38)
Similarly, for the fluxes in the rotor can be written as:
πππ = πΏππππ + πΏππππ (39)
πππ = πΏππππ + πΏππππ (40)
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Where, Ls Lr and Lm are the stator, rotor and the mutual inductances respectively.
Also,
πΏπ = πΏππ + πΏπ
πΏπ = πΏππ + πΏπ
Where πΏππ and πΏππ are the self-inductances of the stator and the rotor respectively.
Using the above equations, the equivalent circuit for the DFIG can be represented in the dq
reference frame as shown in the figure below:
Figure 4. 6 DFIG circuit in synchronous dq reference frame referred to stator [31].
The electromagnetic torque Te generated by the machine can be derived in synchronous dq
reference frame as:
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ππ =3
2[πππ πππ β πππ πππ ] (41)
Assuming the general convention of motor working as the generator. The active power,
reactive power and the torque can be calculated in the synchronous reference as follows:
ππ = β3
2[π£ππ πππ + π£ππ πππ ] (42)
ππ = β3
2[π£ππ πππ β π£ππ πππ ] (43)
ππ = β3
2[π£πππππ + π£πππππ] (44)
ππ = β3
2[π£πππππ β π£πππππ ] (45)
The total power generated by the Doubly Fed Induction generator is:
ππππ‘ππ = ππ + ππ (46)
ππππ‘ππ = ππ + ππ (47)
Here, the dynamic model of DFIG describes the voltage equations, flux equations in the
stationary reference frame for both the stator and the rotor. After that we also deduced the
equations for the active power, reactive power and the electromagnetic torque of the
machine.
4.5 Design of the Control System for DFIG Wind Turbine
The vector control of the induction machine is widely accepted and extended one. The
vector control of the induction machine is understood by the current control loops. The
vector control is an attractive solution for high performance and limited speed range drive
system application [32], [33]. The use of the suitable power converter in the rotor side, the
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overall system control can be performed with low current harmonic distortion in both stator
and rotor side [23], [32]. The main idea behind the vector control of the induction machine
is its mathematical equivalency to the separately magnetized dc machine [33]. The space
vector theory is used to express the three-phase quantities in terms of the space vectors.
This modelling of the induction motor describes the operation of the motor in the transient
and the steady state[34]. The three phase electrical quantities are converted into two
orthogonal components that can be visualized as the vectors. The projection converts the
three-phase time dependent system to the two-component time invariant system. This helps
us to visualize the three-phase induction motor as that of the two-phase system[35]. The
system becomes simpler and simplifies the understanding of the control process.
4.5.1 Rotor side Converter (RSC) Controller
The vector control of the machine is performed in the synchronously rotating dq reference
frame. The stator flux vector position is oriented along the direct-axis [23], [36]. The
implementation of the control of the rotor side converter the stator and rotor currents along
with the stator voltage and rotor position is required to be known. The advantage of the
stator flux orientation is that the torque is only dependent on the quadrature axis component
of the rotor current [33]. The equations obtained for the rotor voltage in synchronous
reference frame as the function of the rotor currents is as shown below:
π£ππ = π ππππ + ππΏπ
π
ππ‘πππ β ππππΏππππ +
πΏπ
πΏπ
π
ππ‘|ππ ββββ | (48)
π£ππ = π ππππ + ππΏπ
π
ππ‘πππ + ππππΏππππ + ππ
πΏπ
πΏπ
π
ππ‘|ππ ββββ |
(49)
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Where,
π = 1 βπΏπ2
πΏπ πΏπ
The stator flux is constant since the grid is connected to the stator of the DFIG, this implies
that the derivative term π
ππ‘|ππ ββββ | is zero [31], [33]. For the transformation in the reference
frame, the angle ΞΈr has to be estimated. The stator and the rotor winding turns ratio must
be considered at the control stages of the induction machine. For the thesis, the rotor current
πππ is set to zero. The block diagram for the rotor side converter control of the induction
machine is provided below form reference [31].
Figure 4. 7 Stator flux orientation vector control of RSC [31].
