Copyright 2019, Aashish Pant

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

ii

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. I’ve learnt a lot from him in

the field of power electronics and semiconductor application.

I’m very grateful to my colleague Mr. Saleh Dinkhah for his continued supervision for the

entirety of the thesis. I’ve 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.


iii

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


iv

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 αβ 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


v

APPENDIX I ................................................................................................70

APPENDIX II ...............................................................................................71


vi

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.


vii

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


viii

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 αβ 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


ix

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


1

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.

• 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.

• 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.

• 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].


2

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


3

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.


4

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].


5

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].

.


6

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 ±30% of the rated speed since the rotor only deals

with the slip power. The range of the speed control is around ±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.


7

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

• The DFIG based power converters are rated at the ±30% of the rated power so this

allows the speed control range of ±30%.


8

• The decoupling of the rotor frequency and the grid frequency makes the systems

variable speed operation possible.

• 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

• The control scheme for DFIG based wind turbine is complex in nature.

• The need for slip rings and the gearbox makes the system vulnerable to fault.

• 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 turbine’s 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


9

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].


10

• 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.

• 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.

• 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 (α,β). This transformation transforms the three phase reference frame to

the two phase stationary reference frame [15].


11

𝑖𝑠𝛼 =2

3(𝑖𝑠𝑎) −

1

3(𝑖𝑠𝑏 − 𝑖𝑠𝑐)

𝑖𝑠𝛽 =2

√3(𝑖𝑠𝑏 − 𝑖𝑠𝑐)

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:

[𝑉𝛼𝑉𝛽

] =2

3[ 1 −

1

2−

1

2

0√3

2−

√3

2 ]

∗ [𝑣𝑎𝑛𝑣𝑏𝑛𝑣𝑐𝑛

]

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.


12

𝑖𝑠𝑑 = 𝑖𝑠𝛼 ∗ 𝐶𝑜𝑠(𝜃) + 𝑖𝑠𝛽 ∗ 𝑆𝑖𝑛(𝜃)

𝑖𝑠𝑞 = 𝑖𝑠𝛽 ∗ 𝐶𝑜𝑠(𝜃) − 𝑖𝑠𝛼 ∗ 𝑆𝑖𝑛(𝜃)

Figure 1. 8 Vectors transformation using Park Transformation [15].


13

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:

• Implementation of the stator flux orientation vector control for rotor side converter.

• Implementation of the grid voltage orientation vector control for the rotor side

controller

• Implementation of the maximum power point tracker (MPPT).

• 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.


14

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.


15

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.


16

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].


17

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:

𝑃𝑚 =

1

2𝜌𝐴𝑉𝑤

3 (1)

The mechanical power and the torque of the wind turbine is given by:

𝑃𝑚 =

1

2𝜌𝜋𝑅2𝑉𝑤

3𝐶𝑝 (2)

𝑇𝑡 =

1

2𝜌𝜋𝑅3𝑉𝑤

2𝐶𝑡 (3)

Where,

ρ = Density of the air = 1.23 Kg/m3

A = π R2 = Cross sectional area of the blade.

R= Radius of the wind turbine.


18

Cp=Power coefficient.

Ct= Torque Coefficient = Cp/λ

λ = Tip Speed Ratio = 𝑅 Ω𝑡

𝑉𝑤

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 (β) and the tip to

speed ratio (λ). 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].

𝐶𝑝 = 0.5176(

116

𝜆𝑖− 0.4𝛽 − 5)𝑒

−21𝜆𝑖 + 0.0068𝜆 (4)

𝜆𝑖 =1

𝜆 + 0.08𝛽−

0.035

𝛽3 + 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.


19

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.


20

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].

𝜆𝑜𝑝𝑡 =𝑅𝜔

𝑉𝑤 𝐶𝑝 = 𝐶𝑝_𝑚𝑎𝑥 𝐶𝑡 = 𝐶𝑡_𝑚𝑎𝑥

The aerodynamic torque extracted by the wind turbine during the maximum power point

is given in [8] is.

