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IMPACT OF WIND TURBINE GENERATORS ON
POWER SYSTEM STABILITY
A THESIS
Submitted by
JEEVAJOTHI R
(Register No.200709201)
In partial fulfillment for the award of the degree
of
DOCTOR OF PHILOSOPHY
DEPARTMENT OF ELECTRICAL & ELECTRONICS
ENGINEERING
KALASALINGAM UNIVERSITY
ANAND NAGAR
KRISHNANKOIL - 626126
AUGUST 2014
iii
ABSTRACT
Power systems are complex systems that have evolved over years in
response to economic growth and continuously increasing power demand.
Wind power generation has experienced a tremendous growth in the past
decade, and has been recognized as an environmental friendly and
economically competitive means of electric power generation. In the near
future, wind power penetration in electrical power systems will increase and
will start to replace the output of conventional synchronous generators
(CSGs). As a result, it may also begin to influence the overall power system
behavior. Hence, the impact of wind power on the dynamics of power systems
should be studied thoroughly in order to identify potential problems and to
develop measures to mitigate those problems.
The dynamic behavior of a power system is determined mainly by the
generators. Wind turbine generators (WTGs) affect the dynamic behavior of
the power system in a way that might be different from CSGs. The major
issues to be considered are voltage stability and transient stability. Transient
stability of a power system is the ability to maintain synchronous operation of
the machines when subjected to a large disturbance. A power system is said to
be voltage stable if it maintains voltage within operational limits.
Dominant WTGs in use at present are fixed-speed squirrel cage
induction generators (SCIGs), variable speed geared drive doubly fed
iv
induction generators (DFIGs), and variable speed direct drive electrically
excited synchronous generators (EESGs) and permanent magnet synchronous
generators (PMSGs). SCIGs are used along with capacitor bank. In DFIGs, the
rotor winding is fed through back-to-back variable frequency, voltage source
converters (VSCs). In EESGs, additional converter is required for exciting its
rotor. In PMSGs, the requirement of a larger pole number can be met with
permanent magnets which allow small pole pitch. Also the absence of field
windings in PMSGs results in higher efficiency.
In this thesis, the model of variable speed direct drive WTGs with
modified controllers is developed. Also it investigates the impact of fixed-
speed SCIGs with capacitor banks, variable speed DFIGs with standard
control and modeled variable speed direct drive EESGs and PMSGs with
modified controllers on power system voltage stability and transient stability.
Since a large proportion of existing wind farms are based on fixed-
speed wind turbines (FSWTs) which are equipped with simple SCIGs, the
voltage stability issue is a key problem. SCIGs consume reactive power during
system contingency, which deteriorates the local grid voltage stability.
DFIGs make use of power electronic converters and are thus able to
regulate their own reactive power to operate at a given power factor as well as
able to control grid voltage. Because of the limited capacity of the pulse-width
modulation (PWM) converter, when the voltage control requirement is beyond
the capability of the DFIG, the voltage stability of the grid is also affected.
v
The synchronous generators are direct drive systems which supplies
more reactive power and thus provides better performances in contrast to
DFIG to recover post-fault voltage. EESG and PMSG are coming under this
direct drive category.
EESGs are salient pole machines and are excited from power grid. For
low speed operation, high pole count synchronous generators are
recommended. With EESGs, over excitation is easily possible. So operation at
unity power factor is utilized to reduce machine side inverter to the real power
value.The direct drive EESG has been modeled with d-q current controlled
converter and a direct drive PMSG has been modeled with maximum power
point tracking (MPPT) controlled dc-dc boost converter, adaptive hysteresis
band current controlled VSC which maintained constant DC link voltage at
different wind speeds and different load conditions respectively.
Simulation has been performed on IEEE 14-bus test system to study the
loading margin, voltage collapse, voltage magnitude and reactive power
delivered by the various WTGs. Further simulation was carried out on IEEE 9-
bus test system to study the rotor angle swing, rotor speed deviation and
oscillation, critical clearing time (CCT), voltage magnitude, active power
support and reactive power support by the different WTGs.
Simulation results demonstrate the superior performance of EESGs
and PMSGs with modified controllers in improving the voltage stability and
transient stability of power system.
vi
ACKNOWLEDGEMENT
First and foremost I thank God for providing His grace and strength
to achieve this work.
I express my sincere gratitude to my Supervisor Dr.D.Devaraj,
Senior Professor and Head, Dept. of Electrical & Electronics Engineering,
Kalasalingam University, for his technical guidance, his intellectual support
and encouragement of my research work. I am extremely grateful for having
the privilege to work under him and learn from his expertise.
I express my sincere thanks to Mr. R.Jeyasingh, Manager,
R.S.Wind Tech. Pvt. Ltd. for the valuable discussions and technical support
towards my research work.
I would like to thank the management and officials of
Kalasalingam University for providing support for doing my research work.
I want to thank my late parents for getting me where I am now. I
want to dedicate the effort done in this project to them who always believed in
me and stood by my decisions.
I am forever indebted to my family for their understanding,
patience and encouragement when it was most required.
Lastly, I offer my regards and blessings to all of those who
supported me in any respect for the successful completion of my research
work.
R.JEEVAJOTHI
vii
TABLE OF CONTENTS
CHAPTER
NO. TITLE
PAGE
NO.
ABSTRACT iii
LIST OF TABLES vii
LIST OF FIGURES viii
LIST OF SYMBOLS & ABBREVIATIONS xx
1 INTRODUCTION 1
1.1 INTRODUCTION 1
1.2 ENERGY CONVERSION FROM WIND 2
1.3 OPERATING CHARACTERISTICS OF WIND
TURBINE
4
1.4 CONTROL OF WIND TURBINE 5
1.4.1 Stall Control 5
1.4.2 Pitch control 6
1.5 TYPES OF WIND TURBINE GENERATORS 8
1.5.1 Fixed Speed Wind Turbine Generators 8
1.5.2 Variable Speed Wind Turbine Generators 9
1.5.2.1 Geared drive Doubly fed
Induction Generator
10
1.5.2.2 Direct drive Synchronous
Generator
11
1.6 POWER ELECTRONIC CONVERTERS IN 13
viii
WIND ENERGY CONVERSION SYSTEMS
1.7 IMPACT OF WIND TURBINE GENERATORS
ON POWER SYSTEM PERFORMANCE
15
1.8 ORGANISATION OF THE THESIS 16
2 LITERATURE SURVEY 19
2.1 INTRODUCTION 19
2.2 MODELING OF WIND TURBINE
GENERATORS
19
2.3 CONVERTER TOPOLOGIES FOR WIND
TURBINE GENERATORS
24
2.4 CONVERTER CONTROL STRATEGIES 26
2.4.1 MPPT Control 26
2.4.2 Control of Voltage Source Converter 27
2.5
IMPACT OF VARIABLE SPEED WIND
TURBINE GENERATORS ON POWER
SYSTEM STABILITY
29
2.6 ISSUES IDENTIFIED 34
2.7 CONCLUSION 36
3 MODELING AND SIMULATION OF WIND
TURBINE GENERATORS
37
3.1 INTRODUCTION 37
3.2 MODELING OF INDUCTION GENERATORS 37
3.3 VARIABLE SPEED WIND TURBINE WITH
DIRECT DRIVE SYNCHRONOUS
GENERATORS
39
3.3.1 Direct drive EESG 41
3.3.2 Direct drive PMSG 41
3.4 MODELING OF DIRECT DRIVE 43
ix
SYNCHRONOUS GENERATORS
3.4.1 Modeling of EESG 43
3.4.2 Modeling of PMSG 44
3.5 MODELING AND CONTROL OF POWER
ELECTRONIC CONVERTERS
46
3.5.1 Full-wave Diode Bridge Rectifier 46
3.5.2 DC-DC Boost Converter 46
3.5.3 Control of DC-DC Boost Converter 49
3.5.4 Modeling of Voltage Source Converter 51
3.5.5 Control of Voltage Source Converter 53
3.5.5.1 d-q Current Control 53
3.5.5.2 Adaptive Hysteresis Band
Current Control
56
3.6 SIMULATION RESULTS 59
3.6 .1 Direct Drive EESG 59
3.6.2 Direct Drive PMSG 67
3.6.2.1 Effect of Pitch control 71
3.6.2.2 Results of constant DC link
voltage control with MPPT at wind
speeds of 12 m/ sec. and at 14 m/sec
73
3.6.2.3 Results of constant DC link
voltage control with adaptive hysteresis
band current controller at load currents
of 50A and 130A
76
3.7 SUMMARY 80
4 IMPACT OF WIND TURBINE GENERATORS
ON POWER SYSTEM VOLTAGE STABILITY
82
4.1 INTRODUCTION 82
4.2 VOLTAGE STABILITY ANALYSIS 82
x
4.2.1 PV curve 83
4.2.2 Loading margin 84
4.3 POWER SYSTEM VOLTAGE STABILITY IN
THE PRESENCE OF WIND TURBINE
GENERATORS
85
4.3.1 Fixed Speed Wind Turbine with Squirrel
cage Induction Generator
86
4.3.2 Variable Speed Wind Turbine with Geared
drive Doubly fed Induction Generators
87
4.3.3 Variable Speed Wind Turbine with Direct
drive Synchronous Generator
88
4.3.3.1 Electrically Excited Synchronous
Generator
88
4.3.3.2 Permanent Magnet Synchronous
Generator
89
4.4 VOLTAGE CONTROLLERS IN WIND
TURBINE GENERATORS
90
4.5 SIMULATION RESULTS 91
4.5.1 Voltage Stability with Conventional
Synchronous Generators
92
4.5.1.1 Computation of Loading
margin
93
4.5.1.2 Voltage Vs time curve after
the contingency
94
4. 5.1.3 Voltage profile 94
4.5.2
Voltage Stability with Wind Turbine
Generators
97
4.5.2.1 Computation of Loading
margin
99
xi
4.5.2.2 Voltage Vs. Time curve after
the Contingency
100
4.5.2.3 Voltage profile 102
4.6 SUMMARY 105
5 POWER SYSTEM TRANSIENT STABILITY IN
THE PRESENCE OF WIND TURBINE
GENERATORS
106
5.1 INTRODUCTION 106
5.2 TRANSIENT STABILITY ANALYSIS 106
5.3 TRANSIENT STABILITY ASSESSMENT 108
5.3.1 Critical Clearing Time 109
5.3.2 Rotor Angle Deviation 109
5.3.3 Rotor Speed Oscillation 110
5.4 TRANSIENT STABILITY IN THE
PRESENCE OF WIND TURBINE
GENERATORS
111
5.4.1 Fixed Speed Wind Turbine Generators 111
5.4.2 Variable Speed Wind Turbine
Generators
112
5.4.2.1 Geared drive Wind Turbine
Generators
112
5.4.2.2 Direct drive Wind Turbine
Generators
113
5.5 SIMULATION RESULTS 114
5.5.1Transient stability with CSGs alone 115
5.4.2 Impact of WTGs on transient stability 119
5.5.2.1 Impact of SCIGs on transient
stability
119
5.5.2.2 Impact of DFIGs on transient
stability
123
xii
5.5.2.3 Impact of EESGs on transient
stability
126
5.5.2.4 Impact of PMSGs on transient
stability
130
5.6 SUMMARY 135
6 SUMMARY OF FINDINGS AND
CONCLUSION
136
6.1 INTRODUCTION 136
6.2 SUMMARY OF THE RESEARCH FINDINGS 136
6.3 SIGNIFICANT RESEARCH CONTRIBUTION 138
6.4 CONCLUSION OF THE THESIS 139
6.5 SUGGESTIONS FOR FUTURE WORK 139
APPENDIX 1 140
APPENDIX 2 145
APPENDIX 3 148
APPENDIX 4 149
REFERENCES 150
LIST OF PUBLICATIONS 157
CURRICULUM VITAE 158
LIST OF TABLES
TABLE TITLE PAGE
xiii
NO. NO.
3.1 Parameters of Wind Turbine 62
3.2 Parameters of Electrically Excited Synchronous
Generator
62
3.3 Parameters of Wind Turbine 67
3.4 Parameters of Permanent Magnet Synchronous
Generator
68
3.5 Converter parameters 68
4.1 Parameters of Conventional Synchronous Generator 92
4.2 Loading Margin under Base case and Contingency
states in p.u.
93
4.3 Voltage magnitude and Reactive power flows with
Conventional Synchronous Generators
95
4.4 Parameters of Fixed Speed SCIG 98
4.5 Parameters of variable speed DFIG 98
4.6 Values of Loading Margin under Base case and
Contingency states in p.u.
99
4.7 Values of voltage magnitude and reactive power in
p.u.
102
5.1 Transient stability assessment with CSGs and fixed and
variable speed WTGs
134
A3.1 Transmission line parameters of IEEE 14 bus test
system
148
LIST OF FIGURES
xiv
FIGURE
NO.
TITLE PAG
E
NO. 1.1 Schematic diagram of Wind Turbine 2
1.2 versus characteristic 3
1.3 Typical wind turbine power output with steady wind
speed
4
1.4 Schematic diagram of stall control 6
1.5 Performance characteristics of wind turbine under pitch
control
7
1.6 Three dimensional view of group of versus
characteristic with pitch angle
8
1.7 Schematic representation of the fixed speed wind turbine
with squirrel cage induction generator
9
1.8 Schematic representation of the variable speed wind
turbine with doubly fed induction generator
10
1.9 Schematic representation of the variable speed wind
turbine with direct drive electrically excited synchronous
generator
12
1.10 Schematic representation of the variable speed wind
turbine with direct drive permanent magnet synchronous
generator
13
1.11 Power electronic converters in wind energy conversion
systems
14
3.1 Equivalent circuit of Fixed Speed Squirrel Cage
Induction Generator 38
3.2 Equivalent circuit of Variable Speed Doubly Fed
Induction Generator
38
3.3 Direct Drive Synchronous Generator 40
3.4 Block diagram representation of the Variable Speed 41
xv
Direct Drive EESG
3.5 Block diagram representation of the Variable Speed
Direct Drive PMSG
42
3.6(i) Electrical model of the EESG 44
3.6(ii) Equivalent circuit of PMSG in d-q reference frame 45
3.7 Three-phase Diode bridge Rectifier 46
3.8 DC-DC Boost Converter Circuit 47
3.9(a) Equivalent circuit of the DC-DC converter in the first
operating phase
48
3.9(b) Equivalent circuit of the DC-DC converter in the second
operating phase
49
3.10 Step and search control strategy to track maximum power 50
3.11 Circuit diagram of a IGBT based DC- AC Single phase
Full bridge Converter
52
3.12 PWM signal for a Voltage Source Converter 52
3.13 Current control scheme of a Voltage Source Converter 55
3.14 Adaptive hysteresis current controller concept 57
3.15 Simulation diagram of direct drive EESG 60
3.16 Simulation diagram of Wind Turbine 61
3.17 Simulation diagram of d-q current control scheme of
VSC
61
3.18 Wind speed 63
3.19 Tip speed ratio 63
3.20 Power coefficient 64
3.21 Mechanical speed of VSWT with direct drive EESG 64
3.22 Real power output of VSWT with direct drive EESG 64
3.23 Reactive power generated by VSWT with direct drive
EESG
65
3.24 Generated phase voltage in p.u. of VSWT with direct 65
xvi
drive EESG
3.25 Vdc link of VSWT with direct drive EESG 65
3.26 Phase voltage in p.u in grid side of VSWT with direct
drive EESG
66
3.27 Injected real power in grid side of VSWT with direct
drive EESG
66
3.28 Injected reactive power in grid side of VSWT with EESG 66
3.29 Simulation diagram of direct drive PMSG 69
3.30 Simulation diagram of MPPT control of DC-DC boost
converter
69
3.31 Simulation diagram of reference current generator of
Adaptive hysteresis band current controlled VSC
69
3.32 Simulation diagram of Adaptive hysteresis bandwidth
calculation
69
3.33 Simulation diagram of switching pulses of VSC 71
3.34 Wind speed profile 71
3.35 Coefficient of Performance 72
3.36 Tip speed ratio 72
3.37 (a) Generator phase Voltage at 12m/sec. 73
3.37 (b) Generator phase Current at 12m/sec. 73
3.38 (a) Generator phase Voltage at 14m/sec. 72
3.38 (b) Generator phase Current at 14m/sec. 72
3.39 (a) DC link Voltage at 12m/sec. 73
3.39 (b) DC link Voltage at 12m/sec. (with zooming) 73
3.39 (c) DC link Voltage at 14 m/sec. 75
3.39 (d) DC link Voltage at 14 m/sec. (with zooming) 76
3.40 Grid Voltage 76
3.41 (a) Grid Current 77
3.41 (b) Inverter output phase Current 77
xvii
3.41 (c) Adaptive hysteresis band at 50 A 77
3.41 (d)(i) DC link voltage at 50 A with Adaptive hysteresis band
current controller
77
3. 41
d)(ii)
DC link voltage at 50 A with Adaptive hysteresis band
current controller (with zooming)
78
3.42 (a) Grid Current 78
3.42 (b) Inverter output phase Current 79
3.42 (c) Adaptive hysteresis band at 130 A 79
3.42 (d)(i) DC link voltage at 130 A 79
3.42(d)(ii) DC link voltage at 130 A (with zooming) 79
4.1 Typical PV curve 83
4.2 One line diagram of IEEE 14- bus system 91
4.3 Loading margin with CSGs 93
4.4 Bus-6 voltage variation after the disconnection of line 6-
11
94
4.5(a) Voltage profile of bus-2 under Base case and
Contingency states in p.u.