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In the block diagram, PLL is used to estimate the rotor angle while in this thesis the rotor
angle is calculated using angle calculation block which will explained in the later section.
4.5.2 Grid Side Converter (GSC) Controller
The GSC is implemented in the DFIG model to regulate the voltage of the DC link at
constant value. The GSC controls the reactive power exchange between the grid and the
rotor of the induction machine. The implemented vector controls the d axis of the dq
rotating reference frame is aligned with the grid voltage π£ππ.
We have,
π£ππ = |π£πββββ | and π£ππ = 0
The basic equations for the voltages dq components of the grid side controller can be
obtained as:
π£ππ = π ππππ + πΏπ
π
ππ‘πππ β πππΏππππ + π£ππ (50)
π£ππ = π ππππ + πΏπ
π
ππ‘πππ + πππΏππππ + π£ππ (51)
The block diagram for the vector control of the grid side converter with grid voltage
oriented vector control is shown below [8], [37]:
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Figure 4. 8 Grid voltage orientation vector control block diagram [37].
In the block diagram, PLL is used to estimate the grid angle while in this thesis the grid
angle is calculated using angle calculation block which will explained in the later section.
The constant gains in the above block diagram are defined as below:
πΎππ =1
32 . π£ππ
(52)
πΎππ =1
β32 . π£ππ
(53)
4.6 Sinusoidal PWM with Third Harmonics Injection
The three phase power converters can be modulated with the use of third harmonics
injection [37]. Without losing the quality of the signal, the output voltage amplitude can be
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significantly improved using the third harmonics injection to the reference signals. The
injection signal can be easily determined with the following formula:
π3_πππ = β
πππ₯{π£πβπ£π
βπ£πβ} + πππ{π£π
βπ£πβπ£π
β}
2 (54)
Where,
V3_inj is the third harmonics injection signal.
π£πβπ£π
βπ£πβ are the reference signal for the phases a, b and c respectively.
Figure 4. 9 Fundamental, third harmonics and injection signal [8].
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The block diagram of the third harmonics injection block is shown in the figure below:
Figure 4. 10 Third Harmonics Injector Block diagram [8].
4.7 Angle Estimation
For the estimation of the rotor angle and the grid angle an angle estimation block is used.
The rotor angle can be calculated as follows:
ππ = tanβ1ππ π½
ππ πΌ (55)
ππ = ππ βπ
2β ππ (56)
ππ = π. ππ (57)
Where,
ππ is the stator angle
ππ is the rotor angle
ππ is the electrical angle
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The stator is directly connected to the grid so that the grid angle is equivalent to the stator
angle. The rotor angle can be estimated from the stator angle using above formulae.
4.8 Current Loops
4.8.1 Tuning of the Regulators
4.8.1.1 Rotor Side Converter Controller Tuning
The equivalent block diagram for the closed loop current control in the rotor side control
block is shown in the block diagram as below from [31].
Figure 4. 11 Current control Loop for rotor side control [37].
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The block diagram shown above can be simplified into the transfer function as below:
πππ(π )
πππβ (π )
=π πΎπ + πΎπ
π 2πΏπ . π + π (π π + πΎπ) + πΎπ
(58)
πππ(π )
πππβ (π )
=π πΎπ + πΎπ
π 2πΏπ . π + π (π π + πΎπ) + πΎπ
(59)
The above transfer function is then compared with the denominator of the second order of
the general control transfer function i.e., π 2 + 2ππππ + ππ2 we have,
πΎπ = π. πΏπππ2 (60)
πΎπ = 2. ππΏππππ2 β π π (61)
This gives the proportional and the integral gain constant for the PI-controller in the rotor
side converter control.
4.8.1.2 Grid Side Converter Controller Tuning
The grid side converter is fed from the grid using the RL-filter. Taking the Laplace
transformation in the voltage equations of the grid side converter yields the following
transfer function:
πππ(π )
πππ(π )=
1
πΏπ . π + π π (62)
πππ(π )
πππ(π )=
1
πΏπ . π + π π (63)
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The block diagram for the grid side converter control loop is shown in the figure below[37].