𝑇𝑡 =1

2𝜌𝜋

𝑅5𝜔2

𝜆𝑜𝑝𝑡2 𝐶𝑡𝑚𝑎𝑥

= 𝐾𝑜𝑝𝑡_𝑡𝜔2 (6)

𝐾𝑜𝑝𝑡_𝑡 =1

2𝜌𝜋

𝑅5

𝜆𝑜𝑝𝑡2 𝐶𝑡𝑚𝑎𝑥

(7)


21

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 ‘inverter I’ 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


22

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:

𝑁𝑠 =120 ∗ 𝑓

𝑃 (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:

𝑆 =(𝜔𝑠 − 𝜔𝑚)

𝜔𝑠 (9)

Here, 𝜔𝑠 and 𝜔𝑚 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


23

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:

𝑉𝑠 = 𝑅𝑠𝐼𝑠 + 𝑗𝜔𝑠𝐿𝜎𝑠𝐼𝑠 + 𝑗𝜔𝑠𝐿𝑚(𝐼𝑠 + 𝐼𝑟) (10)


24

𝑉𝑟

𝑠=

𝑅𝑟

𝑠𝐼𝑟 + 𝑗𝜔𝑠𝐿𝜎𝑟𝐼𝑟 + 𝑗𝜔𝑠𝐿𝑚(𝐼𝑠 + 𝐼𝑟) (11)

Ψ𝑠 = 𝐿𝑠𝐼𝑠 + 𝐿𝑚𝐼𝑟 (12)

Ψ𝑟 = 𝐿𝑟𝐼𝑟 + 𝐿𝑚𝐼𝑠 (13)

Where,

Vs = Stator Voltage.

Is = Current flowing through Stator.

Rs = Stator resistance.

Lσs = 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= Lσs + Lm = Total stator inductance.

Lσr = Rotor side self-inductance.

Lr= Lσr + Lm = Total rotor inductance.

Ψs = Stator flux.

Ψr = Rotor flux.


25

The equations for the active and the reactive power can be obtained as following:

𝑃𝑠 = 3𝑅𝑠|𝐼𝑠|2 + 3𝜔𝑠𝐿𝑚𝐼𝑚{𝐼𝑠𝐼𝑟

∗} (14)

𝑄𝑠 = 3𝜔𝑠𝐿𝑠|𝐼𝑠|2 + 3𝜔𝑠𝐿𝑚𝑅𝑒{𝐼𝑟𝐼𝑠

∗} (15)

The rotor active and the reactive power are obtained as:

𝑃𝑟 = 3𝑅𝑟|𝐼𝑟|2 − 3𝑠𝜔𝑠𝐿𝑚𝐼𝑚{𝐼𝑠𝐼𝑟

∗} (16)

𝑄𝑟 = 3𝑠𝜔𝑠𝐿𝑟|𝐼𝑟|2 + 3𝑠𝜔𝑠𝐿𝑚𝑅𝑒{𝐼𝑠𝐼𝑟

∗} (17)

The expression for the torque is given by the following equation.

𝑇𝑒𝑚 = 3𝐿𝑚

𝜎𝐿𝑟𝐿𝑠𝑝. 𝐼𝑚{Ψ𝑠Ψ𝑟

∗} (18)

Where,

𝜎 = (1 −𝐿𝑚2

𝐿𝑠𝐿𝑟)

The equation for the mechanical power of the DFIG can be written as:

𝑃𝑚 = 𝑃𝑠 + 𝑃𝑟 (19)


26

4.4.2.2 αβ Modelling

The stator voltage, rotor voltage and the fluxes are transformed into the stationary reference

also known as the (α-β) reference frame as below:

𝑉𝛼𝑠 = 𝑅𝑠𝑖𝛼𝑠 +𝑑

𝑑𝑡𝜓𝛼𝑠 (20)

𝑉𝛽𝑠 = 𝑅𝑠𝑖𝛽𝑠 +𝑑

𝑑𝑡𝜓𝛽𝑠 (21)

The rotor voltages can be transformed as follows:

𝑉𝛼𝑟 = 𝑅𝑟𝑖𝛼𝑟 +𝑑

𝑑𝑡𝜓𝛼𝑟 + 𝜔𝑚𝜓𝛽𝑟 (22)

𝑉𝛽𝑟 = 𝑅𝑟𝑖𝛽𝑟 +𝑑

𝑑𝑡𝜓𝛽𝑟 − 𝜔𝑚𝜓𝛼𝑟 (23)