95
4.5(b) Voltage profile of bus-5 under Base case and
Contingency states in p.u.
96
4.6(a) Reactive power flow from bus-1 to bus-2 under Base
case and Contingency states in p.u.
96
4.6(b) Reactive power flow from bus-1 to bus-5 under base
case and contingency states in p.u.
96
4.7 Profile of loading margin 99
4.8 (a) BUS-6 voltage with SCIGs after the disconnection of line
6-11
100
4.8 (b) BUS-6 voltage with DFIGs after the disconnection of line
6-11
101
xviii
4.8 (c) BUS-6 voltage with EESGs after the disconnection of
line 6-11
101
4.8 (d) BUS-6 voltage with PMSGs after the disconnection of
line 6-11
101
4.9(a) Voltage profile of bus-2 under Base case and
Contingency states in p.u.
103
4.9(b) Voltage profile of bus-5 under Base case and
Contingency states in p.u.
103
4.10(a) Reactive power flow from bus-1 to bus-2 104
4.10(b) Reactive power from bus-1 to bus-5 104
5.1 Typical allowable maximum rotor speed deviation and
oscillation duration
111
5.2 One-line diagram of IEEE 9- bus system 115
5.3(a) Voltage at generator buses with CCT with only CSGs 116
5.3(b) Rotor angle deviation at generator bus-2 and bus-3 with
only CSGs
116
5.3(c)(i) Rotor speed oscillation at generator bus-2 and bus-3 with
only CSGs
117
5.3(c) (ii) Rotor speed oscillation at generator bus-2 and bus-3 with
only CSGs
117
5.3(d) (i) Real power at generator buses with only CSGs 118
5.3(d) (ii) Real power at generator buses with only CSGs 118
5.3(e) Reactive power at generator buses with only CSGs 118
5.4(a) Voltage at generator buses with CCT with SCIGs 119
5.4(b) Rotor angle deviation at generator bus-2 and bus-3 with
SCIGs
120
5.4(c)(i) Rotor speed oscillation at generator bus-2 and bus-3 with
SCIGs
121
5.4(c) (ii) Rotor speed oscillation at generator bus-2 and bus-3 with 122
xix
SCIGs
5.4(d) (i) Real power at generator buses with SCIGs 122
5.4(d) (ii) Real power at generator buses with SCIGs 122
5.4(e) Reactive power at generator buses with SCIGs 123
5.5(a) Voltage at generator buses with CCT with DFIGs 123
5.5(b) Rotor angle deviation at generator bus-2 and bus-3 with
DFIGs
123
5.5(c) (i) Rotor speed oscillation at generator bus-2 and bus-3 with
DFIGs
124
5.5(c) (ii) Rotor speed oscillation at generator bus-2 and bus-3 with
DFIGs
124
5.5(d) (i) Real power at generator buses with DFIGs 125
5.5(d) (ii) Real power at generator buses with DFIGs 125
5.5(e) Reactive power at generator buses with DFIGs 126
5.6(a) Voltage at generator buses with CCT with EESGs 126
5.6(b) Rotor angle deviation at generator bus-2 and bus-3 with
EESGs
127
5.6(c)(i) Rotor speed oscillation at generator bus-2 and bus-3 with
EESGs
127
5.6(c)(ii) Rotor speed oscillation at generator bus-2 and bus-3 with
EESGs
128
5.6(d) (i) Real power at generator buses with EESGs 128
5.6(d) (ii) Real power at generator buses with EESGs 128
5.6(e) Reactive power at generator buses with EESGs 129
5.7(a) Voltage at generator buses with CCT with PMSGs 130
5.7(b) Rotor angle deviation at generator bus-2 and bus-3 with
PMSGs
131
5.7(c)(i) Rotor speed oscillation at generator bus-2 and bus-3 with
PMSGs
131
xx
5.7(c) (ii) Rotor speed oscillation at generator bus-2 and bus-3 with
PMSGs
132
5.7(d) (i) Real power at generator buses with PMSGs 133
5.7(d) (ii) Real power at generator buses with PMSGs 133
5.7(e) Reactive power at generator buses with PMSGs 134
A1.1 Illustration of prediction-correction steps 141
A1.2 Flow chart for Continuation power flow 143
xxi
LIST OF SYMBOLS AND ABBREVATIONS
SYMBOLS
- Coefficient of performance
- Tip speed ratio
- Radius of the wind turbine rotor in m
- Angular velocity of the rotor in rad/sec.
Vω - Wind speed in m/sec.
A - Swept area of wind turbine rotor in m2
- Air density in kg/m3
Pt - Power obtained from wind turbine
- Torque developed by the wind turbine
- Stator voltage
- Rotor voltage
- Stator resistance
- Rotor resistance
- Stator current
- Rotor current
- Magnetizing resistance
- Magnetizing inductance
- Magnetizing resistance current
- Stator leakage inductance
- Rotor leakage inductance
- Stator frequency
- Slip frequency
- Rotor speed
- Slip
- d-axis voltage
xxii
- q-axis voltage
- d-axis current
- q-axis current
- d-axis flux linkage
- q-axis flux linkage
- Angular frequency of rotor
- Amplitude of the flux induced by the permanent magnets of
the rotor in the stator phases
-- Number of pole pairs
- Electromagnetic Torque
, , - Phase voltages
- Amplitude of the phase voltage
- Root-mean-square (RMS) value of the phase Voltage
- DC component of the output voltage
- DC component of the output current
- RMS value of input current
- Output power of the rectifier
- Input power of the rectifier
- Input voltage of the boost converter
- Output voltage of the boost converter
- Duty cycle
- Minimum value for inductance
- Minimum value for capacitance
- Output resistance
- Ripple voltage
- Switching frequency
L - Inductance
C - Capacitance
xxiii
- Current through the inductor
- Electric power generated by synchronous generator
- Generator phase voltage
- Generator phase current
- Induced voltage in the armature
If - Field current
ωe - Electrical angular speed
- DC link voltage
- Desired voltage magnitude
- Desired real power
- Desired reactive power
- Actual real power
- Actual reactive power
- Maximum power
- Maximum coefficient of performance
- Optimal tip speed ratio
- Power factor
- Electrical efficiency of generator and inverter
- Rotational d–q transformation matrix
- Variables on the o-d-q frame
- Variables on the a-b-c frame
- Phase angle of in radian
- d-axis voltage at VSWT terminal
- q-axis voltage at VSWT terminal
- d-axis current at VSWT terminal
- q-axis current at VSWT terminal
P - Instantaneous active power output
Q - Instantaneous reactive power output
xxiv
- Instantaneous VSWT voltage magnitude
- d- axis reference current
- q- axis reference current
- a- axis reference current
- b-axis reference current
- c- axis reference current
- Reference phase angle
- Rotational inverse d–q transformation matrix
- Desired current vector of the VSWT
- Actual current vector of the VSWT
- Error signal vector
- Upper limit of the d-axis reference current
- Upper limit of the q-axis reference current
- Lower limit of the d-axis reference current
- Lower limit of the q-axis reference current
- Reactive power capability limits of the inverter
- Apparent power of inverter
- Real power of inverter
- Error signal of grid connected inverter
- Measured line current of the grid connected inverter
- Reference line current of the grid connected inverter
- Measured line current of phase A
- Grid voltage per phase
- Hysteresis bandwidth
, - Switching intervals
- Slope of command current wave
Modulation frequency.
- Moment of inertia
xxv
- Acceleration power
- Rotor angle
- Input mechanical power
- Output electrical power
xxvi
ABBREVATIONS
ABH - Adaptive Band Hysteresis
AVR - Automatic voltage regulator
CCT - Critical clearing time
CCT - Critical clearing time
CPF - Continuation power flow
CSC - Current source converter
CSG - Conventional synchronous generator
DDSG - Direct drive synchronous generators
DFIG - Doubly fed induction generator
EESG - Electrically excited synchronous generator
FRC - Fully rated converter
FSWT - Fixed-speed wind turbine
GSC - Grid side converter
GUI - Graphical user interface
HAWT - Horizontal axis wind turbine
IG - Induction Generator
LVRT - Low Voltage Ride Through Function
MPPT - Maximum power point tracking
PLL - Phase locked loop
PMSG - Permanent magnet synchronous generator
PSAT - Power system analysis toolbox
PWM - Pulse-width modulation
RSC - Rotor side converter
SCIG - Squirrel cage induction generator
STATCOM - Static synchronous compensator
SVC - Static VAR compensator
TSR - Tip speed ratio
xxvii
UPF - Unity power factor
VSC - Voltage source converter
VSWT - Variable speed wind turbine
WECS - Wind energy conversion system
WPP - Wind power plant
WTG - Wind turbine generator
1
CHAPTER 1
INTRODUCTION
1.1 INTRODUCTION
As a result of increasing environmental concern, more and more
electricity is generated from renewable sources. Renewable energy can
contribute to securing energy supplies and smoothen the transition to a fossil-
free energy. At present renewable energy provides 19% of electricity
generation worldwide.
Wind power is one of the most competitive renewable energy
technologies and, in developed countries with good wind resources, onshore
wind is often competitive with fossil fuel-fired generation. Wind power
generation has experienced a tremendous growth in the past decade, and has
been recognized as an environmental friendly and economically competitive
means of electric power generation.
The size of wind turbines and wind farms are increasing quickly; a
large amount of wind power is integrated into the power system. A huge
penetration of wind energy in a power system may cause important problems
due to the random nature of the wind and the characteristics of the wind
generators. In large wind farms connected to the transmission network
(110 kV – 220 kV) the main technical constraint to take into account is the
power system transient stability that could be lost. Another major technical
issue to be considered is the voltage instability and voltage collapse problem.
The aim of this research is to evaluate the impact of strategically placed
2
WTGs on power system stability with respect to the variation in load and
occurrence of contingencies.
This chapter explains the energy conversion from wind, control of
wind turbine, operating characteristics of wind turbine, types of WTGs, power
electronic converters in WECS and the impact of WTGs on performance of
power system. The objectives of this research work are explained in detail.
Further it also includes in an outline of the dissertation.
1.2 ENERGY CONVERSION FROM WIND
In a wind turbine, the aerodynamic rotor converts the wind power
into mechanical power which in turn is converted into electricity through the
generators. Figure 1.1 shows the schematic diagram of wind turbine.
Figure 1.1 Schematic diagram of Wind Turbine
3
The wind turbines can be classified into horizontal axis and vertical axis wind
turbines. A horizontal axis wind turbine has its blades rotating on an axis
parallel to the ground. A vertical axis wind turbine has its blades rotating on
an axis perpendicular to the ground. The output power of the wind turbine
is given by,
(1.1)
where A is the swept area of wind turbine rotor.
The performance of wind turbine is characterized by the non-
dimensional curve of coefficient of performance , as a function of tip-speed
ratio . as a function of is expressed by equation (1.2) and it is shown in
Figure 1.2.
Figure 1.2 versus characteristic
(1.2)
The tip-speed ratio is given by the expression,
(1.3)
where is the radius of the wind turbine rotor in m, is the angular
velocity of the rotor in rad/sec. and is the velocity of the wind in m/sec. It
can be observed from Figure 1.1 that is maximum when is equal to 7.5. In
4
general,
(1.4)
Combining equations (1.2), (1.3) and (1.4), the expression for
torque developed by the wind turbine is written as
(1.5)
The power extracted from the wind is maximum when the power
coefficient is at its maximum. This occurs at a defined value of the tip
speed ratio (TSR). Hence, for each wind speed; there is an optimum rotor
speed where maximum power is extracted from the wind. Therefore, if the
wind speed is assumed to be constant, the value of depends on the wind
turbine rotor speed. Thus, by controlling the rotor speed, the power output of
the turbine is controlled.
1.3 OPERATING CHARACTERISTICS OF WIND TURBINE
All wind machines share certain operating characteristics, such as
start-up wind speed cut-in, rated and cut-out wind speeds. Figure 1.3 shows a
typical wind turbine power output with steady wind speed.
Figure 1.3 Typical wind turbine power output with steady wind speed
5
Some of the common terminologies associated with the operation
of WTG are defined below.
Start-up wind speed is the wind speed that will turn an unloaded rotor.
Cut-in speed is the minimum wind speed at which the blades will turn
and generate usable power. The cut-in wind speed of most turbines is
around 12 Km/h.
The rated speed is the minimum wind speed at which the wind turbine
will generate its designated rated power.
Cut-out speed is the maximum wind speed that the wind turbines cannot
operate normally.
The theoretical maximum amount of energy in the wind that can be
collected by a wind turbine rotor is approximately 59%. This value is known
as the Betz limit
1.4 CONTROL OF WIND TURBINE
The rotor power is limited by generator rating. At high wind
speeds, the power is regulated by any one of the following controls:
1.4.1 Stall Control
Stall control works by increasing the angle at which the relative
wind strikes the blades called angle of attack, and it reduces the induced drag
associated with lift. Stall control is simple because it can be made to happen
passively (it increases automatically when the winds speed up), but it increases
the cross-section of the blade face-on to the wind, and thus the ordinary drag.
When a fully stalled turbine blade stopped, has the flat side of the blade facing
directly into the wind. Figure 1.4 shows a schematic diagram of stall control.
6
Figure 1.4 Schematic diagram of Stall control
The length, width, profile are designed in such a way that, wind
turbine creates turbulence above rated wind speed.
A fixed speed wind turbine inherently increases its angle of attack
at higher wind speed as the blades speed up. A natural strategy, then, is to
allow the blade to stall when the wind speed increases. This technique was
successfully used on many early horizontal axis wind turbines (HAWTs).
However, on some of these blade sets, it was observed that the degree of blade
pitch tended to increase audible noise levels.
1.4.2 Pitch Control
Pitch angle control is the most common means for adjusting the
aerodynamic torque of the wind turbine when wind speed is above rated
speed. Pitch control is to work at the most efficient operating level or
maximum power output level. This allows a good level of control over the
angle of attack, thus control over the torque. The purpose of this control is to
extend the range of operation of the wind turbine beyond the rated wind speed
upto the cut-off speed. But for this pitch control, the machine should be
stopped as soon as the wind speed reaches the rated wind speed. If the wind
7
turbine is operated beyond the rated wind speed without stall or pitch control,
the turbine will absorb more power from the wind than its capability to
withstand. So, the control limits the power absorbed by the turbine from the
wind to its capacity, even though much higher amount of power is available in
the wind. Since the absorbed power is much less than the available power,
naturally, the efficiency will be less, which means that the will be less or
TSR is either more or less than the optimum. Figure 1.5 shows the
performance characteristics of wind turbine under pitch control (Sachin
Khajuria et al 2012).
Figure 1.5 Performance characteristics of wind turbine under pitch
control
Beyond rated wind speed, optimum power generation or maximum
cannot be expected because the intention of the controller is only to
increase the grid-connected duration in a day, i.e. overall energy per day and
not power at each moment. Figure 1.6 shows the three dimensional view of
group of versus characteristic with pitch angle. (Jianzhong Zhang et al
2008) clearly depicts this concept.
8
Figure 1.6 Three dimensional view of group of versus characteristic
with pitch angle
The pitch angle controller used employs a PI controller. As long as
the wind turbine output power is lower than the rated power of the wind
turbine, the error signal is negative and pitch angle is kept at its optimum
value. But once the wind turbine output power exceeds the rated power
the error signal are positive and the pitch angle changes to a new value, at a
finite rate, thereby reducing the effective area of the blade resulting in the
reduced power output.
.
1.5 TYPES OF WIND TURBINE GENERATORS
WTGs are of two types: fixed and variable speed.
1.5.1 Fixed Speed Wind Turbine Generators
Fixed speed WTGs are squirrel cage induction generators (SCIGs)
with capacitor bank for self-excitation. Figure 1.7 shows the schematic
representation of the fixed speed SCIG with capacitor bank. In fixed speed
WTGs, owing to the different operating speeds of the wind turbine rotor and
the generator, a gearbox is necessary to match these speeds. The generator slip
9
slightly varies with the amount of generated power and is therefore not
entirely constant. However, because these speed variations are in the order of
1 %, this wind turbine type is normally referred to as constant-speed or fixed-
speed.
In fixed speed WTGs, (Camm E H et al 2009), the turbine speed is
fixed (or nearly fixed) to the electrical grid’s frequency, and generates real
power (P) when the turbine shaft rotates faster than the electrical grid
frequency creating a negative slip (positive slip and power is motoring
convention). The fixed speed WTGs only reach peak efficiency at a particular
wind speed. Fixed speed WTGs cannot have an optimal TSR and hence the
efficiency will not be maximized. Power can only be controlled through pitch
angle variations.
Figure 1.7 Schematic representation of the fixed speed wind turbine with
squirrel cage induction generator
1.5. 2 Variable Speed Wind Turbine Generators
Variable speed operation continuously adapt the rotational speed to
the present wind speed, so that, ideally the maximum obtainable power is
produced by the wind energy conversion system (WECS). Variable speed
operation yields 20 to 30 percent more energy than the fixed speed operation,
providing benefits in reducing power fluctuations and improving VAR supply.
10
Variable speed wind turbines are connected to the grid through power
electronic converters and maximize effective turbine speed control.
Variable speed generators are classified according to drive trains as
direct drive and geared drive systems.