Figure 4. 12 Current control Loop for grid side converter [37].
The current loops in the control block diagram can be modelled using the transfer function
as shown below:
πππ (π )
πππ β (π )
=π πΎπ + πΎπ
π 2πΏπ + π (π π + πΎπ) + πΎπ
(64)
πππ (π )
πππ β (π )
=π πΎπ + πΎπ
π 2πΏπ + π (π π + πΎπ) + πΎπ
(65)
By comparing the transfer function of the current loops with the denominator of the
standard second order control equation π 2 + 2ππππ + ππ2 we get, the values for Kp and Ki
for the grid side converter.
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πΎπ = πΏπππ2 (66)
πΎπ = 2. πΏππππ2 β π π (67)
The gain for the PI controller for the grid side converter is thus found and are tuned with
the equivalent gain constants.
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CHAPTER 5
SIMULATION
5.1 Model Description
In this chapter, the mathematical models of the Doubly Fed Induction Generator are
realized using Matlab/Simulink. The model consists of wound induction generator, back to
back PWM converters, controller block, wind turbine aerodynamics and grid block. The
measurement block is also present and the output block which consists of the scope from
Matlab to view the results in the Simulink environment.
Figure 5. 1 Modelling of vector control of DFIG using Matlab/Simulink.
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The asynchronous wound induction generator from the Simscape library is used as the
induction generator for the thesis. The stator of the generator is connected directly to grid
while the rotor of the converter is connected to the back to back converter and to the grid.
The IGBT based converters are used for the simulation purpose. One of the IGBT converter
is connected to the rotor of the DFIG while the other converter is connected to the grid
through the filter circuit. The DC link capacitor decouples the operation of the converters
so that the individual control of the converter is made possible. The aerodynamics model
generates the torque to drive the machine based on the formulas given in the previous
chapters. The vector control of the machine is implemented in the controller block. The
controller block consists of the rotor side controller and the grid side controller for the
respective converters. The pulse signal to drive the converters are generated at the
controller block.
5.2 Block Description
The individual block diagram used in the simulation is explained in detail in this section.
The parameter used for the individual blocks is explained in this section.
5.2.1 Wound Induction Generator
The wound induction machine is used from the simscape library as the generator for the
DFIG. The block uses the parameters like nominal power, voltage, inductance and the
resistance for both the stator and the rotor, the mutual inductance, inertia of the machine,
the friction factor and the pole pairs. The mechanical torque is the input to the generator
which is derived from the aerodynamic model based on the wind speed. The figure below
shows the block of the wound generator in Matlab/Simulink.
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Figure 5. 2 Wound Induction Generator Block from simulation.
The block also offers the several measurement parameters as an output from the generator.
The rotor angle, rotor speed and the electromagnetic torque is extracted from the
measurement input block.
The parameters used in the wound generator are summarized in the table below:
Table 5. 1 Generator Parameters
Parameters Values
Number of Pole Pairs 2
Stator Voltage (L-L) 690 V
Rotor Voltage 2070 V
Stator Resistance 0.0026 ohm
Stator Inductance 0.000087 H
Mutual Inductance 0.0025 H
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Table 5. 1 Continued
Rotor Resistance 0.0029 ohm
Rotor Inductance 0.00087 H
Stator Rotor Turns Ratio 1/3
Inertia 127 Kg.m2
Friction Factor 0.001 N.m.s
5.2.2 Wind Turbine Aerodynamics Block
The wind turbine aerodynamic block calculates the torque as an output which is fed to the
induction generator. The wind Turbine model uses wind speed, generator speed and the
pitch angle as the input parameters. The radius of the blade, and the wind speed is used to
derive the power coefficient Cp(Ξ», Ξ²). Then, the torque calculated. The figure below shows
the block which performs the aerodynamic calculation of the turbine torque.
Figure 5. 3 Aerodynamics of wind turbine.