Similarly, the fluxes in the stator and the rotor can be represented in the stationary reference

frame as follows:

𝜓𝛼𝑠 = 𝐿𝑠𝑖𝛼𝑠 + 𝐿𝑚𝑖𝛼𝑠 (24)

𝜓𝛽𝑠 = 𝐿𝑠𝑖𝛽𝑠 + 𝐿𝑚𝑖𝛽𝑠 (25)

𝜓𝛼𝑟 = 𝐿𝑟𝑖𝛼𝑟 + 𝐿𝑚𝑖𝛼𝑟 (26)

𝜓𝛽𝑟 = 𝐿𝑟𝑖𝛽𝑟 + 𝐿𝑚𝑖𝛽𝑠 (27)

The equivalent circuit of the machine in the αβ reference frame is shown below:


27

Figure 4. 5 The equivalent DFIG circuit in αβ reference frame [31].

The equation of the active and the reactive power can be calculated in the stationary

reference frame as below:

𝑃𝑠 =3

2(𝑣𝛼𝑠𝑖𝛼𝑠 + 𝑣𝛽𝑠𝑖𝛽𝑠) (28)

𝑄𝑠 =

3

2(𝑣𝛽𝑠𝑖𝛼𝑠 − 𝑣𝛼𝑠𝑖𝛽𝑠) (29)

Similarly, the active and the reactive power in the rotor side can be calculated as follows:

𝑃𝑟 =

3

2(𝑣𝛼𝑟𝑖𝛼𝑟 + 𝑣𝛽𝑟𝑖𝛽𝑟) (30)

𝑄𝑟 =

3

2(𝑣𝛽𝑟𝑖𝛼𝑟 − 𝑣𝛼𝑟𝑖𝛽𝑟) (31)


28

The equation for the electromagnetic torque in stationary reference frame is given by:

𝑇𝑒𝑚 =

3

2𝑝(𝜓𝛽𝑟𝑖𝛼𝑟 − 𝜓𝛼𝑟𝑖𝛽𝑟) (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:

𝑣𝑑𝑠 = 𝑅𝑠𝑖𝑑𝑠 +𝑑𝜓𝑑𝑠

𝑑𝑡− 𝜔𝑠𝜓𝑞𝑠 (33)

𝑣𝑞𝑠 = 𝑅𝑠𝑖𝑞𝑠 +𝑑𝜓𝑞𝑠

𝑑𝑡+ 𝜔𝑠𝜓𝑑𝑠 (34)

Similarly, the rotor voltages in synchronously rotating dq reference frame can be written

as follows:

𝑣𝑑𝑟 = 𝑅𝑟𝑖𝑑𝑟 +𝑑𝜓𝑑𝑟

𝑑𝑡− 𝜔𝑟𝜓𝑞𝑟 (35)

𝑣𝑞𝑟 = 𝑅𝑟𝑖𝑞𝑟 +𝑑𝜓𝑞𝑟

𝑑𝑡+ 𝜔𝑠𝜓𝑑𝑟 (36)

The fluxes in the stator can be written as follows:

𝜓𝑑𝑠 = 𝐿𝑠𝑖𝑑𝑠 + 𝐿𝑚𝑖𝑑𝑟 (37)

𝜓𝑑𝑠 = 𝐿𝑠𝑖𝑞𝑠 + 𝐿𝑚𝑖𝑞𝑟 (38)

Similarly, for the fluxes in the rotor can be written as:

𝜓𝑑𝑟 = 𝐿𝑚𝑖𝑑𝑠 + 𝐿𝑟𝑖𝑑𝑟 (39)

𝜓𝑞𝑠 = 𝐿𝑚𝑖𝑞𝑠 + 𝐿𝑟𝑖𝑞𝑟 (40)


29

Where, Ls Lr and Lm are the stator, rotor and the mutual inductances respectively.