1.5.2.1 Geared Drive Doubly Fed Induction Generator
The wind turbines, which use gear ratios bigger than 1, is
categorized as geared drive systems. Wind turbines with doubly fed induction
generator (DFIG) comes under this category. A gearbox, located between the
rotor shaft and the generator shaft, is used for increasing the rotational speed
of the generator input shaft while decreasing the torque. By the help of the
increased rotational speed of the generator input shaft, a small number of poles
is sufficient to obtain the desired frequency as the generator output. Smaller
and cheaper generators can be used in these systems. On the other hand,
because of the gearbox, the complexity of the system is higher than direct
drive systems and these systems are less reliable. Besides, due to the failure in
the gearboxes, the operation and maintenance cost of these systems are higher.
In DFIG, the stator winding of the generator is coupled to the grid,
and the rotor winding to a power electronic converter. Usually a back-to-back
VSC with current control loop is used. In this way, the electrical and
mechanical rotor frequencies are decoupled, because the power electronic
converter compensates the difference between mechanical and electrical
frequency by injecting a rotor current with variable frequency. Figure 1.8
shows the schematic representation of the variable speed wind turbine with
DFIG.
11
Figure 1.8 Schematic representation of the variable speed wind turbine
with doubly fed induction generator
1.5.2.2 Direct drive synchronous generator
In direct drive systems, the gear ratio is equal to one, which means
the rotor of the wind turbine is directly coupled with the generator. A low
speed multi pole synchronous generator with the same rotational speed as the
wind turbine rotor converts the mechanical energy into electricity. The
generator can have a wound rotor or a rotor with permanent magnets. The
stator is not coupled directly to the grid but to a power electronic converter.
This may consist of a back-to-back voltage source converter or a diode
rectifier with a single VSC. The power electronic converter makes it possible
to operate the wind turbine at variable speed.
Figure 1.9 shows the schematic representation of the variable speed
wind turbine with direct drive electrically excited synchronous generator
(EESG).
12
Figure 1.9 Schematic representation of the variable speed wind turbine
with direct drive electrically excited synchronous generator
EESGs are salient pole machines excited from power grid. For low
speed operation, high pole count synchronous generators are recommended.
With EESGs, over excitation is easily possible. So, operation at unity power
factor is utilized to reduce machine side inverter to the real power value. High
pole count increases the field ampere turns which leads to increase in
excitation losses.
PMSGs eliminate the excitation losses which leads to an increase in
efficiency and reduce thermal problems on the rotor side. No brushes and slip
rings are necessary, thus reduces the maintenance costs (Andreas Binder et al
2005).
Figure 1.10 shows the schematic representation of the variable
speed wind turbine with direct drive permanent magnet synchronous
generator.
13
.
Figure 1.10 Schematic representation of the variable speed wind turbine
with direct drive permanent magnet synchronous generator
1.6 POWER ELECTRONIC CONVERTERS IN WIND ENERGY
CONVERSION SYSTEMS
In variable speed drives, the changes in the rotational speed of the
rotor directly affects the rotational speed of the generator input shaft. This
situation gives rise to the variable frequency problem. The frequency of the
grid is stable with a close range of variation at 50 Hz. The frequency of a
generator is determined by the number of poles of the generator and the
rotational speed of the generator input shaft. The variable frequency problem
can be solved by employing power electronic converters between the
generator and the grid. These power electronic converters are simply a rectifier
that converts the alternative current (AC), which has unstable frequency, to
direct current (DC) and an inverter, which converts DC to AC with stable
frequency. Figure 1.11 shows the power electronic converters used in wind
energy conversion systems.
14
Figure 1.11 Power electronic converters in wind energy conversion
systems
Fixed speed WTGs generally have a capacitor bank for self-
excitation.
Power converters such as Static Kramer drive and SCR converter,
Back-to-back pulse width modulation (PWM) converter and matrix converters
are generally used in DFIGs (Jamal A Baroudi et al 2007). An AC/DC/AC
IGBT-based PWM converter is used in this work. It has standard rotor speed
control and voltage control. The grid side converter controls the transfer of
real and reactive power between the grid and the DC link. A constant DC link
is maintained.
Power converters such as thyristor supply-side inverter, hard-
switching supply-side inverter, intermediate DC/DC converter and back-to-
back PWM converters are generally used in direct drive synchronous
generators (DDSGs).
For direct drive EESG, rectifier and voltage source converter
(VSC) circuit with LC harmonic filter combination is used. This diode rectifier
converts ac power generated by the wind generator into dc power in an
uncontrollable way. Current-controlled VSCs can generate an ac current which
follows a desired reference waveform and so can transfer the captured real
power along with controllable reactive power.
15
For direct drive PMSG, diode rectifier, DC-DC boost converter and
VSC circuit are used.
1.7 IMPACT OF WIND TURBINE GENERATORS ON POWER
SYSTEM PERFORMANCE
An important issue when integrating large scale wind farms with
the grid is their impact on the system stability. System stability is largely
associated with power system faults in a network such as tripping of
transmission lines, loss of production capacity (generator unit failure) and
short circuits. These failures disrupt the balance of power (active and reactive)
and change the power flow. Though the capacity of the operating generators
may be adequate, large voltage drops may occur suddenly. The unbalance and
re-distribution of real and reactive power in the network may force the voltage
to vary beyond the boundary of stability. A period of low voltage (brownout)
may occur and possibly be followed by a complete loss of power (blackout).
The faults occurring on the power system faults are cleared by the
relay action of the transmission system either by disconnection or by
disconnection and fast reclosures. In all these situations, the result is a short
period with low or no voltage followed by a period when the voltage returns.
The wind farm nearby will see this event.
In the early days of the development of wind energy, only a few
wind turbines were connected to the grid. In this situation, when a fault
somewhere in the line caused the voltage at the wind turbine to drop, the wind
turbine was simply disconnected from the grid and was reconnected when the
fault was cleared and the voltage returned to normal. Because, the penetration
of wind power in the early days was low, the sudden disconnection of a wind
16
turbine or even a wind farm from the grid did not cause a significant impact on
the stability of the power system.
With the increasing penetration of wind energy, the contribution of
power generated by a wind farm can be significant. If the entire wind farm is
suddenly disconnected at full generation, the system will lose further
production capability. Unless the remaining operating power plants have
enough “spinning reserve”, to replace the loss within very short time, a large
frequency and voltage drop will occur and possibly followed by complete loss
of power. Therefore, the new generation of wind turbines is required to be able
to “ride through” during disturbances and faults to avoid total disconnection
from the grid. In order to keep the system stability, it is necessary to ensure
that the wind turbine restores normal operation in an appropriate way and
within appropriate time. This could have different focuses in different types of
wind turbine technologies, and may include supporting the system voltage
with reactive power compensation devices, such as interface power
electronics, SVC, STATCOM and keeping the generator at appropriate speed
by regulating the power etc.
1.8 ORGANISATION OF THE THESIS
This thesis is organized into six chapters namely; the introduction,
literature review, modeling and simulation of variable speed direct drive
synchronous generators, impact of WTGs on voltage stability of power
system, power system transient stability in the presence of WTGs and
summary of findings and conclusion. The summary of each chapter is given
below:
Chapter 1 explains about the energy conversion from wind, control
of wind turbine with stall and pitch control, operating characteristics of wind
turbine, fixed and variable speed WTGs, power electronic converters in
17
WECSs and impact of WTGs on power system performance. It also presents
the objectives of this research work in detail.
Chapter 2 discusses the summary of literature review undertaken
in modeling of fixed and variable speed WTGs, various converter topologies
for WTGs, control strategies and impact of variable speed WTGs on power
system stability.
Chapter 3 describes the modeling of fixed speed SCIG and
variable speed DFIG, special features of variable speed direct drive
synchronous generators, modeling of direct drive EESG, modeling of direct
drive PMSG, modeling of full-wave diode bridge rectifier, modeling and
control of DC-DC boost converter, modeling of VSC, d-q current control of
VSC, adaptive hysteresis band current control of VSC. This chapter also
discusses the simulation results of modeled variable speed direct drive EESG
and PMSG with modified controllers and presents a summary of results.
Chapter 4 describes the voltage stability analysis using PV curve
and loading margin, voltage stability analysis including fixed speed SCIGs,
variable speed DFIGs, variable speed direct drive EESGs and PMSGs. This
chapter also presents the simulation results related to impact on voltage
stability by computing loading margin, voltage vs. time curve during
contingency and voltage profile and presents a brief summary of results.
Chapter 5 describes the transient stability in power system,
transient stability computation using CCT, rotor angle deviation, rotor speed
oscillation, active power support and reactive power support. This chapter also
presents the simulation results with CSGs alone and with WTGs and presents
a brief summary of results.
18
Chapter 6 summarises the research findings and significant
research contributions. It also presents some area for future research work and
concludes the thesis.
At the end of the thesis, a list of relevant references and appendices
are given.
19
CHAPTER 2
LITERATURE SURVEY
2.1 INTRODUCTION
Wind power is one of the fastest growing electricity generation
sources with 20% annual growth rate for the past 10 years. The vast majority
of wind turbines that are currently installed use one of the three main types of
electromechanical conversion system: Squirrel cage induction generator,
Doubly fed induction generator and Direct drive synchronous generator.
Often, they are directly connected to the transmission grid and will, sooner or
later, replace conventional power plants. Such wind farms will be expected to
meet very high technical requirements, such as to perform frequency and
voltage control, to regulate active and reactive power and to provide quick
responses during transient and dynamic situations in the power system. This
chapter reviews the recent publications in dynamic models of WTGs, power
electronic converters for WTGs and the impact of WTGs on the performance
of power system.
2.2 MODELING OF WIND TURBINE GENERATORS
A wide variety of wind turbine technologies are in use today. A
typical wind turbine employs a blade and hub rotor assembly to extract power
from the wind, a gear train to step up the shaft speed at the slowly spinning
rotor to the higher speeds needed to drive the generator, and an induction
generator as an electromechanical energy conversion device. Induction
machines are popular as generating units due to their asynchronous nature,
since maintaining a constant synchronous speed in order to use a synchronous
generator is difficult due to variable nature of wind speed. Power electronic
20
converters are used to regulate the real and reactive power output of the
turbine.
A wind farm typically consists of a large number of individual
WTGs connected by an internal electrical network. In the near future, wind
turbines may start to influence the behavior of electric power systems by
interacting with conventional synchronous generators (CSGs) and loads. To
study the impact of wind farms on the dynamics of the power system, an
important requirement is to develop appropriate wind farm models to represent
the dynamics of many individual WTGs.
Wind turbine models that can be integrated into power system
simulation software need to be developed. (Slootweg J G et al 2003) presented
a general model of wind speed, rotor and rotor speed controller,
generator/converter, pitch angle controller, voltage controller and protection
system used to represent all types of variable speed wind turbines in power
system dynamic simulations. Also, it has been shown experimentally that in
variable speed wind turbines, the shaft properties are hardly reflected at the
grid connection due to the decoupling effect of the power electronic
converters.
Dynamic models of wind farms with fixed speed WTGs are
presented in various literatures. A typical fixed speed SCIG employs a
capacitor bank arrangement. Some authors have modeled fixed speed SCIGs
with control strategies also. (Mihet-Popa L et al 2004) presented a fixed speed
SCIG model which uses an alternative control strategy, where the rotational
speed is the controlled variable and it is tested during normal operation and
transient grid fault events. (Wei Qiao et al 2007) explained a detailed model
and three reduced order equivalent model of fixed speed SCIG and explained
about how to choose an appropriate wind farm model for power system
dynamic and transient studies.
21
Variable speed DFIGs are generally more complex and expensive than
fixed speed SCIGs. DFIGs have independent active real and reactive power
control. DFIGs have some advantages over full converter machines as well.
DFIGs are to be rated for 30% output power of the generator, thus decreasing
the cost relative to DDSGs.
DFIGs have started to influence the behavior of electrical power
systems. Detailed DFIG models to study the impact of wind turbines on
electrical power system behavior are needed. (Slootweg J G et al 2001)
simulated a DFIG model equipped with rotor speed, pitch angle and terminal
voltage controllers.
Grid codes demand complete models and simulation studies to
avoid the detrimental impact on the network while connecting WTGs.
(Ekanayake J B et al 2003) developed a dynamic model with reduced order
double cage representation for the DFIG and its associated control and
protection circuits which is suitable for inclusion in large power system
transient stability programs. (a) A high proportional gain in the rotor converter
limited the rotor current during the fault to a level below the trip setting of the
crowbar circuit and (b) fast-acting reactive power control (applied through
either converter) improved the stability of the generator. Voltage control using
the rotor side converter is likely to be preferred to using the network side
converter for this task. This is mainly because of the reduction in the converter
rating requirement as reactive power injection through the rotor circuit is
effectively amplified by a factor of 1/slip.
A DFIG model which has the form of traditional generator model
and hence is easy to integrate into the power system is developed by (Yazhou
Lei et al 2006). In this, the power electronic converter is simulated as a
22
controlled voltage source, regulating the rotor current to meet the requirement
of real and reactive power production.
The dynamic behavior of WTGs is quite different from that of
CSGs. It is to be expected, therefore, that the dynamic performance of power
systems may change as traditional generation is replaced by increasing number
of WTGs. Dynamic interactions of the models of converter control, pitch
control and the wind turbine are analyzed by (Ian A Hiskens 2012) and is
governed by interactions between the continuous dynamics of state variables,
and discrete events associated with limits. Switching hysteresis is proposed for
eliminating deadlock situations created by interactions. The dynamic
characteristics of this WTG that are important from the grid perspective are
dominated by the response of controllers that regulate active power, pitch
angle and terminal voltage.
To analyse the dynamic performance and grid impact analysis
capability of VSWT system with an EESG, (Seul-Ki Kim et al 2007) proposed
a model of EESG with fixed-pitch stall regulated wind turbine, diode rectifier
and a six-IGBT VSC with controllable power inverter strategy intended for
capturing the maximum energy from varying wind speeds and maintaining
reactive power generation at a pre-determined level for constant power factor
or voltage regulation.
Direct drive PMSG plays an important role in the modern wind
generating systems. The PMSG model described in (Ming Yin et al 2007)
includes pitch angle control and a drive train. PMSG model was established in
the d-q synchronous rotating reference frame. The pitch angle control in wind
turbine model used wind speeds and electric power output as the input signals
to ensure normal operation in high wind speed. The speed control is realized
through field orientation where the d-axis current is set to zero and the q-axis
23
current is used to control the rotational speed of the generator according to the
variation of wind speed.
An aggregate model reduces the simulation time without
significantly compromising the accuracy of the results in comparison to the
detailed model during transient interaction between a large wind farm and a
power system. (Conroy J et al 2009) modeled an aggregate PMSG wind farm
which employs a braking resistor in the DC circuit to satisfy the latest grid
code requirements. This system is relevant for transient stability studies of
large-scale systems.
(Rolan A et al 2009) modeled the wind speed, wind turbine and
drive train of a variable speed direct drive PMSG. The maximum power point
tracking (MPPT) concept utilized here adjusts the generator rotor speed
according to instantaneous wind speed. (Cultura A B et al 2011) developed a
PMSG model with diode rectifier, boost dc to dc converter and inverter.
A reliable and speedy simulation of the PMSG is significant which
is achieved by (Junfei Chen et al 2012). They replaced the PMSG’s power
electronic device with math equivalence and developed models of windmill,
PMSG and its control, VSC, dc-line, filter and grid. Control includes MPPT,
independent active and reactive power control and variable speed constant
frequency operation.
The control scheme in (Ziping Wu et al 2012) comprised of MPPT
and double PWM active/reactive power independent control strategy. A
DC-link over-voltage protection scheme is also designed. This model
possessed desirable capabilities of operation at the maximum power point as
well as enhanced low voltage ride through (LVRT) function.
24
2.3 CONVERTER TOPOLOGIES FOR WIND TURBINE
GENERATORS
The WTG system requires a power conditioning circuit called
power converter that is capable of adjusting the generator frequency and
voltage to the grid. Several types of converter topologies have been developed
in the last decades; each of them have some advantages and disadvantages.
Most of the proposed converters require line filters and transformers to
improve the power quality and step-up the voltage level, respectively. These
heavy and bulky components significantly increase the tower construction, and
turbine installation and maintenance costs. Recent advances in power
semiconductors and magnetic materials have led to the development of new
topologies of converters, which would be a possible solution to reduce the
size, weight, and cost of power converters.
Several types of converter topologies have been developed in the
last decades. They are: diode rectifier based converter, back to back converter,
matrix converter, Z-source converter, improved Z-source converter,
cycloconverter, and multilevel converter.
(Jamal A Baroudi et al 2007) presented a comprehensive review of
past and present converter topologies applicable to PMSGs, IGs, EESGs and
DFIGs. The different generator–converter combinations are compared on the
basis of topology, cost, efficiency, power consumption and control
complexity.
(Kawale Y M et al 2009) carried out an analysis to test the behavior
of PMSG with different converter topologies. (Jamil M et al 2012) presented a
review of recent and past converter topologies on PMSGs.
25
(Md Rabiul Islam et al 2013) conducted a comprehensive study of
power converter technologies, current research and development.
Mainly two converter topologies are currently used in the
commercial WTG systems. They are: diode rectifier based converter and back
to back converter. In diode rectifier based converter, variable frequency and
variable magnitude AC power from the WTG is converted to a DC power by a
diode rectifier circuit and then converted back to an AC power at different
frequency and voltage level by a controlled inverter. The diode rectifier based
converter system transfers power in a single direction e.g. from generator to
the grid. This type of power converter is normally used in an EESG or a
PMSG based WTG system instead of an induction generator (IG). In EESG
based system, to achieve variable speed operation, the systems use an extra
excitation circuit, which feeds the excitation winding of EESG. The PMSG
based WTG systems are equipped with a step-up chopper circuit. The step-up
chopper adapts the rectifier voltage to the DC-link voltage of the inverter.