The optimum value of lambda is obtained from the Cp(Ξ», Ξ²) and tip to speed ratio curve.
The optimum value of the power coefficient is the maximum value obtained from the curve
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and it is obtained to be 49% which is not practically viable. So, the value of Cp is chosen
to be at 44%. The rated parameters used in the aerodynamics block is shown below:
Table 5. 2 Aerodynamics Properties
Parameters Rated Values
Wind Speed 12 m/s
Radius 32 m
Beta 0 deg
Gear box Ratio 74
Density of Wind 1.23 Kg/m3
5.2.3 Controller Block
5.2.3.1 Rotor Side Controller
The vector control of the block diagram presented in the previous section is implemented
in this section. The reference voltage for the rotor side converter is generated using the
vector control. The block also consists of the Maximum Power Point Tracking block which
maximizes the efficiency of the system by tracking the optimum operational speed. The
block consists of the several transformation blocks which transforms the voltages and
currents in the abc reference frame to the stationary reference frame and then to the
synchronously rotating dq- reference frame. The PI controllers are used for the control. The
gains of the PI controller are tuned which was explained in the previous section. The
generated reference voltage is then fed to the PWM generator block from the
Matlab/Simulink library. This block generates the pulse signal for the control of the rotor
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side converter. The figure below shows the Indirect Speed controller MPPT used in the
control block.
Figure 5. 4 Indirect Speed Controller MPPT in Simulink.
5.2.3.2 Grid Side Controller
The grid side converter control discussed in the previous section is implemented in this
section. The grid side converter (GSC) controls the dc-link voltage and regulates the
reactive power exchange with the grid. The grid voltage orientation vector control is
implemented. The control of the grid side converter requires the transformation of the abc
-reference frame to the synchronously rotating dq reference frame. The grid side current in
the decoupled synchronous reference frame is controlled using the PI controllers. The PI
controllers are tuned using the gain parameters derived in the previous section. The current
outputs of the PI controller are then converted into the voltages converted back to the abc-
reference frame. The signal is then applied to the PWM generator to generate the pulse
signal for the grid side controller.
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5.2.4 Third Harmonics Injection
To maximize the output of the converter, third harmonics is injected in the reference signal.
The injection of the third harmonics in the reference voltage increases the output voltage,
maintaining the output power quality. The relevant theory and the block diagram of the
third harmonics as presented in previous chapter. The block diagram shown below is used
for the injection of the third harmonics in the reference signal.
Figure 5. 5 Third harmonics Injector implementation in Matlab/Simulink.
5.3 Result/Validation
The performance of the system under the rated condition is observed in this section. The
rated wind speed is 12m/s. At the rated condition, the mechanical power output produced
from the generator should be 1.5MW.
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5.3.1 Simulation at Rated Speed
The rated wind speed of the wind turbine is 12m/s. The turbine, gearbox and the generator
system are designed in such a way that it reaches the synchronous speed of the generator
at wind speed of 12m/s. At the synchronous speed of the generator the rotor current is
almost constant since the slip of the system is equal to zero.
Figure 5. 6 Speed of the rotor in radians per second.
Figure 5. 7 Three phase stator voltage.
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Figure 5. 8 Three phase stator current.
Figure 5. 9 Three phase rotor current.
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Figure 5. 10 The torque produced from the system.
Figure 5. 11 The mechanical power generated from the wind turbine.
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Figure 5. 12 Stator Power produced in the DFIG.
Figure 5. 13 Rotor Power produced at the rated speed.
From above simulation results, the frequency of the rotor current is almost constant since
the machine is operating at the synchronous speed and the slip of the system is zero. The
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rotor frequency depends on the slip so the rotor current as if it is DC. The torque fairly
follows the reference torque. The mechanical power for the system is 1.5 MW for the
system. At the synchronous speed, there is no power generated at the rotor since the slip of
the system is zero. All the power generated in the system is supplied by the stator.
For the further detail control analysis, the d-q component analysis is done in the below
section. The d-q components of the currents in the rotor side controller are shown in the
figure below:
Figure 5. 14 The direct axis component of the rotor current.