Also,

𝐿𝑠 = 𝐿𝜎𝑠 + 𝐿𝑚

𝐿𝑟 = 𝐿𝜎𝑟 + 𝐿𝑚

Where 𝐿𝜎𝑠 and 𝐿𝜎𝑟 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:


30

𝑇𝑒 =3

2[𝜓𝑞𝑠𝑖𝑑𝑠 − 𝜓𝑑𝑠𝑖𝑞𝑠] (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:

𝑃𝑠 = −3

2[𝑣𝑞𝑠𝑖𝑞𝑠 + 𝑣𝑑𝑠𝑖𝑑𝑠] (42)

𝑄𝑠 = −3

2[𝑣𝑞𝑠𝑖𝑑𝑠 − 𝑣𝑑𝑠𝑖𝑞𝑠] (43)

𝑃𝑟 = −3

2[𝑣𝑞𝑟𝑖𝑞𝑟 + 𝑣𝑑𝑟𝑖𝑑𝑟] (44)

𝑄𝑟 = −3

2[𝑣𝑞𝑟𝑖𝑑𝑟 − 𝑣𝑑𝑟𝑖𝑞𝑠] (45)

The total power generated by the Doubly Fed Induction generator is:

𝑃𝑇𝑜𝑡𝑎𝑙 = 𝑃𝑠 + 𝑃𝑟 (46)

𝑄𝑇𝑜𝑡𝑎𝑙 = 𝑄𝑠 + 𝑄𝑟 (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


31

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:

𝑣𝑑𝑟 = 𝑅𝑟𝑖𝑑𝑟 + 𝜎𝐿𝑟

𝑑

𝑑𝑡𝑖𝑑𝑟 − 𝜔𝑟𝜎𝐿𝑟𝑖𝑞𝑟 +

𝐿𝑚

𝐿𝑠

𝑑

𝑑𝑡|𝜓𝑠⃗⃗⃗⃗ | (48)

𝑣𝑞𝑟 = 𝑅𝑟𝑖𝑞𝑟 + 𝜎𝐿𝑟

𝑑

𝑑𝑡𝑖𝑞𝑟 + 𝜔𝑟𝜎𝐿𝑟𝑖𝑑𝑟 + 𝜔𝑟

𝐿𝑚

𝐿𝑠

𝑑

𝑑𝑡|𝜓𝑠⃗⃗⃗⃗ |

(49)


32

Where,

𝜎 = 1 −𝐿𝑚2

𝐿𝑠𝐿𝑟

The stator flux is constant since the grid is connected to the stator of the DFIG, this implies

that the derivative term 𝑑

𝑑𝑡|𝜓𝑠⃗⃗⃗⃗ | is zero [31], [33]. For the transformation in the reference

frame, the angle θr 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

𝑖𝑑𝑟 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].


33

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 𝑣𝑑𝑔.

We have,

𝑣𝑑𝑔 = |𝑣𝑔⃗⃗⃗⃗ | and 𝑣𝑞𝑔 = 0

The basic equations for the voltages dq components of the grid side controller can be

obtained as:

𝑣𝑑𝑓 = 𝑅𝑓𝑖𝑑𝑔 + 𝐿𝑓

𝑑

𝑑𝑡𝑖𝑑𝑔 − 𝜔𝑎𝐿𝑓𝑖𝑞𝑔 + 𝑣𝑑𝑔 (50)

𝑣𝑞𝑓 = 𝑅𝑓𝑖𝑞𝑔 + 𝐿𝑓

𝑑

𝑑𝑡𝑖𝑑𝑔 + 𝜔𝑎𝐿𝑓𝑖𝑑𝑔 + 𝑣𝑞𝑔 (51)

The block diagram for the vector control of the grid side converter with grid voltage

oriented vector control is shown below [8], [37]:


34

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:

𝐾𝑝𝑔 =1

32 . 𝑣𝑑𝑔

(52)

𝐾𝑞𝑔 =1

−32 . 𝑣𝑑𝑔

(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


35

significantly improved using the third harmonics injection to the reference signals. The

injection signal can be easily determined with the following formula:

𝑉3_𝑖𝑛𝑗 = −

𝑚𝑎𝑥{𝑣𝑎∗𝑣𝑏

∗𝑣𝑐∗} + 𝑚𝑖𝑛{𝑣𝑎

∗𝑣𝑏∗𝑣𝑐

∗}

2 (54)

Where,

V3_inj is the third harmonics injection signal.

𝑣𝑎∗𝑣𝑏

∗𝑣𝑐∗ are the reference signal for the phases a, b and c respectively.

Figure 4. 9 Fundamental, third harmonics and injection signal [8].