Controlling the inductor current in the step-up chopper can control the
generator torque and speed. In this converter system, the grid side converter
(GSC) controls the active and reactive power delivered to the grid.
The back to back converter consists of controlled rectifier and
controlled inverter based converter. The controlled rectifier gives the
bidirectional power flow capability, which is not possible in the diode rectifier
based power conditioning system. Moreover, the controlled rectifier strongly
reduces the input current harmonics and harmonic losses. The grid side
converter enables to control the active and reactive power flow to the grid and
keeps the DC-link voltage constant. The generator side converter works as a
driver, controlling the magnetization demand and the desired rotor speed of
the generator. The decoupling capacitor between GSC and rotor side converter
(RSC) provides independent control capability of the two converters. The back
26
to back converter can be used for PMSG and SCIG based wind power
generation systems.
2.4 CONVERTER CONTROL STRATEGIES
Wind energy, even though abundant, varies continually as wind
speed changes throughout the day. The amount of power output from a WECS
depends upon the accuracy with which the peak power points are tracked by
the MPPT controller of the WECS irrespective of the type of generator used.
2.4.1 MPPT Control
A concise review of MPPT control methods proposed in various
literatures for controlling WECS with various generators have been presented
in (Jogendra Singh Thongam et al 2011).
The maximum power extraction algorithms researched so far can be
classified into three main control methods, namely TSR control, power signal
feedback (PSF) control and hill-climb search (HCS) control.
The TSR control method regulates the rotational speed of the
generator in order to maintain the TSR to an optimum value at which power
extracted is maximum. This method requires both the wind speed and the
turbine speed to be measured or estimated in addition to requiring the
knowledge of optimum TSR of the turbine in order for the system to be able to
extract maximum possible power.
In PSF control, it is required to have the knowledge of the wind
turbine’s maximum power curve, and track this curve through its control
mechanisms. The maximum power curves need to be obtained via simulations
or off-line experiment on individual wind turbines. In this method, reference
power is generated either using a recorded maximum power curve or using the
27
mechanical power equation of the wind turbine where wind speed or the rotor
speed is used as the input.
The HCS control algorithm continuously searches for the peak
power of the wind turbine. It can overcome some of the common problems
normally associated with the other two methods. The tracking algorithm,
depending upon the location of the operating point and relation between the
changes in power and speed, computes the desired optimum signal in order to
drive the system to the point of maximum power.
(Kesraoui M et al 2010) proposed a variable speed PMSG with gear
box, a diode bridge rectifier, a MPPT controlled dc-to-dc boost converter and
a current controlled VSC. The MPPT extracts maximum power from the wind
turbine from cut-in to rated wind velocity by sensing only dc link power. This
MPPT is an advanced HCS control called as step and search control which
senses VDC alone and controls the same. This approach is utilized in this
thesis.
The effectiveness of the WECS can be greatly improved, under grid
fault, by using an appropriate control. (Errami Y et al 2013) proposed a
control strategy which combines MPPT and a pitch control scheme to
maximize the generated power. This control strategy not only captures the
maximum wind energy, but also maintains the frequency and amplitude of the
output voltage.
2.4.2 Control of Voltage Source Converter
The utilization of VSC for the interconnection of WECS to the grid
requires application of control systems capable of regulating the active and
reactive output current, ensuring high power quality levels and achieving high
immunity to grid perturbations.
28
The VSC control ensures that the strict power quality standards
(frequency, power factor, harmonics, flicker, etc) are met. In the case of a grid
fault, the WECS should remain connected; thus they should cope with sudden
and important loads, and even assist the grid in voltage or frequency control.
The increasing requirements for WECS to remain connected and to provide
active grid support have added stringent control objectives for the power
converters.
The hysteresis band current control technique has proven to be
most suitable for all the applications of current controlled VSCs (Murat Kale
et al 2005). The hysteresis band current control is characterized by
unconditioned stability, fast response, and good accuracy. At the same time,
the basic hysteresis technique exhibits several undesirable features; such as
uneven switching frequency that causes acoustic noise and difficulty in
designing input filters. The current control with a fixed hysteresis band has the
disadvantage that the switching frequency varies within a band because peak-
to-peak current ripple is required to be controlled at all points of the
fundamental frequency wave.
Adaptive Band Hysteresis (ABH) control with phase locked loop
(PLL) is based on indirect PQ power control. It is similar to the voltage
oriented control (VOC)-PI control strategy. Hysteresis control is known to
exhibit high dynamic response as this control is to minimize the error in one
sample. As the typical sampling frequencies are in the range of 50-100 kHz,
this means a very high bandwidth. A constant band for the hysteresis
comparator leads to variable switching frequency. An on-line adaptation of the
band can be done in order to keep the switching frequency quasi-constant. The
PLL is used in order to orientate the output of the P and Q controller with grid
angle and for grid monitoring.
29
Even if this strategy is using a PLL for orientation of the reference
currents, it will exhibit improved performances under grid voltage variations
due to the higher bandwidth of the current controller that help in order to keep
the currents under the trip limits.
An adaptive hysteresis band current controller proposed in
(Murat Kale et al 2005) for active power filter changes the hysteresis
bandwidth according to modulation frequency, supply voltage, dc capacitor
voltage and slope of the reference compensator current wave. Hysteresis band
can be modulated as a function of and so that the modulation frequency
remains nearly constant.
(Giraldo E et al 2014) proposed an adaptive control strategy for a
WECS based on PWM- current source converter (CSC) and PMSG. Reactive
power is generated according to the capacity of the converter, the wind
velocity and the load profile. It uses an adaptive PI which is self-tuned based
on a linear approximation of the power system calculated at each sample time.
2.5 IMPACT OF WIND TURBINE GENERATORS ON POWER
SYSTEM STABILITY
With the scenario of wind power constituting up to 20% of the electric
grid capacity in the future, the need for systematic studies of the impact of
WTGs on both voltage stability and transient stability of the grid has
increased.
(Milano F 2002) used a power system analysis (PSAT)/Matlab toolbox
for electric power system analysis and control. PSAT includes power flow,
continuation power flow, optimal power flow, small signal stability analysis
and time domain simulation. All operations can be assessed by means of
30
graphical user interfaces (GUIs) and a simulink-based library provides a user
friendly tool for network design.
The impact of WTGs on the operation of power system stability is
discussed in many literatures. In (Muljadi E et al 2008), voltage stability is
analysed by using (P-V) curves of the system at the point of interconnection
(POI) for the base case as well as for contingencies. Also they analysed the
transient stability with and without the wind power plant (WPP).
Under the condition of sudden short circuit disturbance, (Hosaka N
et al 2008) investigated grid voltage characteristics with IG, PMSG and found
that PMSG gives a better voltage support performance both during and after
the fault.
In (Devaraj D et al 2011), loading margin, voltage collapse and
voltage magnitude are examined for investigating the long term voltage
stability. They examined the system with SCIG, DFIG and DDSG and found
that DDSG has the potential to improve the long term voltage stability of the
grid by injecting reactive power.
Some authors have introduced modified controllers in WTGs and
analysed its performance. (Nayeem Rahmat Ullah et al 2007), (Shu J
et al 2009) and (Rahimi M et al 2010) have introduced modified controllers
with DFIGs. (Nayeem Rahmat Ullah et al 2007) introduced variable power
factor operation in DFIG with P/Q control in VSC and investigated possible
improvements in grid voltage and transient stability by comparing it with
fixed-speed SCIG, variable speed full power converter WTG with standard
control.
(Shu J et al 2009) introduced a controller in a DFIG WECS which
consists of two control loops. In steady state, the main control loop ensures
31
that the wind power generators without wind speed measurement can perform
active power control tasks below the nominal wind speed while the auxiliary
stability control loop restraining the wind power system oscillations by
eliminating the system unbalancing energy during system disturbances. The
control strategy adjusted the power of the DFIG WECS accurately under wind
speed fluctuation and when a disturbance occurs in the system, the strategy is
effective in improving the power system transient stability in different
operating conditions without deteriorating the system voltage stability.
(Rahimi M et al 2010) proposed a nonlinear control scheme applied
to the GSC of DFIGs. It stabilized the internal dynamics and limits the dc-link
voltage fluctuations during the fault. It also introduced a coordinated control
of RSC and GSC to improve the LVRT capability. The proposed ride-through
approaches limit the peak values of rotor current and dc-link voltage at the
instants of occurring and clearing the fault. They also limited the oscillations
of electromagnetic torque, and consequently, improved the DFIG voltage dip
behavior. This system also has a stator damping resistor which is used to limit
the rotor inrush current and to reduce the oscillations and settling time of
DFIG transient response during the voltage dip. Also, the GSC is controlled to
limit the dc-link overvoltage during the voltage drop. It is found that the
dynamics of the GSC and dc-link voltage exhibit non minimum phase
behavior, and thus there is an inherent limitation on the achievable dynamic
response during the fault.
(De Rijcke S et al 2012) proposed voltage control and reactive
power support with DDSGs and revealed that preferred mode for voltage
support during a voltage dip depends on the grid characteristics, short-circuit
power and X-R ratio. Also, it is found that the angle stability of induction
motor loads and nearby CSGs could be improved by adding reactive power
support by these DDSGs.
32
(Londero R et al 2014) presented two control strategies for fully
rated converter (FRC) and DFIG. One control strategy is with GSC at unity
power factor (UPF), which is usually adopted, and the second control strategy
is GSC controlling reactive power. They have considered wind turbine
capability curves and its variable limits, since they are subjected to several
limitations that changes with the operating point and wind speed. They also
considered the dynamic models of over excitation limiter (OEL) and on-load
tap changers (OLTC) combined with static and dynamic loads using time
domain simulations. Different penetration levels of wind generation are
analyzed. It is found that long-term voltage stability could be improved when
GSC of DFIG is controlling reactive power. It is concluded that capability
curve plays an important role in this analysis since reactive power is a key
requirement to maintain voltage stability.
(Revel G et al 2014) exploited the ability of PMSG WECS to
rapidly modify its active and reactive power and provide additional support to
the power grid and enhance the overall stability of the system. Three control
loops are incorporated to achieve supporting tasks such as short-term
frequency regulation, oscillation damping and voltage regulation.
Recent grid codes require the wind farms not only to ride through
the fault disturbances but also support the stability of nearby grid during
severe network disturbances. (Mokui H T et al 2012) proposed various
operational strategies i.e. without reactive power support, considering reactive
power support complying with the Danish grid codes (with and without
considering overloading of the converter currents). Control strategies enabled
the DDSGs to inject the required reactive power in order to help stabilize the
nearby fixed speed SCIGs during faults.
33
The impact of WTG on transient stability is investigated by a
number of authors: (Muyeen S M et al 2007), (Djemai Naimi et al 2008),
(Folly K A et al 2009) and (Nanou S et al 2011).
Transient stability analysis using six-mass, three-mass and two-
mass drive train models have not been reported sufficiently in the literature.
The (Muyeen S M et al 2007) have examined the effects of inertia constant,
spring constant and damping constant on stability using the above mentioned
drive train models and concluded that two-mass shaft model is sufficient for
the transient stability analysis of WTGs.
(Djemai Naimi et al 2008) investigated the angular stability by
using critical clearing time (CCT) by replacing the power generated by fixed
speed SCIG by variable speed DFIG, increasing gradually a rate of wind
power penetration and changing the location of wind resources.
(Folly K A et al 2009) analysed the transient stability by connecting
fixed speed SCIG, variable speed DFIG and DDSG to a power system
network. They analysed the system under two scenarios: CSG without an
automatic voltage regulator (AVR), CSG equipped with an AVR. In the first
case, fixed speed SCIG performed poorly and contributed negatively to the
transient stability of the power system's network as compared to both the
variable speed DFIG and DDSG. In the second case, level of penetration of
the SCIG was increased without losing its stability.
(Nanou S et al 2011) examined DDSG WTG equipped with GSC
control strategy and found that transient stability can be further improved if
the power electronic converters can withstand an additional amount of reactive
current during low voltage conditions. They also found that, if the wind farm
active and reactive power injection is reconfigured in order to satisfy typical
34
present-day grid codes, transient stability margins can be significantly
improved.
2.6 ISSUES IDENTIFIED
Identified that the positive point behind using IGs in WECS is that
it has no synchronization problem with grid. While integrating with grid, it
works as an induction motor with positive slip and draws electrical energy
from grid and after it captures the wind speed and starts rotating more than the
rotating magnetic field of stator ie under negative slip, instead of consuming
electrical energy, it starts delivering the electrical energy to grid. Therefore the
synchronization difficulty of interconnecting direct drive synchronous
generators with grid is completely avoided with IGs.
Identified that the DFIG equipped wind turbine is currently the
most popular one due to its capability of controlling reactive power, high
energy efficiency, and the fact that the converter rating of appropriately 20% -
30% of the total machine power is needed.
Direct drive wind turbine is the second most common WT in the
MW range in the market while the most common is the one based on the
geared drive DFIG WT. However, the direct drive WT will replace the DFIG
in the near future.
Recently, larger systems use EESGs. In comparison to IG, the use
of SG is advantageous since they are self-excited machines and the pole pitch
of the machine can be smaller. From the literature review, it is identified that
the modeling of EESGs has not been reported sufficiently in the literature. In
this work, variable speed direct drive EESG and PMSG with modified
controllers are modeled. Various converter topologies and different control
schemes have been analysed in detail in the literature. At the generator side,
35
diode rectifier is a widely used and accepted option. Both direct drive EESG
and PMSG can utilized this diode rectifier.
The use of MPPT techniques would cost more than a simple lookup
table method. However, higher order control and converter designs increase
efficiency of the overall system. The inclusion of a DC-boost stage helps
reduce the control complexity of the grid inverter with a small increase in cost.
In order to maximize the benefits of the WECS, a compromise between
efficiency and cost must be made. Thus direct drive PMSG model with MPPT
and DC-DC boost converter can be developed.
Adaptive hysteresis band current control is a known technique. But,
majority of the literatures have demonstrated the suitability of adaptive
hysteresis band current control of VSC in active power filters. The adaptive
hysteresis band current control of VSC can be utilized for WECS also to
maintain a constant DC link voltage and hence to improve its capability in
injecting reactive power to enhance the stability of the system.
It is also identified that only a few literatures have compared the
performance of impact of WTGs with CSGs. This work attempts to compare
the performance of different WTG categories such as fixed speed SCIG,
variable speed geared drive DFIG with standard control and variable speed
direct drive EESG and PMSG with the CSGs.
Direct drive WTGs such as EESGs and PMSGs which are less
common in the WT market are focused in the thesis. Both these WTGs are
modeled in detail in this thesis.The objectives of the thesis are:
1. To model and simulate a direct drive EESG with d-q current
controlled VSC.
36
2. To model and simulate a direct drive PMSG with MPPT controller, a
DC-DC boost converter and an adaptive hysteresis band current
controller for VSC to maintain a constant DC link voltage.
3. Investigating the impact of variable speed direct drive EESG and
PMSG with modified controllers, variable speed geared drive DFIG
on voltage stability and transient stability of power system.
2.7 CONCLUSION
This chapter has reviewed the various models proposed in the
literature for fixed speed, variable speed geared drive and direct drive WTGs
suitable for dynamic analysis. The various converter topologies proposed in
the literature for WTGs are also discussed. Further various MPPT control
algorithms, current control algorithms for VSC are also reviewed. The papers
which discuss impact of WTGs on power system voltage stability and
transient stability are also analysed. Finally, various technical issues to be
addressed with respect to modeling and impact analysis are also reported in
this chapter.
37
CHAPTER 3
MODELING AND SIMULATION OF WIND TURBINE
GENERATORS
3.1 INTRODUCTION
In many Countries, there is a tendency towards increasing the
amount of electricity generated from wind turbines. Hence, wind turbines will
start to replace the output of conventional generators. As a result, it may begin
to affect the overall behavior of the power system. Hence the impact of wind
power on the dynamics of power system should be investigated.
This chapter develops mathematical models suitable for analyzing
the impact of variable speed wind turbine (VSWT) on the dynamics of power
systems. The variable speed WTGs commonly used are geared drive DFIG,
direct drive EESG and PMSGs. MATLAB/Simulink is used to simulate the
developed models and the simulation results obtained under different
operating conditions are presented.
3.2 MODELING OF INDUCTION GENERATORS
This section presents the equivalent circuit of fixed speed SCIG
and variable speed DFIG suitable for analyzing the impact of WTG on
stability studies (Andreas Petersson 2005). Figure 3.1 shows the equivalent
circuit of fixed speed SCIG and Figure 3.2 shows the equivalent circuit of
variable speed DFIG.