Figure 5. 15 The quadrature axis component of the rotor current.
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In this above figure, the vector controls the d-axis of the reference frame is aligned with
the stator flux. The quadrature axis of the rotor current controls the torque of the machine.
The variation in the torque is proportional to the q-axis rotor current. The direct axis current
is kept at zero.
The figure below shows the reference voltages generated in the d-q reference frame. The
reference voltages are transformed back to abc-frame to feed the PWM generator.
Figure 5. 16 The direct axis reference rotor voltage.
Figure 5. 17 The quadrature axis reference rotor voltage.
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The grid side converter simulation results are presented in this section. The grid side
converter controls the dc bus voltage and regulates the reactive power exchange with the
grid. The dc bus voltage, direct and the quadrature axis current of the grid side controller
is as obtained from Matlab/Simulink is shown in the figure below:
Figure 5. 18 The DC-bus voltage.
Figure 5. 19 The direct axis current in grid side converter.
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Figure 5. 20 The quadrature axis current in the grid.
The direct axis grid current is responsible to maintain the dc bus voltage at the constant
reference voltage of 975 volts. The quadrature axis grid current is set to zero since there is
no reactive power exchange between the grid and the DFIG. The generator is operated at
unity power factor so, there is no reactive power generation.
5.3.2 Operation of the Wind Turbine at the Sub Synchronous Speed
The operation of the machine at the sub synchronous speed was observed in
Matlab/Simulink. The DFIG was operated at the speed below the synchronous speed by
applying the wind velocity of 10 m/s. The simulation is performed for 10 seconds in Matlab
/Simulink. The graph below gives the speed, stator voltage and the currents in the stator
and the rotor as below:
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Figure 5. 21 Speed, stator voltage, stator and rotor currents in sub synchronous speed.
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Here, it is observed that since the machine is operating at the sub synchronous speed the
machine runs at certain slip. Since there is slip the current in the rotor circuit operates at
the slip frequency.
5.3.3 Variable Speed Operation of Wind Turbine
For the variable speed operation of the wind turbine simulation is performed at various
wind speed. At the interval of every 10 seconds, velocity of the wind speed is changed.
The simulation is performed by reducing the machines inertia to half value for faster
simulation. The table below summarizes the wind speed at given interval.
Table 5. 3 Variation of wind velocity with time for simulation.
Time Wind Velocity
0-10 second 9 m/s
10-20 second 12 m/s
20-30 second 13 m/s
30-40 second 12 m/s
The result obtained from Matlab/Simulink is shown below:
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Figure 5. 22 Rotor speed, stator current and rotor current variation with wind speed.
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From the above result, when the machine is operated at the synchronous frequency the
rotor currents acts as dc but when the machine is operated at the sub synchronous or hyper
synchronous speed the rotor current has certain frequency given by the slip of the machine.
The operation of the maximum power point tracking can be observed from the above result.
When the wind velocity is changed, the rotor speed changes to new operating point to
maximize the power.
Again, the section below presents the effect of the wind velocity on the power generated
at the stator and at the rotor. The simulation results shown below is the stator power and
the rotor power for the variable wind velocity.
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Figure 5. 23 Variation of stator and rotor power with wind speed.
The above results illustrate the changes in the stator power and the rotor power based on
the operating speed of the DFIG. When the machine is operated at the synchronous speed
as seen in the time interval of 10-20 seconds and 30-40 seconds. All the power produced
in the system is due to stator. The rotor power is zero at this interval is zero since the slip
of the system is zero. When the machine is operated at the sub-synchronous speed as seen
in the interval 0-10 seconds. The rotor draws the power from the grid while the stator
supplies the power. When the machine is operated at the super synchronous speed, time
interval 20-30 second, the rotor and the stator both supplies power to the grid. The total
power produced in the system is sum of the stator power and the rotor power which is
equivalent to the total mechanical power.