36

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:

𝜃𝑠 = tan−1𝑉𝑠𝛽

𝑉𝑠𝛼 (55)

𝜃𝑟 = 𝜃𝑠 −𝜋

2− 𝜃𝑒 (56)

𝜃𝑒 = 𝑝. 𝜃𝑚 (57)

Where,

𝜃𝑠 is the stator angle

𝜃𝑟 is the rotor angle

𝜃𝑒 is the electrical angle


37

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].


38

The block diagram shown above can be simplified into the transfer function as below:

𝑖𝑑𝑟(𝑠)

𝑖𝑑𝑟∗ (𝑠)

=𝑠𝐾𝑝 + 𝐾𝑖

𝑠2𝐿𝑟 . 𝜎 + 𝑠(𝑅𝑟 + 𝐾𝑝) + 𝐾𝑖

(58)

𝑖𝑞𝑟(𝑠)

𝑖𝑞𝑟∗ (𝑠)


𝑠2𝐿𝑟 . 𝜎 + 𝑠(𝑅𝑟 + 𝐾𝑝) + 𝐾𝑖

(59)

The above transfer function is then compared with the denominator of the second order of

the general control transfer function i.e., 𝑠2 + 2𝜉𝜔𝑛𝑠 + 𝜔𝑛2 we have,

𝐾𝑖 = 𝜎. 𝐿𝑟𝜔𝑛2 (60)

𝐾𝑝 = 2. 𝜎𝐿𝑟𝜉𝜔𝑛2 − 𝑅𝑟 (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:

𝑖𝑑𝑔(𝑠)

𝑉𝑑𝑓(𝑠)=

1

𝐿𝑓 . 𝑠 + 𝑅𝑓 (62)

𝑖𝑞𝑔(𝑠)

𝑉𝑞𝑓(𝑠)=

1

𝐿𝑓 . 𝑠 + 𝑅𝑓 (63)


39

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:

𝑖𝑑𝑠(𝑠)

𝑖𝑑𝑠∗ (𝑠)


𝑠2𝐿𝑓 + 𝑠(𝑅𝑓 + 𝐾𝑝) + 𝐾𝑖

(64)

𝑖𝑞𝑠(𝑠)

𝑖𝑞𝑠∗ (𝑠)


𝑠2𝐿𝑓 + 𝑠(𝑅𝑓 + 𝐾𝑝) + 𝐾𝑖

(65)

By comparing the transfer function of the current loops with the denominator of the

standard second order control equation 𝑠2 + 2𝜉𝜔𝑛𝑠 + 𝜔𝑛2 we get, the values for Kp and Ki

for the grid side converter.


40

𝐾𝑖 = 𝐿𝑓𝜔𝑛2 (66)

𝐾𝑝 = 2. 𝐿𝑓𝜉𝜔𝑛2 − 𝑅𝑓 (67)

The gain for the PI controller for the grid side converter is thus found and are tuned with

the equivalent gain constants.


41

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.


42

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.


43

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


44

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(λ, β). 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(λ, β) and tip to speed ratio curve.

The optimum value of the power coefficient is the maximum value obtained from the curve


45

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


46

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.


47

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.


48

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.


49

Figure 5. 8 Three phase stator current.

Figure 5. 9 Three phase rotor current.


50

Figure 5. 10 The torque produced from the system.

Figure 5. 11 The mechanical power generated from the wind turbine.


51

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


52

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.


53

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.


54

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.


55

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:


56

Figure 5. 21 Speed, stator voltage, stator and rotor currents in sub synchronous speed.


57

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:


58

Figure 5. 22 Rotor speed, stator current and rotor current variation with wind speed.


59

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.


60

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.


61

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.


62

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


63

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.


64

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.


65

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


66

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.


67

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70

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


i=1;

for lambda=0.1:0.0001:13.4



Ct(i)=Cp(i)/lambda;

i=i+1;

end

lambda_n=[0.1:0.0001:13.4];

plot(lambda_n,Cp)


71

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 REGULATORS—Rotor 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;


72

% TURBINE AERODYNAMICS

N=74; %Gearbox ratio

Radius=32; %Radius

ro=1.225; %Air Density


i=1;

for lambda=0.1:0.0001:14



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 REGULATORS—Grid 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;

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