38
Figure 3.1 Equivalent circuit of fixed speed squirrel cage induction
generator
Figure 3.2 Equivalent circuit of variable speed doubly fed induction
generator
The voltage equations of DFIG as shown in Figure 3 .2 are given by
(3.1)
(3.2)
(3.3)
(3.4)
where, - stator voltage
- rotor voltage ,
- stator resistance
39
- rotor resistance
- stator current
- rotor current
- magnetizing resistance,
- magnetizing inductance
- magnetizing resistance current
- stator leakage inductance
- rotor leakage inductance
-stator frequency
- slip frequency
-rotor speed and
- slip
3.3 VARIABLE SPEED WIND TURBINE WITH DIRECT DRIVE
SYNCHRONOUS GENERATORS
In direct drive synchronous generators, rotor and generator shafts
are mounted to the same shaft without gear-box. The synchronous generator is
designed with more number of poles for low speed operation. Synchronous
generators are suitable for high capacities. Higher speed operation create no
problems other than difficulties in manufacturing of synchronous generators
with large capacities. It can be utilized independently. The output voltage of
the synchronous generator terminals can be regulated. The power factor of the
front and rear phases and the reactive power can be controlled. No impact is
generated during paralleling connection to the network.
It can either be an EESG or a PMSG. For a large DDSG, with a
diameter of several meters, the air-gap should not exceed few millimeters, to
avoid excessive magnetization requirements. Direct drive generator has a large
40
diameter to produce higher torque because the torque is proportional to the
square of air gap diameter.
Absence of gearbox consequently decrease the operation and
maintenance cost. Moreover, direct drive systems are more reliable and
operate for a relatively longer time with fewer problems due to the reduced
complexity. In order to produce electricity at the desired frequency in low
rotational speeds; the pole number of the generators in direct drive systems is
high. Hence, the generators used in these systems are bigger, heavier and more
expensive.
For allowing variable speed operation, the synchronous generator
must be connected to the grid through a frequency converter. Figure 3.3 shows
the principal arrangement of a direct drive synchronous generator.
Figure 3.3 Direct drive synchronous generator
The major components in frequency converters are diode rectifier,
dc link and pulse-width modulated inverter. The generator is connected to an
intermediate DC-circuit by a diode rectifier. The grid-side connection is
realized by a self commutated PWM converter that imposes a pulse-width
modulated voltage to the AC-terminal. The PWM converter is connected to
the network through a filter, symbolized by the L-C circuit. The level of
harmonics in the voltage at the connection point is extremely low.
41
3.3.1 Direct drive EESG
The block diagram representation of the variable speed direct drive
EESG is shown in Figure 3.4.The system includes a fixed-pitch, stall regulated
wind turbine, an EESG and a controllable power electronics system, which
consists of a six-diode rectifier and three phase VSC with d-q current control.
Figure 3.4 Block diagram representation of the Variable Speed Direct
Drive EESG
Taking admissible current loading and air gap flux density of the
machine, the main dimensions of bore diameter and axial stack length are
determined by torque which at low speed is high. As winding temperature rise
at low speed is determined by copper losses, and may be expressed with
current loading and winding current density, for a given torque, the flux
density in air gap is fixed. So exciting ampere turns yield an increase of
excitation losses.
3.3.2 Direct Drive PMSG
The block diagram representation of the variable speed direct drive
PMSG is shown in Figure 3.5.The system consists of a pitchable wind turbine,
a PMSG, a passive rectifier, a MPPT controlled dc-to-dc boost converter and
an adaptive hysteresis band current controlled VSC.
42
Figure 3.5 Block diagram representation of the Variable Speed Direct
Drive PMSG
The high field ampere turns, with more number of poles in EESGs
explains the need to utilize permanent magnets. With increased pole count in
PMSGs, due to lower flux per pole, the danger of demagnetization decreases;
hence smaller magnets and hence reduced costs are possible for high pole
count machines. In a PMSG,
Total magnetic loading = (no. of poles)* (flux/pole)
For a single machine, total magnetic loading is constant. So if number
of poles is increased, flux per pole will get decreased.
PMSG is a salient pole type machine which has larger air gap. High
pole count in PMSG reduces the armature reaction which reduces the
demagnetizing effect.PMSGs have several advantages over EESGs. They are:
Higher power to weight ratio
Improvement in efficiency
High energy and light weight
No additional power supply for the field excitation
Higher reliability without slip rings.
43
PMSGs are still considerably more expensive and require more
advanced rectifiers because they won’t allow for reactive power or voltage
control.PMSGs with light weight and low cost are most suitable for
applications in WECS.
3.4 MODELING OF DIRECT DRIVE SYNCHRONOUS GENERATORS
This section presents the mathematical modeling of direct drive
synchronous generators suitable for analyzing the impact of WTG on stability
studies.
3.4.1 Modeling of EESG
The EESG model takes into account the dynamics of the stator,
field, and damper windings. The equivalent circuit of the model is represented
in the rotor reference frame (q-d frame). All rotor parameters and electrical
quantities are viewed from the stator. They are identified by primed variables.
The subscripts used in model are defined as follows:
d,q: d and q axis quantity
R,s: Rotor and stator quantity
l,m: Leakage and magnetizing inductance
f,k: Field and damper winding quantity
The electrical model of the EESG is shown in Figure 3.6(i) and the
related equations are given below:
44
Figure 3.6(i) Electrical model of the EESG
(3.5)
(3.6)
where, and are the d and q axis voltages, is the stator resistance,
and are the d and q axis currents, and are the d and q axis flux
linkages and is the angular frequency of rotor. This model assumes
currents flowing into the stator windings.
3.4.2 Modeling of PMSG
The mode of operation of PMSG is dictated by the sign of the
mechanical torque (positive for motor mode, negative for generator mode).
The electrical and mechanical parts of the machine are represented by a
separate second-order state-space model.
The sinusoidal model assumes that the flux established by the
permanent magnets in the stator is sinusoidal, which implies that the
electromotive forces are sinusoidal. The equivalent circuit of PMSG is
represented in Figure 3.6 (ii).
45
Figure 3.6(ii) Equivalent circuit of PMSG in d-q reference frame
The equivalent circuit implements the following equations which are
expressed in the rotor reference frame (d-q frame). All quantities in the rotor
reference frame are referred to the stator.
(3.7)
(3.8)
(3.9)
where, is the d-axis inductance, is the q-axis inductance, is the
amplitude of the flux induced by the permanent magnets of the rotor in the
stator phases, p is the number of pole pairs and is the electromagnetic
torque.
46
3.5 MODELING AND CONTROL OF POWER ELECTRONIC
CONVERTERS
3.5.1 Full-wave Diode Bridge Rectifier
The output voltage of synchronous generator is rectified using a
three-phase passive bridge rectifier. This rectifier consists of a three-phase
diode bridge, comprising diodes D1 to D6 which converts ac power generated
by the wind generator into dc power in an uncontrollable way. Figure 3.7
shows the three-phase diode bridge rectifier (Pejovic P 2007).
Figure 3.7 Three-phase diode bridge rectifier
3.5.2 DC-DC Boost Converter
DC-DC boost converter is a most efficient topology which ensures
good efficiency along with low cost. A DC-DC boost converter is connected
next to full-wave diode bridge rectifier to raise the voltage of the diode
rectifier. A capacitor C1 is connected across rectifier to lessen the variation in
the rectified AC output voltage waveform from the bridge. Figure 3.8 shows
the arrangement of the DC-DC boost converter circuit.
47
Figure 3.8 DC-DC Boost converter circuit
The model of the boost converter is needed to simulate and
analyze the behavior. The input and output voltage of the boost converter
under an ideal condition can be related as
(3.10)
is the input voltage, is the output voltage and is duty cycle. Given the
value of D, it is possible to find the minimum values for inductance and
capacitance using the equations given below.
(3.11)
(3.12)
where, is the ripple voltage, is the output resistance and is the
switching frequency.
An important consideration in DC-DC converters is the use of
synchronous switching which replaces the flywheel diode with a power IGBT
with low "On" resistance, thereby reducing switching losses. This is achieved
by using a PWM switched mode control design or PWM. The PWM performs
the control and regulation of the total output voltage.
If the semiconductor device is in the off-state, its current is zero,
and hence, its power dissipation is zero. If the device is in the on-state, the
voltage drop across it will be close to zero, and hence, the dissipated power
48
will be very small. The most common strategy for controlling the power
transmitted to the load is the PWM. A control voltage is compared to a
triangular voltage. The triangular voltage determines the switching frequency.
The switch T is controlled according to the difference of the voltage. The
variation of the voltage across the inductance L and the current through the
capacity depend on the operating mode. The two operating modes are:
a. T state-on and D state-off
During this time period, the equivalent diagram of the circuit is
presented in Figure 3.9(a). In this time period the inductance L stores energy.
Figure 3.9(a) Equivalent circuit of the DC-DC converter in the first
operating mode
During this period, the output voltage and the current through
the inductor satisfies the following equations:
(3.13)
b. T state-off and D state-on
In the moment when the transistor switch in OFF state, the voltage
across the inductor will change the polarity and diode will switch in ON state.
The equivalent diagram of converter during this period is shown in
Figure 3.9(b).
49
Figure 3.9(b) Equivalent circuit of the DC-DC converter in the second
operating mode
During this period, the output voltage and the current through
the inductor satisfy the following equations:
(3.14)
3.5.3 Control of DC-DC Boost Converter
The electric power generated by synchronous generator is given
by (Kesraoui M et al 2010)
(3.15)
where, is the generator voltage and is the generator current.
For an ideal system, equation (1.4) and (3.1) can be equated.
(3.16)
(3.17)
where, is the induced voltage in the armature and is the stator resistance.
Using equations (1.1) to (1.5) and (3.1) to (3.3), is expressed as
(3.18)
where, is the field current, is the electrical angular speed and is the
generator voltage.
Maximum power occurs when
(3.19)
50
The maximum power can be tracked by searching the rectified dc
power, rather than environmental conditions, such as wind speed and
direction. The step and search control strategy for tracking maximum power is
explained below:
The step and search control strategy makes use of the fact that the
generated voltage and VDC depend upon the speed of the turbine. Therefore,
instead of sensing the turbine speed, it senses the VDC and tries to control the
same. The set point for this voltage is not constant. That is because the wind
speed is varying every now and then which causes the optimum turbine speed
to vary frequently. The set point is floating and has to be decided by trial and
error method. The method is called Peak seeking. Figure 3.10 shows the step
and search control strategy to track maximum power.
Figure 3.10 Step and search control strategy to track maximum power
The strategy is to start with any arbitrary set point (A) i.e. reference
dc voltage and check the output dc power. Then give a small increment to the
set point. Again check the output at point B. If the output has increased, give
an additional increment and check the output once again. Incrementing the set
point by small steps should be continued till the stage (H) when the increment
does not yield favorable result. At this stage, a small decrement to the set point
51
should be given. The set point will be moving back and forth around the
optimum value. Thus the power output could be maximized. In this method,
after giving increment to the set point, both the power output as well as the
voltage level has to be checked. Four possibilities arise.
Power increased – voltage increased
Power increased – voltage decreased
Power decreased – voltage increased
Power decreased – voltage decreased
Only when power output and the voltage are increased (case 1) the
set point has to be incremented. If the wind speed changes from one value to
another, the turbine is not being operated at the maximum power point at the
new value. The MPPT controller has to search for the new maximum power
point for the new wind speed.
Thus depending upon the MPPT controller output, dc-dc boost
converter switch operates and maintains a constant VDC link across the
capacitor Co.
MPPT control the output power as well as adjust the electrical
torque, the speed of the generator is indirectly controlled and then it obtains
the optimum speed for driving the power to the maximum point.
3.5.4 Modeling of Voltage Source Converter
Figure 3.11 shows the circuit diagram of a IGBT based dc- ac
single phase full bridge converter. The model of VSC is needed to simulate the
circuit and to analyze its behavior.
52
Figure 3.11 Circuit diagram of a IGBT based DC- AC Single phase Full
bridge Converter
Figure 3.12 PWM signal for a voltage source converter
The DC voltage which is obtained from converter output is given to
the inverter, for converting it to a smooth sinusoidal waveform. An inductor
current flowing through filter and load voltage are considered as state
variables. The state variables with S1 and S3 ON (d interval) and S1 and S3 OFF
(1-d interval) are expressed as:
(3.20)
(3.21)
The basic operation of the dc–ac full-bridge switching converter is
that each pair of switches, S1–S3 and S2–S4, are operated alternately for each
switching period with their duty cycle (d). The duty cycle (d) is the ratio of the
ON time (ton) to the switching period (T), d= ton /TS= ton fs, as shown in
Figure 3.10.
53
3.5.5 Control of Voltage Source Converter
3.5.5 .1 d-q current control
Current-controlled VSCs can generate an ac current which follows
a desired reference (Chen Z et al 2001) waveform and can transfer the
captured real power along with controllable reactive power. d-q current
control method is employed to control the VSC.
Main control targets are the desired real and reactive power,
and to be followed by actual real and reactive power, and .
and can be calculated by using the following equations (3.22), (3.23) &
(3.24).
(3.22)
(3.23)
(3.24)
where, is the electrical efficiency of generator and inverter.
The desired values are specified according to power control
strategy of the VSWT. The strategy is to capture the maximum energy from
varying wind speed while maintaining reactive power generation
(Seul-Ki Kim et al 2007).
Below the rated wind speed, the real power of the VSWT is
regulated to capture the maximum wind energy from varying wind speed. The
maximum power available can be described by (3.23). This simply means that
the maximum power is obtained by varying the turbine speed with wind speed
such that it is on the track of the maximum power curve (Patel M R
1999) and (Muljadi E et al 2001) at all times.
54
Specify the desired real power of the inverter using equation
(3.22). Above the rated wind speed, the maximum power control is overridden
by stall regulation for constant power. In this thesis, the wind blade is assumed
to be ideally stall regulated at rated power so that rotor speed keeps constant at
rated speed under high wind speeds.
Specify the desired reactive power using equation (3.24). The
voltage magnitude of the VSWT terminal is to be kept constant at a specified
level. Therefore, the target for reactive control is the desired voltage
magnitude .
By using equations (3.22), (3.23) and (3.24), once the target values
are determined, d–q transformation control is applied to enable real and
reactive component of ac output power to be separately controlled. The basic
concept of d–q control is as follows: variables in the a–b–c coordinate may be
transformed into those in the d–q coordinate rotating at synchronous speed by
the rotational d–q transformation matrix (Machowski J 1997).
(3.25)
where,
= variables on the o-d-q frame
= variables on the a-b-c frame
= phase angle of in radian
55
In the three-phase balanced system, the instantaneous active and
reactive power outputs, P and Q, of the wind turbine are described by equation
(3.26).
(3.26)
where, , are d- and q-axis voltage at VSWT terminal [V]
Here, is identical to the magnitude of the instantaneous voltage
at the wind generation system and is zero in the rotating d-q coordinates, so
equation (3.26) may be simplified into equations (3.27) and (3.28).
(3.27)
(3.28)
where, is the instantaneous VSWT voltage magnitude. Since the voltage
magnitude remains almost constant as grid ac voltage, the real and reactive
power can be controlled by regulating the q- and d-axis current, and ,
respectively.
Figure 3.13 Current control scheme of a voltage source converter
56
Through appropriate proportional-integral (PI) control gains, errors
between and and between and (or between and
depending on reactive power control mode) in Figure 3.13 are processed into
the q- and d-axis reference current and , respectively, which are
transformed into the a-, b- and c- axis reference current by
the d-q to abc transformation block. The PLL block generates a signal
synchronized in phase to the inverter output voltage to provide the
reference phase angle for the rotational inverse d–q transformation
.When the desired currents on the a-b-c frame are set, a pulse width
modulation (PWM) technique is applied. In the PWM generator block, the
desired current vector and the actual current vector of the VSWT
are compared. The error signal vector is compared with a triangular
waveform vector to create switching signals for the six IGBTs of the VSC.
The upper and lower limits of the q-axis reference current and
are usually set at 1.1 to 1.5 times the VSC’s rated current to protect the system
from excessive heating. The d-axis reference current limits and
may be specified based on (3.27) and (3.28) and reactive power
capability limits of the inverter, (3.29).
(3.29)
The d-q current control strategy is utilized to control the VSC used
in EESG.
3.5.5.2 Adaptive hysteresis band current control
Another commonly used control strategy for VSC is hysteresis
band current control.
57
Hysteresis control is known to exhibit high dynamic response as it
minimizes the error in one sample.The fixed hysteresis band method has the
drawbacks of variable switching frequency, heavy interference, harmonic
content around the switching side band and irregularity of the modulation
pulse position. These drawbacks result in high current ripples and acoustic
noise. To overcome these drawbacks, adaptive hysteresis band current control
technique is used which adjusts the hysteresis bandwidth as a function of the
reference compensator current variation, to optimize the switching frequency
and THD of supply current. Switching frequency varies with respect to the
band size, the inverter and the grid parameters.
The VSC can act both as an inverter and as a rectifier. The VSC
requires a minimum dc link voltage in order to operate, and here a DC-DC
boost converter is introduced to increase the voltage level for the VSC.
Variable voltage and frequency supply is invariably obtained from the three-
phase VSC. Adaptive hysteresis type modulation is used to obtain variable
voltage and constant frequency supply. Adaptive hysteresis current control in
VSC forces the IGBT’s to switch only when it is necessary to keep on tracking
the reference of the current.
Figure 3.14 Adaptive hysteresis band current controller concept
Figure 3.14 illustrates the concept of adaptive hysteresis band
current control. The adaptive hysteresis band current control of three phase
58
grid connected VSC and its working as explained in (Murat Kale et al 2005) is
considered here.
The adaptive hysteresis band current controller adjusts the
hysteresis band width, according to the measured line current of the grid
connected inverter. Let be the reference line current and be the measured
line current of the grid connected inverter. The error signal can be written
as:
(3.30)
When the measured line current Ia of phase A tends to cross the
lower hysteresis band at point 1, then switch S1 is switched ON. When this
touches the upper band at point P, switch S4 is switched ON. The expression
for adaptive hysteresis bandwidth is derived as below.