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5.3.4 Reactive Power Control
The reactive power exchange between the grid and the DFIG is controlled by the grid side
converter. The quadrature axis of the grid current in the grid side controller performs the
control of the reactive power exchange. The simulation results below illustrate the reactive
power exchange between the DFIG and the grid.
Figure 5. 24 The reactive power exchange control with the grid.
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When the reactive power is drawn from the grid, the quadrature axis current is negative
and when the reactive power is supplied to the grid quadrature axis current is positive.
When there is no exchange of the reactive power, the quadrature axis current is zero.
5.3.5 Third Harmonics Injection
In this section, the reference signal obtained from injection of third harmonics and the
voltage reference without third harmonics is compared. The voltage output can be
maximized with the injection of the third harmonics in the reference signal without
compromising with the power quality.
Figure 5. 25 Reference signal without third harmonics and with third harmonics.
5.3.6 Symmetrical Voltage Dip Analysis
The performance and the protection of the converters during the occurrence of scheduled
or unforeseen voltage dips is analyzed in this section. When the voltage dip occurs in the
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system the current and the voltage spikes to much greater value so, some sort of protection
must be provided to the converters until the stator flux settles at the new operating point.
This protection is provided by the crowbar. The crowbar helps to speed up the transition
of the stator flux and also protects the converter by dissipating the energy produced in the
system to the resistor. The simulation of the symmetrical voltage dip and protection offered
by the crowbar is presented in this section.
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Figure 5. 26 Crowbar Protection and voltage dip analysis.
From the above simulation, the protection of the DFIG by using crowbar was performed.
The voltage dip at 4 second was applied to the system in which the stator voltage reduces
to 10 percent of the stator voltage. During this period very large magnitude of the rotor
current was produced. The rotor side converter was turned off during this period for safety
purposes and the crowbar system was activated. The crowbar dissipated energy generated
and speed up the transition of the stator flux so that the control of the converter can be
regained.
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CHAPTER 6
CONCLUSION AND FUTURE WORKS
6.1 Conclusion
In this thesis, the vector control of the induction machine with stator flux orientation for
the rotor side converter and the grid voltage orientation vector control for the grid side
converter was performed. The thesis analyzes the operation of the DFIG on variable wind
condition with maximum power point tracking. The successful control of the induction
machine was achieved to generate the power. The operation of the DFIG in different
operating speed was observed and the system was subjected to the variable wind speed.
The injection of the third harmonics signal to the reference voltage was also performed.
The reference output signal was compared. The symmetrical voltage dip was analyzed, and
the system was protected using the crowbar.
Vector control of the DFIG is very important control technique that offers the dynamic
control of the machine. The current loops are studied in detail. DFIG based WECS is one
of the important and most popular wind turbines. The low rating sizing of the converter
and the variable speed application to be able to operate and control the turbine in sub-
synchronous and super-synchronous mode makes the DFIG scheme more popular.
6.2 Future Works
Wind energy is one of the most emerging field of energy. The more intensive and wide
research on the renewable energy to reduce the environmental hazards caused by the fossil
fuels. Variable speed wind energy is one of the most important renewable energy. It offers
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the work for the Doubly Fed Induction Generator (DFIG) was done while the induction
generator was connected to the grid. The system control was performed based on the
current loops. This model can be further expanded to the stand-alone operation of the wind
turbine with changes in the controller blocks. The stator of the model is directly connected
to the grid. The stator flux for this model is provided by the grid, in the standalone
implementation the stator flux must be estimated. The integration of the turbine with the
other micro sources. The hybrid system has higher efficiency and adds more to the power
system stability and security. The turbine model along with other sources can increase the
stability as well as minimize the power system fluctuations.
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APPENDIX I
Plotting of the Power coefficient Vs Tip to speed ratio curve:
%Cp and Ct curves
beta=0; %Pitch angle
i=1;
for lambda=0.1:0.0001:13.4
lambda_i(i)=(1./((1./(lambda+0.08.*beta)-(0.035./(beta^3+1)))));
Cp(i)=0.5176.*(116./lambda_i(i)-0.4.*beta-5).*(exp(-21./lambda_i(i)))+0.0068*lambda;
Ct(i)=Cp(i)/lambda;
i=i+1;
end
lambda_n=[0.1:0.0001:13.4];
plot(lambda_n,Cp)
hold on
beta=5; %Pitch angle
i=1;
for lambda=0.1:0.0001:13.4
lambda_i(i)=(1./((1./(lambda+0.08.*beta)-(0.035./(beta^3+1)))));
Cp(i)=0.5176.*(116./lambda_i(i)-0.4.*beta-5).*(exp(-21./lambda_i(i)))+0.0068*lambda;
Ct(i)=Cp(i)/lambda;
i=i+1;
end
lambda_n=[0.1:0.0001:13.4];
plot(lambda_n,Cp)
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APPENDIX II
The initialization Program for the Matlab is presented in this section.
clc
close all
clear all
%DFIG INITIALIZATION PARAMETERS
f= 60; %Stator frequency
Ps= 2.2e6; %Rated stator Power
p= 2; %Pole pair
n= 60*f/p; %Rated rotational speed
Vs= 690; %Rated Voltage of stator
Is=2000; %Rated Current in stator
Tem=5.5e5; %Rated Torque
u=1/3 %Stator to rotor winding turns ratio
Vr=Vs/u; %Rated rotor voltage (v)
S_max=1/3; %Maximum slip
Vr_sta=(Vr*S_max)*u; %Rated voltage in rotor winding referred to stator
Rsta=2.6e-3; %Stator resistance in ohms
Lsi=0.087e-3; %Leakage inductance for both stator and rotor in H
Lmag=2.5e-3; %Magnetizing inductance in H
Rrot=2.9e-3; %resistance in rotor referred to stator (ohm)
Ls=Lmag+Lsi; %stator inductance (H)
Lrot=Lmag+Lsi; %Rotor inductance (H)
Vbus=975; %Dc bus voltage referred to stator (V)
sigma=1-Lmag^2/(Ls*Lrot);
Fs=Vs*sqrt(2/3)/(2*pi*f) %stator flux (Wb)
J=127; % Machine inertia
D=1e-3; %Damping constant
fsw=5e3; %switching frequency
Ts=1/fsw/60; %sampling
%PI REGULATORSβRotor Side
tau_i=(sigma*Lr)/Rr;
tau_n=0.05/4;
wn=100*(1/tau_i);
wnn=1/tau_n;
Kpid=(2*wn*sigma*Lr)-Rr;
Kpiq=Kpid;
Kiid=(wn^2)*Lr*sigma;
Kiiq=Kiid;
Kpn=(2*wnn*J)/p;
Kin=((wnn^2)*J)/p;
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% TURBINE AERODYNAMICS
N=74; %Gearbox ratio
Radius=32; %Radius
ro=1.225; %Air Density
beta=0; %Pitch angle
i=1;
for lambda=0.1:0.0001:14
lambda_i(i)=(1./((1./(lambda+0.08.*beta)-(0.035./(beta^3+1)))));
Cp(i)=0.5176.*(116./lambda_i(i)-0.4.*beta-5).*(exp(-21./lambda_i(i)))+0.0068*lambda;
Ct(i)=Cp(i)/lambda;
i=i+1;
end
lambda_n=[0.1:0.0001:11.8];
plot(lambda_n,Cp)
%MPPT
Cpmax=0.44;
Opt_Lambda=6.8;
Kopt=((0.5*ro*pi*(Radius^5)*Cpmax)/(Opt_Lambda^3));
plot(lambda_n,Cp)
%GRID SIDE
Cbus=80e-3;
Rg=10e-6;
Lg=200e-6;
Kpg=1/(1.5*Vs*sqrt(2/3));
Kqg=-Kpg;
%PI REGULATORSβGrid side
tau_ig=Lg/Rg;
wng=60*2*pi;
kpidg=(2*wng*Lg)-Rg;
kpiqg=kpidg;
Kiidg=(wng^2)*Lg;
Kiiqg=Kiidg;
Rcrowbar=0.1;