(3.31)
(3.32)
where, L is the line inductance, is the grid voltage per phase and be the
DC link voltage. From Figure 3.8 we obtain,
(3.33)
(3.34)
(3.35)
where, and are the respective switching intervals and is the
modulation frequency. Simplifying the above equations the hysteresis
bandwidth (HB) is obtained as:
(3.36)
59
where,
is the slope of command current wave. The profile of
and are same as but have phase difference. According to
and
voltage, the hysteresis bandwidth is changed to minimize the influence of
current distortion on modulated waveform. Thus the switching signals for the
VSC are generated by the adaptive hysteresis band current controller. The
VSC used in PMSG is controlled by the adaptive hysteresis band current
control technique.
3.6 SIMULATION RESULTS
3.6 .1 Direct Drive EESG
This section presents the details of the simulation carried out to
demonstrate the effectiveness of the modeling of variable speed direct drive
EESG. Table 3.1 and Table 3.2 provides the parameters of wind turbine and
parameters of the EESG respectively. MATLAB/SIMULINK is used to
simulate the modeled systems. The performance of the WTG modeling has
been examined under two different wind speeds. The comprehensive
simulation results are presented below. Simulation diagrams implemented in
MATLAB/SIMULINK are given below. Figure3.15 represents the simulation
diagram of direct drive EESG, Figure 3.16 represents the simulation diagram
of wind turbine and Figure 3.17 represents the simulation diagram of d-q
current control scheme of VSC.
60
Figure 3.15 Simulation diagram of direct drive EESG
load
grid
Vabc (pu)
qref
Pref
Pmeas
q
Iabc (pu)
wt
pulses
series converter controller
0
1
0
q
Continuous
powerguiGenerator speed (pu)
Pitch angle (deg)
Wind speed (m/s)
Tm (pu)
WIND TURBINE MODEL
1.0
v+-
v+-
v+-
v+-
ABC
+
-
Universal Bridge
A
B
C
abc
n2
Three-phase
Transformer1A
B
C
a
b
c
n2
Three-phase
Transformer
A
B
C
A
B
C
a
b
c
Pm
Vf _
m
A
B
C
ga
ga'
gb
gb'
gc
gc'
+
-
a
b
c
Subsystem4
Signal 1
Signal Builder1
Pmeas
Qmeas
Iabc pu
Vabc pu
wind gen speed
pitch angel
cp
Vdc
Tm
Vf
SCOPES
A B C
In
InitMean
Mean Value
[Pinv]
-T-
[Pmeas]
[cp]
[Vdc]
[wind]
[Vf]
[Tm]
[TSR]
[Qinv]
[wr]
[Tm]
[wind]
[pitch]
[Tm]
[Tm]
[wr]
[wr]
[Vabcs]
[Pinv]
[Qinv]
[Iabcp]
[Iabcp]
[Vabcp]
[Iabc]
[Vabcp]
[Vf]
[cp]
[Vdc]
[Qmeas]
[Pmeas]
[Iabc]
[Vabc]
[wr]
[pitch]
[Vabc] signal magnitude
Fourier
1
v ref
v d
v q
v stab
Vf
Excitation
System
Demux
Vabc_B1
Iabc_B1
wr
Tm
Pitch_angle (deg)
Pmes
Qmes
Cp
TSR
0
A
B
C
a
b
c
A
B
C
a
b
c
A
B
C
a
b
c
V
IPQ
Active & Reactive
Power2
66ohms
<Stator v oltage v q (pu)>
<Stator v oltage v d (pu)>
<Rotor speed wm (pu)>
61
Figure 3.16 Simulation diagram of wind turbine
Figure 3.17 Simulation diagram of d-q current control scheme of VSC
9 m/sec
1/normal speed
Pwind*Pnormal/pelctrical
1
Tm (pu)
u(1)^3
wind_speed^3
1/1
pu->pu
-K-
pu->pu
45 lambda
betacp
cp(lambda,beta)
Product
Product
[cp]
-K-
Avoid division
by zero
Avoid division
by zero
1/9
1/wind_base
1/2
1/cp_nom
Iabc (pu)2
Iabc (pu)1
3
Wind speed
(m/s)
2
Pitch angle (deg)
1
Generator speed (pu)
Pwind_pu
lambda_pu
wind_speed_pu
Pm_pu
1
pulses
dq0
sin_cosabc
dq0_to_abc
Transformation
abc
sin_cosdq0
abc_to_dq0
Transformation.1
V0
Terminator2
Selector
Vd Vq
Product
hypot
Vr
Freq
Sin_Cos
wt
Discrete
Virtual PLL
50 Hz
Uref Pulses
Discrete
PWM Generator
PI
PI
Demux
Demux
Demux
Demux
7
wt
6
Iabc (pu)
5
q
4
Pmeas
3
Pref
2
qref
1
Vabc (pu) Vd Vq inv erter
modulation index
62
Table 3.1 Parameters of wind turbine
Rating 1.5MW
Blade radius 38m
No. of Blades 3
Air density 0.55kg/m3
Rated wind speed 12 m/sec.
Rated speed 2.808 rad/sec.
Cut-in speed 4m/sec.
Cut-out speed 25 m/sec.
Blade pitch angle 00
Stator resistance 0.003 Ω
Stator inductances 0.02µH
Table 3.2 Parameters of electrically excited synchronous generator
Rating 1.75MVA
Rated RMS line to neutral voltage 1.269kV
Rated RMS line current 0.433kA
Number of poles 84
Base angular frequency 171.98rad/sec.
Inertia constant of generator 0.588 sec.
The rating of the inverter is 1.2 MVA and its PWM switching
frequency is 20 kHz. The capacitor value of grid interface rectifier is 6900 µF
and dc link voltage is 3.35 kV. The transformer rating of grid connected side is
2.2 kV/132 kV. The p.u. voltage magnitude of primary of the transformer is
0.99 p.u. The grid voltage is 132 kV.
63
For the variable speed operation of the WECS, a step change in
wind speed is applied in MATLAB, with a step size of 0.5, a wind speed of 12
m/sec. and 11.5 m/sec. is considered in this system is shown in Figure 3.18.
Figure 3.18 Wind speed
A glitch occurred in Figures 3.21 to 3.26 is due to this change in
wind speed.
Figure 3.19 Tip speed ratio
The power coefficient in Figure 3.20 is maintained at the maximum
of 0.44, which indicates that the turbine speed is “well controlled” and
maintained an optimum TSR (Figure 3.19) to capture the maximum energy.
The meaning of the term “well controlled” mentioned above is clearly
explained. With the d-q current control in VSC, the current of converter is
controlled and maintained at the desired value. When the current is controlled,
torque and speed of WTG are controlled in turn. When the mechanical angular
64
speed is controlled, TSR could be maintained at the optimum value. This
could maintain a maximum coefficient of performance.
Figure 3.20 Power coefficient
Figure 3.21 Mechanical speed of VSWT with direct drive EESG
Figure 3.21 shows the turbine angular speed variation in response
to the varying wind speed. The rotor speed has varied smoothly in response to
changes in wind speed, owing to the inertia of the turbine and generator.
Figure 3.22 Real power output of VSWT with direct drive EESG
65
Figure 3.23 Reactive power generated by VSWT with direct drive EESG
Figure 3.22 &3.23 present the real and reactive power of the
VSWT. The real and reactive power has varied smoothly. This is possible due
to the inertia smoothing effect and VSC interface control.
Figure 3.24 Generated phase voltage in p.u. of VSWT with direct drive
EESG
The VSWT voltage variation is given in Figure 3.24 and the
voltage magnitude fluctuated with wind speed.
Figure 3.25 link of VSWT with direct drive EESG
66
Figure 3.25 shows the dc link voltage and it was maintained at a
level 3.35 kV sufficient to meet the ac conversion requirement. The grid
voltage is 132kV.
Figure 3.26 Phase voltage in p.u in grid side of VSWT with direct drive
EESG
To see the performance of the system, additional load was
added. The VSWT with DDSG system has the capability to supply reactive
demand to the power grid and maintained the load voltage at a constant
specified level, as shown in Figure 3.26.
Figure 3.27 Injected real power in grid side of VSWT with direct drive
EESG
Figure 3.28 Injected reactive power in grid side of VSWT with EESG
67
Figure 3.27 shows the simulation waveform of injected real power
1.5 MW and Figure 3.28 shows the injected reactive power 0.25 MVAR in
grid side of VSWT.
3.6.2 Direct Drive PMSG
This section presents the details of the simulation carried out to
demonstrate the effectiveness of the modeling of proposed adaptive hysteresis
controlled VSWT driven PMSG with MPPT. The system consists of a dc –dc
converter which is controlled by MPPT with step and search control strategy
and VSC with adaptive hysteresis band current control technique Simulation
results are taken for two wind speeds 12 and 14 m/sec. and different load
conditions. Table 3.3 shows the parameters of the wind turbine model. Table
3.4 shows the basic parameters used for the direct-drive generator model.
Table 3.5 shows data used for the dc-dc converter of the VSWT. The
comprehensive simulation results are presented below.
Table 3.3 Parameters of Wind Turbine
Rating 1.5MW
Blade radius 38m
No. of Blades 3
Air density 0.55kg/m3
Rated wind speed 12.4 m/sec.
Rated speed 3.07rad/sec.
Cut-in speed 4m/sec.
Cut-out speed 25m/sec.
Blade pitch angle 00 at 12m/sec. and 4/0.7 degree/sec. at
14m/sec.
68
Table 3.4 Parameters of Permanent Magnet Synchronous Generator
Rating 1.75MVA
Rated RMS line to neutral voltage 1.269kV
Rated RMS line current 0.445kA
Number of poles 64
Base angular frequency 171.98rad/sec.
Inertia constant of generator 0.588 sec.
Stator resistance 0.003 Ω
Stator inductances 0.02µH
Table 3.5 Converter parameters
Figures 3.29 -3.33 show the simulation diagram of direct drive
PMSG, MPPT control of DC-DC boost converter, reference current generator
of adaptive hysteresis band current controlled VSC, adaptive hysteresis
bandwidth calculation and switching pulses of VSC respectively.
Low voltage side capacitor C1 5000 μF
High voltage side capacitors 8000 μF
Inductor L 5mH
Switching frequency 20kHz
69
Figure 3.29 Simulation diagram of direct drive PMSG
load
p ref
1
Iabc*
I abc
Vdc
Out1
Iabc*
Out3
ref cur gen
Continuous
powergui
HB
Iabc*
Iabc
pulses
inverter switching pulses
ica
Va
Vdc
HB1
hys band cal
g
A
+
-
dc dc converter
Generator speed (pu)
Pitch angle (deg)
Wind speed (m/s)
Tm (pu)
Tip speed ratio
Wind Turbine1
v+-
Vdc2
Vabc
v+-
Va2
Vabc
Iabc
A
B
C
a
b
c
VIM1
[A2]
V1
g
A
B
C
+
-
Universal Bridge2
A
B
C
+
-
Universal Bridge
invvol
To Workspace3
A
B
C
a
b
c
n2
Three-phase
Transformer
1.75 MVA 2 .2 kV / 130 kV
A
B
C
Vabc
Iabc
A
B
C
a
b
c
Three-Phase
V-I Measurement
Signal 1
Signal Builder1
Scope8
Rate Limiter
R
C
Pulse
mA
B
C
Tm
PMSG
L1
Idc
Iabc1
i+
-
Ia1
[A]
I2
[Id]
[Qmeas]
[Pmeas]
[Iq]
[Vdc]
[wind]
[wr]
[Tm]
[pitch]
[Vs]
[Vs]
-1
Gain
[pitchangle]
[wind]
[pitch][Tm]
[Tm]
[wr]
[wr]
[Iabc]
[Vabc]
c
Diode2
Vabc_B1
Iabc_B1
wr
Tm
Pitch_angle (deg)
Pmes
Qmes
c
A
B
C
a
b
c
Out1
MPPT
PI
PI Controller
6 Iabc
5 Iabc*1
4 Vdc1
3 Va
2 ica
1
Vdc<Rotor speed wm (pu)>
<Stator v oltage v d (pu)>
<Stator v oltage v q (pu)>
<Stator current is_q (A)>
<Stator current is_d (A)>
70
Figure 3.30 Simulation diagram of MPPT control of DC-DC boost
converter
Figure 3.31 Simulation diagram of reference current generator of
Adaptive hysteresis band current controlled VSC
Figure 3.32 Simulation diagram of Adaptive hysteresis bandwidth
calculation
71
Figure 3.33 Simulation diagram of switching pulses of VSC
Figure 3.34 Wind speed profile
3.6.2.1 Effect of pitch control
A wind turbine of 1.5 MW rating has been connected to the
1.75MVA, 2.2kV PMSG. The rating of the inverter is 1.2 MVA.
Figure 3.34 shows the wind speed profile in which at t = 10 sec.,
wind speed is changed from 12 to 14 m/sec. in step.
Since 12.4 m/sec. is the rated wind speed, at 12m/sec., pitch angle
need not be activated. During this period, is obtained as 0.44. At
t=10 sec., as the wind speed is 14m /sec., which is above rated wind speed of
12.4 m/sec. , pitch control is activated. As the wind speed increases, the power
generated by the wind turbine also increases. Once the maximum rating of the
power converter is reached, the pitch angle is increased (directed to feather) to
shed the aerodynamic power.
72
Here the pitch rate is chosen to be 4/0.7 degrees. That is, the pitch
angle can be ramped up at 4 degrees per second and it can be ramped down at
0.7 degrees per second.
Small changes in pitch angle can have a dramatic effect on the
power output. Cp has changed to 0.39 at 14m/sec. as shown in Figure 3.35.
Figure 3.35 Coefficient of Performance
Figure 3.36 shows the variation of tip speed ratio with time. From
figure 3.36, it is observed that the turbine speed is well controlled to maintain
an optimum tip speed ratio of 7 from 0 to 10 sec. at wind speed of 12m/sec.
When wind speed is increased to 14m/sec., the optimum TSR is normally
higher than the value at 12m/sec., but due to pitch control, it is kept at 7 itself.
In general, three bladed wind turbines operate at a TSR of between 6 and 8,
with 7 being the most widely reported value (Muljadi E et al 2001).
Figure 3.36 Tip speed ratio
73
This indicates that the turbine speed is well controlled to maintain
an optimum tip speed ratio to capture maximum energy. It shows that the
MPPT controller is able to track maximum power and keep of the wind
turbine very close to maximum Betz's coefficient of 0.593. It is the maximum
fraction of the power in a wind stream that can be extracted.
3.6.2.2 Results of constant DC link voltage control with MPPT at wind
speeds of 12 m/ sec. and at 14 m/sec.
Simulation results of generator phase voltage and generator phase
current at 12 m/sec. with zooming effect between 0.2 to 0.4 sec. are shown in
Figure 3.37 (a) & Figure 3.37 (b).
Figure 3.37 (a) Generator phase Voltage at 12m/sec.
Figure 3.37 (b) Generator phase current at 12m/sec.
The Figure 3.38 (a) & Figure 3.38 (b) show the generator phase
voltage and generator phase current at 14 m/sec.
74
Figure 3.38 (a) Generator phase Voltage at 14m/sec.
Figure 3.38 (b) Generator phase Current at 14m/sec.
At 12m/sec., the generator rms phase voltage is1.03 kV and
generator rms phase current is 210.49 A. At 14m/sec., the generator rms phase
voltage is 1.27 kV and generator rms phase current is 459.25 A. The power
output at 14m/sec. is higher than at 12 m/sec. So with increase in wind speed,
power output of wind generator also increases.
With MPPT control under both wind speed conditions, the
switching signals to boost converter are controlled in such a way that DC link
voltage across Co is maintained constant which is shown in Figures 3.39(a-d).
Figure 3.39(a) and Figure 3.39(c) show the DC link voltage from t=
0 to 1 sec. at 12 m/sec. and 14 m/sec. respectively. Simulation result of DC
link voltage with zooming effect between 0.2 to 0.4 sec. is shown in Figure.
3.39(b) and Figure 3.39(d). In the WECS with MPPT control proposed in this
75
work, it is possible to maintain a DC link voltage of 4.369 kV under the wind
speeds of 12m/sec. and 14m/sec.
Figure 3.39 (a) DC link Voltage at 12m/sec.
Figure 3.39 (b) DC link Voltage at 12m/sec. (with zooming)
Figure 3.39 (c) DC link Voltage at 14 m/sec.
76
Figure 3.39 (d) DC link Voltage at 14 m/sec. (with zooming)
3.6.2.3 Results of constant DC link voltage control with adaptive
hysteresis band current controller at load currents of 50 A and
130 A
To analyse the dynamic response of adaptive hysteresis current
controller, the grid current is increased from 50 A to 130 A by applying load.
The adaptive hysteresis current controller acts under this condition and made
the load current to track the reference current command at a faster rate and
avoided the grid waveforms getting distorted. Figure 3.38 shows the grid
voltage at the point of common coupling.
Figure 3.40 Grid Voltage
Figures 3.41 (a-d) show the grid rms current of 50A and inverter
output rms phase current, corresponding hysteresis band and DC link voltage
at 50A of grid current.
77
Figure 3.41 (a) Grid Current
Figure 3.41 (b) Inverter output phase Current
Figure 3.41 (c) Adaptive hysteresis band at 50 A
Figure 3.41 (d)(i) DC link voltage at 50 A with Adaptive hysteresis band
current controller
78
Figure 3. 41 (d) (ii) DC link voltage at 50 A with Adaptive hysteresis band
current controller (with zooming)
With adaptive hysteresis current controller, it is possible to
maintain a DC link voltage of 4.369 kV which is the value maintained with
MPPT algorithm in dc-dc converter under variable wind speeds.
Figures 3.42 (a-d) show the grid current of 130 A and inverter
output rms phase current, corresponding hysteresis band and DC link voltage
at 130 A of grid current.
Figure 3.42 (a) Grid Current
Figure 3.42 (b) Inverter output phase Current
79
Figure 3.42 (c) Adaptive hysteresis band at 130 A
As indicated in Figure 3.41 (c) and Figure 3.42 (c), the adaptive
hysteresis band is varied according to the variation in load in order to maintain
the constant switching frequency of operation.
Figure 3.42 (d)(i) DC link Voltage at 130 A
Figure 3.42 (d) ii. DC link Voltage at 130 A (with zooming)
80
3.7 SUMMARY
In electric utilities perspective, grid interface of intermittent
generation sources such as wind turbine has been a challenge because such
interface may lower power quality of power systems. Therefore,
comprehensive impact studies are necessary before adding wind turbines to
real networks. In addition, users or system designers who intend to install or
design wind turbines in networks must ensure that their systems have well
performed while meeting the requirements for grid interface.
This chapter presents models of two direct drive WTGs. First is the
VSWT with EESG and d-q current controlled VSC. Second is the VSWT with
PMSG, MPPT controlled DC-DC converter and adaptive hysteresis band
current controlled VSC. They have been simulated in MATLAB/ Simulink.
By using function and control blocks provided in the MATLAB software,
VSWT is built. Dynamic responses were simulated and analyzed based on the
modeled system.
With d-q current controlled VSC, desired real power and reactive
power are maintained in the EESG. It supplied the necessary reactive demand
during additional load and maintained the terminal voltage magnitude at a
specified level.
The VSWT with PMSG has been simulated with MPPT algorithm.
Simulation results have shown that the proposed set up is effective in tracking
the maximum power. Adaptive hysteresis band current control in VSC is
tested under transient grid currents. Fast dynamic response and constant
switching frequency characteristics of the adaptive hysteresis band current
control maintained the DC link voltage constant.
81
The work illustrated in this chapter may provide a reliable tool for
evaluating the performance of a direct drive variable speed WTGs and to
analyse its impacts on power networks in terms of dynamic behaviors.
82
CHAPTER 4
IMPACT OF WIND TURBINE GENERATORS ON POWER SYSTEM
VOLTAGE STABILITY
4.1 INTRODUCTION
Recently, wind power generation has been experiencing a rapid
development in many Countries. The size of wind turbines and wind farms are
increasing quickly; a large amount of wind power is integrated into the power
system. As the wind power penetration into the grid increases quickly, the
influence of wind turbines on the power quality and voltage stability is
becoming more and more important. Voltage stability is one of the important
aspects in maintaining the security of the power system. This chapter explains
the voltage instability phenomenon in power system and the tools available for
assessing the voltage stability level of the power system. Further, the impact of
wind power on voltage control and voltage stability of power system is also
investigated. Simulation results based on IEEE 14-bus system are also
presented.
4.2 VOLTAGE STABILITY ANALYSIS
Voltage stability is the ability of a power system to maintain steady
acceptable voltages at all buses in the system under normal operating
conditions and after being subjected to a disturbance. Instability occurs in the
form of a progressive fall in voltage in some buses. A possible result of
voltage instability is a loss of load in an area.
The factors contributing to voltage stability are the generator
reactive power limits, load characteristics, the characteristics of the reactive
83
power compensation devices and the action of voltage control devices.
Contingencies such as unexpected line outages in stressed system may often
result in voltage instability which may lead to voltage collapse. Unavailability
of sufficient reactive power sources to maintain normal voltage profiles at
heavily loaded buses are the prime reasons for the voltage instability.
Although the voltage instability is a localized problem, its impact
on the system can be wide spread as it depends on the relationship between
transmitted active power, injected reactive power and receiving end voltage.
The voltage instability in line overload or voltage limit violation in
the contingency state which may lead to partial or total blackout of the
system.If load is supplied by transformers with ULTC, the tap-changer action
try to raise the load voltage. This has lower effective load impedance and due
to that receiving end voltage goes low still further.
4.2.1 PV curve
The relationship between transferred power (P) and the voltage (V)
can be illustrated by the PV curve.
Figure 4.1 Typical PV curve
84
Figure 4.1 shows a typical PV curve. PV curves are used to analyze
the voltage stability. The curve shows how the voltage falls as the demand
increases. At the “knee” of the PV curve, the voltage drops rapidly with an
increase in load demand. Load flow solutions do not converge beyond this
point, which indicates that the system has become unstable. This point is called
the critical point .The critical point of the PV curve defines the maximum
demand that can be served (the ‘Power Limit’) for a particular power factor and
the associated critical voltage. The upper part of the PV curve is considered to
be stable whilst the lower part is considered to be unstable. Consequently
normal operation is restricted to the upper part of the curve alone.
The voltage at the load point is influenced by the power delivered
to the load, the reactance of the line, and the power factor of the load. The
voltage has two solutions; the higher one is the stable solution and the lower
one is the unstable solution. The load at which the two solutions have one
value indicates the steady state voltage collapse point.
4.2.2 Loading Margin
The loading margin is the difference between the present
operating point of the system and knee (critical loading) point of the PV curve.
It represents the additional power that may be transferred to the load that is
located in a node or in a load zone so that power system initially found in a
stable zone moves to the final state that corresponds to the voltage stability
limit (Jan Machowski et al 2008).
Loading margin is usually calculated starting from the current
operating point and assuming small load increments, for which a new load
flow calculation is performed until the nose of the P-V curve is reached. For
load flow calculations, it is necessary to represent the input of active and
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reactive power, P and Q. Wind turbines with induction generators must be
represented with an induction machine, with the active power P set to the
momentary value. Based on the machine impedance, the load flow program
will then calculate the reactive power consumption Q corresponding to the
terminal voltage. Variable speed wind turbines however have reactive power
controllability. Therefore, the most suitable representation is a fixed PQ
representation or if the wind turbine is set to voltage control, a PV
representation.
At the loadability limit, or tip of the nose curve, the system
Jacobian of the power flow equations will become singular as the slope of the
nose curve become infinite. Thus the traditional Newton- Raphson (NR)
method of obtaining the load flow solution will break down. In this case, a
modification of the Newton- Raphson method known as the continuation
power flow method is employed. The continuation power flow method
employs an additional equation and unknown into the basic power flow
equations. The additional equation is chosen specifically to ensure that the
augmented Jacobian is no longer singular at the loadability limit. The
additional unknown is often called the continuation parameter. The
continuation power flow analysis uses iterative predictor and corrective steps.
The details of continuation power flow method are given in Appendix 1.
4.3 POWER SYSTEM VOLTAGE STABILITY IN THE PRESENCE
OF WIND TURBINE GENERATORS
When the penetration of wind generation is high, it is important to keep
WTGs on line as much as possible during grid disturbances as per grid code
requirements. Therefore, there is a significant interest in investigating the
dynamic performance and characteristics of the system under high penetration
86
of wind generation. This section investigates the effects of wind turbines on
power system voltage stability.
In transmission networks and distribution grids, node voltage and
reactive power are correlated and therefore node voltages can be controlled by
adjusting the reactive power generation or consumption of generators. Fixed
speed wind turbines have SCIG that always consume reactive power and
consequently, it is present practice to provide capacitor banks at each wind
turbine. A variable-speed wind turbine with a voltage controller effectively
performs voltage control task. Unfortunately, this does not come for free. The
variable-speed wind turbines require power electronic converters with a rating
that is higher than the rating for operation at unity power factor.
4.3.1 Fixed Speed Wind Turbine with Squirrel cage Induction
Generator
SCIG always consume reactive power. The amount of reactive
power consumption is governed by rotor speed, active power generation and
terminal voltage. SCIG cannot be used for voltage control because the reactive
power exchange with the grid cannot be controlled but is governed by the
above factors. In the case of large wind turbines or wind farms and/or weak
grids, the reactive power consumption may cause severe node voltage drops.
Therefore, the reactive power consumption of the generators is in most cases
compensated by capacitors. By adding compensating capacitors, the impact of
the wind turbine on the node voltage is reduced, but the voltage control
capabilities as such are not enhanced. To enhance the voltage control
capability and hence to improve the voltage stability of the system, power
electronic based reactive power compensation devices like static VAR
compensator (SVC) and static synchronous compensator (STATCOM) have to
be installed at the terminals of the WTG.
87
4.3.2 Variable Speed Wind Turbine with Geared drive Doubly fed
Induction Generator
The reactive power generation of a DFIG can be controlled by the
rotor current. Here, there is no unique relationship between reactive power and
other quantities, such as rotor speed and active power generation. Instead, at a
particular rotor speed and the corresponding active power generation, a widely
varying amount of reactive power can be generated or consumed. The amount
of reactive power is, to a certain extent, affected by rotor speed and active
power generation, as in the case of SCIG even though it does not depend on
these quantities. The reason is that both generator torque and reactive power
generation depend directly on the current that the power electronic converter
feeds into the rotor. The part of the current that generates torque depends on
the torque set point that the rotor speed controller derives from the actual rotor
speed. The current that is needed to generate the desired torque determines, in
turn, the converter capacity that is left to circulate current to generate or
consume reactive power.
Since the DFIG is able to generate or consume reactive power, it
can well contribute to voltage stability enhancement. But, this requires power
electronic converters with a rating that is higher than the rating for operation at
unity power factor.
The converter current rating for reactive power consumption can be
lower than for reactive power generation. The reason is that the generator in
this wind turbine type is grid coupled. The magnetizing current can be drawn
from the grid instead of being provided by the converter. In this mode of
operation, reactive power is consumed and fewer converters current is needed
than for the generation of the same amount of reactive power. Full voltage
control capability requires that reactive power can be both generated and
88
consumed. Therefore, reactive power generation is the determining factor in
sizing the converter when equipping a DFIG based wind turbine with a voltage
controller. The relative increase of converter size is largest in the case of the
DFIG based wind turbine.
4.3.3 Variable Speed Wind Turbine with Direct drive Synchronous
Generator
In WTGs with DDSGs, the reactive power exchange with the grid
is not determined by the properties of the generator but by the characteristics
of the GSC. The generator is fully decoupled from the grid. Therefore, the
reactive power exchange between the generator and the generator side of the
converter as well as between the grid side of the converter and the grid are
decoupled. This means that the power factor of the generator and the power
factor of the grid side of the converter can be controlled independently. As the
generator and the grid are decoupled, the rotor speed hardly affects the grid
interaction. The reactive power is changed by controlling the GSC.
4.3.3.1 Electrically excited synchronous generator
The voltage stability depends on the balance of reactive power
demand and generation in the system. Like a conventional power plant, the
direct drive EESG supplies reactive power to the grid when it is needed,
regulating system voltage and stabilizing weak grids. Each wind turbine
maintains precise torque and pitch regulation, controlling power and speed
during changing wind and grid conditions. With a control system, direct drive
EESG will be able to operate more like a conventional power plant.
Electrically excited synchronous generator has wound rotor with electrical
excitation, and over excitation is easily possible. The operation of the
generator at unity power factor is utilized to reduce machine side inverter
power rating to the real power value.
89
With the ability to supply and regulate reactive and active power to
the grid when it is needed, direct drive EESG is becoming a standard feature
in large wind farms. It provides smooth fast voltage regulation by delivering
controlled reactive power through all operating conditions. WECS with
controlling capability ensures that the reactive power performance of a wind
power plant can meet—and often exceed—the performance of a conventional
(non-wind) power plant. Even when wind turbines are not generating rated
active power, the reactive power control feature can provide reactive power.
The provision of continued voltage support and regulation provides
grid benefits not possible with conventional generation, while mitigating
adverse voltage impacts of wind turbines being off-line due to wind
conditions. This feature can eliminate the need for grid reinforcements
specifically designed for no-wind conditions, and may allow for more
economic commitment of other generating resources that will enhance grid
security by reducing the risk of voltage collapse. With increased pole count,
field ampere turns increase. The number of turns of exciting field winding
yields an increase in excitation losses.
4.3.3.2 Permanent magnet synchronous generator
The excitation losses which occur in direct drive electrically excited
synchronous generator are eliminated here due to the usage of permanent
magnets. This leads to increase in efficiency and reduces the thermal problems
on the rotor side. Thus they are more efficient than CSGs.The design of the
permanent magnet circuit has to take into account the demagnetization limit,
which may be reached by high stator current loading (over load condition )
which causes opposing stator field on rotor trailing magnet edge. With
increased pole count due to lower flux per pole, the danger of demagnetization
decreases, hence smaller magnets and thus results in reduced cost for high
90
pole count machines. Further no brushes and slip rings are necessary, which
reduces maintenance costs.
The main advantages of direct drive PMSG are the full decoupling
between the RSC and GSC. In fact, in case of grid disturbances, the GSC is
controlled so that it can support the voltage recovery by supplying reactive
power and at the same time it ensures the grid stability. No significant
mechanical stress (torque or speed) occurs due to their high dynamic
compared to electrical dynamics (O B K Hasnaoui et al 2006).
The direct drive PMSG is able to ride through the balanced voltage
grid fault by reducing active power and supplying the maximum possible
reactive power to maintain the current constant until clearance of the voltage
fault. Due to decoupling between RSC and GSC, the dynamic behavior of the
generator is slightly affected in presence of grid fault, this disturbance creates
a slight increase in speed of the generator.
4.4 VOLTAGE CONTROLLERS IN WIND TURBINE
GENERATORS
Wind turbines equipped with a voltage controller compensate the
grid voltage drop and keep the voltage at its reference value. The variable-
speed wind turbines with a voltage controller have the capability of controlling
terminal voltage independent of the grid voltage, unless their operating limits
are exceeded. Thus, the voltage magnitude is maintained above 0.95 p.u. The
terminal voltage variation is smooth in the case of variable-speed wind
turbines with voltage control.
It is more expensive to equip a DFIG based wind turbine with a
voltage controller than a direct-drive wind turbine. However, this conclusion is
not necessarily correct. The converter in a direct-drive wind turbine is larger
91
and thus more expensive than in a DFIG based wind turbine. This means that,
although the relative increase in converter cost will be smaller in the case of
the direct-drive wind turbine, the absolute cost increase may be substantially
higher.
This voltage control capability could improve the voltage stability
margin at distribution and transmission levels.
4.5 SIMULATION RESULTS
This section presents the details of the simulation study carried out
on IEEE 14- bus system for analysis of voltage stability using the WTGs.
Figure 4.2 shows the one line diagram of IEEE 14- bus system.
Figure 4.2 One line diagram of IEEE 14- bus system
IEEE 14- bus system consists of 5 generator buses, 11 load buses
and 20 transmission lines. The transmission line parameters of IEEE 14- bus
92
system are given in Appendix 3. For this test system, based on the contingency
analysis conducted at different loading conditions, 3 single line outages 2-3,
5-6, 7-9 were identified as most severe cases.
4.5.1 Voltage Stability with Conventional Synchronous Generators
CSG has inbuilt AVR which could maintain the voltage level
within limit.
PSAT, a MATLAB based open source package is utilized for
system analysis. CPF is used to compute the loading margin. The CPF
algorithm consists of a predictor step which computes a normalized tangent
vector and a corrector step that can be obtained either by means of a local
parameterization or a perpendicular intersection. is the loading parameter,
which is used to vary base case generator and load powers. Table 4.1 shows
the parameter values of conventional synchronous generator.
Table 4.1 Parameters of Conventional Synchronous Generator
Parameters Values
Power, voltage and frequency ratings 1.75 MVA, 2.2kV, 50Hz
Stator resistance Rs and Leakage Reactance Xl 0.01 p.u., 0.1010p.u.
d- axis reactances Xd, X’d, X’’d 1.45 p.u., 0.28 p.u.,0.11 p.u.
d- axis open circuit time constants T’d0 and T’’d0 3.4 s,0.06 s
q- axis reactances Xq, X’q, X’’q 1.42 p.u., 1.07 p.u., 0.11 p.u.
q- axis open circuit time constants T’q0 and T’’q0 2.7 s, 0.321 s
Inertia constants H , damping 0.588 s,2 p.u.
Speed and active power additional signals Kw, Kp 0.0 p.u., 0.0p.u.
Percentage of active and reactive power at bus 1p.u., 1p.u.
d- axis additional circuit leakage time constant Taa 0.0 s
93
4.5.1.1 Computation of loading margin
Loading margin is the difference between operating point of the
system and knee (critical loading) point of the system. Table 4.2 shows the
values of loading margin under base case and contingency states in p.u. and
Figure 4.3 shows the profile of loading margin under base case and
contingency states with only CSGs.
Table 4.2 Loading Margin under Base case and Contingency states in p.u.
Condition Loading margin with CSGs
Base case 1.7118
Line outage 2-3 1.2613
Line outage 5-6 1.2711
Line outage 7-9 1.3569
Figure 4.3 Loading margin with CSGs
From figure 4.3, it is found that, under the contingency states, the
loading margin has reduced much from the base case value.
4.5.1.2 Voltage Vs. Time curve after the contingency
0
0.5
1
1.5
2
Base
case
Line
outage
2-3
Line
outage
5-6
Line
outage
7-9
Load
ing m
argin
in p
.u.
Loading margin with CSGs
Loading margin with
CSGs
94
One high voltage line 6-11 is disconnected to analyze the variation
of voltage with respect to time. The voltage drop in bus-6 is measured and
plotted. Figure 4.4 shows the variation at bus-6 voltage after the disconnection
of line 6-11.
Figure 4.4 Bus-6 voltage variation after the disconnection of line 6-11
After the line disconnection, the bus-6 voltage drops due to the
increasing reactive losses in the line, and due to the reduced line charging.
But, the voltage magnitude at bus 6 is within the acceptable limit
(Vbus 6 < 0.95 p.u.).
4.5.1.3 Voltage profile
The values of voltage magnitude at bus-2 and bus-5 and the
reactive power flow from bus-1 to bus-2 and reactive power flow from bus-1
to bus-5 under base case and contingency states with CSGs are given in
Table 4.3.
95
Table 4.3 Voltage magnitude and Reactive power flows with
Conventional Synchronous Generators
Condition
Bus-2 Bus-5
Voltage
magnitude
with CSGs
Q from bus-1
to bus-2
Voltage
magnitude
with CSGs
Q from bus-
1 to bus-5
Base case 1.045 1.0598 1.0029 1.0721
Line outage 2-3 1.01 -0.38062 1.0029 0.09865
Line outage 5-6 1.02 -0.3996 1.0051 0.08885
Line outage 7-9 1.03 -0.38065 0.99916 0.1158
Figure 4.5 (a) shows the voltage profile of bus-2 under base case
and contingency states in p.u. Figure 4.5(b) shows the voltage profile of bus-5
under base case and contingency states in p.u.
Figure 4.5(a) Voltage profile of bus-2 under Base case and Contingency
states in p.u.
0.99 1
1.01 1.02 1.03 1.04 1.05
Base
case
Line
outage
2-3
Line
outage
5-6
Line
outage
7-9 Volt
age
mag
nit
ude
in p
.u.
Voltage magnitude of bus-2 with CSGs
V magnitude with
CSGs
96
Figure 4.5(b) Voltage profile of bus-5 under Base case and Contingency
states in p.u.
Figure 4.6(a) shows the reactive power flow from bus-1 to bus-2
and Figure 4.6(b) shows the reactive power from bus-1 to bus-5.
Figure 4.6(a) Reactive power flow from bus-1 to bus-2 under Base case
and Contingency states in p.u.
Figure 4.6(b) Reactive power flow from bus-1 to bus-5under base case
and contingency states in p.u.
97
Under base case and under severe contingencies considered,
voltage magnitude is 1 p.u. and above at both bus-2 and bus-5. Negative value
of reactive power from bus-1 to bus-2 shows that bus-1 receives reactive
power from bus-2. Similarly positive value of reactive power from bus-1 to
bus-5 shows that bus-1 delivers reactive power to bus-5.
4.5.2 Voltage Stability with Wind Turbine Generators
The impact of WTGs on voltage stability is analysed by replacing
the CSGs with fixed speed SCIG, variable speed DFIG, EESG and PMSG.
Fixed speed SCIG and variable speed DFIG in MATLAB /PSAT library are
connected at bus-1 of IEEE 14-bus system. Fixed speed SCIG has capacitor
banks. Reactive power absorbed by the SCIGs is compensated by capacitor
banks connected with it. Variable speed DFIG with standard control inbuilt in
MATLAB /PSAT consists of a wound rotor induction generator and an
AC/DC/AC IGBT-based PWM converter. The stator winding is connected
directly to the 50 Hz grid while the rotor is fed at variable frequency through
the AC/DC/AC converter. The DFIG technology allows extracting maximum
energy from the wind for low wind speeds by optimizing the turbine speed,
while minimizing mechanical stresses on the turbine during gusts of wind. It
has standard rotor speed control and voltage control inbuilt in it. The variable
speed operation of DFIG technology allows the current to be controlled. Here,
the torque gets controlled which in turn could optimize the turbine speed.
The modeled controllable power inverter strategy of VSWT with
direct drive EESG and VSWT with direct drive PMSG along with the power
converters implemented in MATLAB/SIMULINK and presented in chapter 3
are converted to MATLAB codings and interconnected with the PSAT. To
facilitate the measurement of reactive power delivered from one bus to
another bus MATLAB/SIMULINK model is converted to MATLAB code.
98
The 360 numbers of fixed speed SCIG, VSWT with DFIG, VSWT with direct
drive EESGs and PMSGs of 1.5 MW are connected at bus-1. The parameter
values of SCIG and DFIG used in the analysis are given in Table 4.4 and
Table 4.5 respectively. The parameters of variable speed EESG and PMSG
presented in Table (3.1 -3.5) of chapter 3 are considered here also.
Table 4.4 Parameters of Fixed Speed SCIG
Parameters Values
Power, voltage and frequency ratings 1.75 MVA, 2.2kV, 50Hz
Stator resistance Rs and Reactance Xs 0.01 p.u., 0.101 p.u.
Rotor resistance Rr and Reactance Xr 0.01 p.u., 0.08 p.u.
Magnetization Reactance Xm 3 p.u.
Inertia constants Hwr Hm and Ks 2.5KWs/KVA, 0.588 KWs/KVA,
0.3 p.u.
Number of poles and gearbox ratio 4 , 1/89
Blade length and number 75m, 3
Table 4.5 Parameters of Variable speed DFIG
Parameters Values
Power, voltage and frequency ratings 1.75 MVA, 2.2kV, 50Hz
Stator resistance Rs and Reactance Xs 0.01 p.u., 0.101p.u.
Rotor resistance Rr and Reactance Xr 0.01 p.u., 0.08p.u.
Magnetization Reactance Xm 3 p.u.
Inertia constants Hm 0.588 KWs/KVA
Pitch control gain and time constant Kp, Tp 10p.u, 3 sec
Voltage control gain Kv 10p.u
Power control time constant Te 0.01 sec.
Number of poles and gearbox ratio 4 , 1/89
Blade length and number 75 m, 3
99
Pmax and Pmin 1p.u., 0p.u.
Qmax. And Qmin +0.7 p.u., -0.7 p.u.
4.5.2.1 Computation of loading margin
The values of loading margin under base case and contingency
states with CSGs and with SCIGs, DFIGs, EESGs and PMSGs connected at
bus-1 are given in Table 4.6. The profile of loading margin under base case
and contingency states is given in Figure 4.7.
Table 4.6 Values of Loading Margin under Base case and Contingency
states in p.u.
Condition With SCIG
at bus-1
With DFIG
at bus-1
With EESG
at bus-1
With PMSG
at bus-1
Base case 1.08 1.3 1.72 1.724
Line outage 2-3 0.905 0.964 1.28 1.28
Line outage 5-6 0.818 0.971 1.29 1.292
Line outage 7-9 0.978 1.030 1.370 1.3711
Figure 4.7 Profile of loading margin
By using the reactive power injection facility of variable speed
WTGs, maximum deliverable power has been increased. In other words, the
100
voltage stability margin has been increased by reactive power injection from
variable speed WTGs.
With fixed speed SCIG which is less capable of injecting reactive
power integrated into the system, loading margin is much lesser. VSWTs
namely DFIGs, direct drive EESGs and PMSGs have much influence in
improving the loading margin. Direct drive EESGs and PMSGs which are
implemented with modified control strategies in VSC have more influence
than DFIGs. Moreover it is found that voltage stability improvement is larger
when the control strategy is modified in a variable speed WTG, rather than
when standard variable speed WTGs are used.
4.5.2.2 Voltage Vs time curve after the contingency
To analyse the performance of the system under contingency, line
6-11 is disconnected and the system is analysed. After the line disconnection,
voltage drops due to increasing reactive losses in the line and the reduction in
reactive power produced by the inherent shunt capacitance in a line. The
voltage drop in bus-6 is measured. Figures 4.8 (a-d) represent the BUS-6
voltage after the disconnection of line 6-11 and the response of system with
SCIGs, DFIG, EESGs, and PMSGs.
Figure 4.8 (a) BUS-6 voltage with SCIGs after the disconnection of line 6-11
101
Figure 4.8 (b) BUS-6 voltage with DFIGs after the disconnection of line 6-11
Figure 4.8 (c) BUS-6 voltage with EESGs after the disconnection of line 6-11
Figure 4.8 (d) BUS-6 voltage with PMSGs after the disconnection of line 6-11
With SCIGs integrated into the power system, the transmission
level voltage (Bus-6) drops further. The voltage at bus 6 is now below the
acceptable limit (Vbus 6 < 0.95 p.u.). The tap-changing action restores the
voltage to some extent but unfortunately has a negative impact on the grid-side
voltage, and initiated a voltage collapse event with SCIGs and DFIGs.
102
A possible voltage collapse event is avoided with variable speed
WTGs equipped with modified power-electronics control. In this case, the
wind turbine system utilizes its reactive-power injection capability to maintain
voltage on the transmission level within the allowable limit (±5% deviation)
after the grid disturbance. Voltage level is restored by the wind farm action,
and part of the load-side voltage is restored, by a few transformer tap
movements. Transmission level voltage reduction, due to this tap movement is
counteracted by subsequent reactive power injection by the wind farm. The drop
in voltage during voltage collapse is compensated by injecting the required
reactive power using the with modified power-electronics control in direct
drive WTGs.
4.5.2.3 Voltage profile
Table 4.7 Values of voltage magnitude and reactive power in p.u.
Condition Bus-2 Bus-5
SCIG DFIG EESG PMSG SCIG DFIG EESG PMSG
Base case
Voltage
magnitude
0.95 0.98 1.05 1.05
Voltage
magnitude
0.94 0.96 1.0032 1.0032
Line outage
2-3 0.6 0.95 1.0140 1.0142 0.6530 0.96 1.004 1.0041
Line outage
5-6 0.65 0.957 1.0230 1.0233 0.654 0.953 1.0069 1.007
Line outage
7-9 0.69 0.967 1.0321 1.0325 0.65 0.948 1.0009 1.001
Base case
Reactive
power
0.963 0.993 1.061 1.061
Reactive
power
1.004 1.026 1.073 1.073
Line outage
2-3 -0.53 -0.36 -0.33 -0.33 0.063 0.093 0.103 0.1031
Line outage
5-6 -0.53 -0.37 -0.34 -0.34 0.0578 0.083 0.109 0.110
Line outage
7-9 -0.5
-
0.356 -0.33 -0.33 0.0752 0.108 0.140 0.141
The values of voltage magnitude at bus-2 and bus-5, reactive
power flow from bus-1 to bus-2 and , reactive power flow from bus-1 to bus-
5 under base case and contingency states with SCIGs, DFIGs, EESGs and
103
PMSGs at bus-1 are given in Table 4.9. Figure 4.9(a) shows the voltage
profile of bus-2 under base case and contingency states in p.u., Figure 4.9(b)
shows the voltage profile of bus-5 under base case and contingency states in
p.u., Figure 4.10(a) shows the reactive power flow from bus-1 to bus-2 and
Figure 4.10(b) shows the reactive power flow from bus-1 to bus-5.
Figure 4.9(a) Voltage profile of bus-2 under Base case and Contingency
states in p.u.
Figure 4.9(b) Voltage profile of bus-5 under Base case and Contingency
states in p.u.
104
Figure 4.10(a) Reactive power flow from bus-1 to bus-2
Figure 4.10(b) Reactive power from bus-1 to bus-5
It is observed from figures 4.9 and 4.10 that variable speed
WTGs have greater influence in providing reactive power compensation.
Under base case, voltage at bus-2 and bus-5 are within acceptable limits
(Vbus5 > 0.95 p.u.). Because the contingencies considered are severe, voltage
magnitude dropped much during line outages. Fixed speed SCIG is incapable
of maintaining the voltage magnitude within acceptable limits. But, variable
speed WTGs supplied the necessary reactive power and maintained the
voltage within acceptable limits. DFIG with standard control of VSC is
inferior in supplying reactive power than the direct drive WTGs with modified
controller for VSC.
105
4.6 SUMMARY
In this chapter, grid-assisting possibility namely voltage stability
support offered by modern variable speed wind turbines with
power-electronics-based converters is investigated. Tests are carried out to
study the loading margin, voltage collapse, voltage magnitude and reactive
power delivered of the system when connected only with CSGs and with fixed
speed and variable speed WTGs.
It was found that fixed speed WTG is incapable of avoiding a
voltage collapse event and dynamic models of variable speed direct drive
WTGs with modified controllers could assist the grid to delay or prevent a
voltage collapse event. In the cases demonstrated in this thesis, instability is
completely avoided with variable speed direct drive WTGs with modified
controllers. The improvement of voltage stability of a system when connected
with these modified power-electronics control is large compared to the system
with only CSGs and standard power electronic controlled variable speed
WTGs.
106
CHAPTER 5
POWER SYSTEM TRANSIENT STABILITY IN THE
PRESENCE OF WIND TURBINE GENERATORS
5.1 INTRODUCTION
The dynamic behavior of a power system is determined mainly
by the generators. Until now, nearly all power has been generated with
conventional synchronous generators. In the literature, the behavior of grid
connected synchronous generator under various circumstances has been
thoroughly studied. Wind turbines use other types of generators such as
SCIG or generators that are grid coupled via power electronic converters.
The interaction of these generator types with the power system is different
from that of a conventional synchronous generator. As a consequence wind
turbines affect the dynamic behavior of the power system in a way that
might be different from synchronous generators.
This chapter discusses how the transient stability is assessed
using rotor angle deviation and CCT. The impact of fixed speed SCIG,
variable speed DFIG, direct drive EESG and PMSG with modified
controllers on power system transient stability is also investigated.
5.2 TRANSIENT STABILITY ANALYSIS
Power system transient stability phenomena are associated with
the operation of synchronous machines in parallel, and become important
with long-distance high power transmissions.
107
Analysis of transient stability of power systems involves
analyzing the dynamic response of the system to large disturbances. There
are sudden disturbances such as sudden change of load, switching
operation, loss of generation and fault. Following such disturbances in
power system, rotor angular differences, rotor speeds, and power transfer
undergo fast changes whose magnitudes are dependent upon the severity of
disturbances. For a large disturbance, changes in angular differences may
be so large as to cause the machine to fall out of step. This type of
instability is known as transient instability. Transient stability is a fast
phenomenon, usually occurring within one second for a generator close to
the cause of disturbance.
Transient stability is the ability of a power system to maintain
synchronous operation of the machines when subjected to large
disturbances. Stability depends on both the initial operating state and the
severity of the disturbance. Generally, the loss of synchronism develops in a
very few seconds after the occurrence of disturbance.
During a fault, electrical power from the nearby generators is
reduced drastically. In some cases, the system may be stable even with
sustained fault; whereas in other cases system will be stable only if the fault
is cleared with sufficient rapidity. Whether the system is stable on the
occurrence of a fault depends not only on the system itself, but also on the
type of fault, location of fault, fault clearing time and the method of fault
clearing.
Transient stability analysis involves some mechanical properties
of the machines in the system. After every disturbance, the machines must
adjust the relative angles of their rotors to meet the condition of the power
transfer involved. The problem is mechanical as well as electrical in nature.
108
The dynamics of the machine, in a classical model can be
represented by the following differential equation:
(5.1)
Here, , , and M are the angle, input mechanical power,
output electrical power and moment of inertia respectively of the machine.
The above equation is called swing equation. Swing equation can be written
for each machine of the system. Solution of swing equation will show how
the rotor angles vary with respect to time following a disturbance. The plot
of is called the swing curve of the machine. Once the swing
curve is plotted, the stability of the system can be assessed.
Swing curve provide information regarding the stability of the
system. They show any tendency of to oscillate and/or increase beyond
the point of return. If increases continuously with time, the system is
unstable. Whereas, if starts decreasing after reaching a maximum value it
is inferred that the system will remain stable.
5.3 TRANSIENT STABILITY ASSESSMENT
Transient stability assessment (TSA) is part of dynamic security
assessment of power systems which involves the evaluation of the ability of
a power system to maintain synchronism under severe but credible
contingencies.
For transient stability assessment of large power systems,
time-domain simulation is done. In time-domain simulation, two
approaches are available, i.e., backward Euler and trapezoidal rule, which
are implicit-stable algorithms and solve together called simultaneous
implicit (SI) method. This method is numerically more stable than the
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partitioned explicit method, which solves differential and algebraic
equations separately is given in Appendix 2.
In transient stability studies, calculation of critical fault clearing
time and computation of rotor angle deviation are used for assessing the
performance of the power system.
5.3.1 Critical Clearing Time
Generating units may lose synchronism with the power system
following a large disturbance and be disconnected by their own protection
systems if a fault persists on the power system beyond a critical period. The
CCT is the maximum time interval by which the fault must be cleared in
order to preserve the system stability. The critical period will depend on
number of factors:
The nature of the fault (e.g. a solid three phase bus fault or a line
to ground fault midway on a transmission circuit);
The location of the fault with respect to the generation; and;
The capability and characteristics of the generating unit.
The calculation of the critical clearing time for a generating unit
for a particular fault is determined by carrying out a set of simulations in
time domain in which the fault is allowed to persist on the power system for
increasing amounts of time before being removed.
5.3.2 Rotor angle deviation
Transient stability mainly depends on the balance between real
power generation and demand. The rotor angle of a generator depends on
the balance between the electromagnetic torque due to the generator
electrical power output and mechanical torque due to the input mechanical
power through a prime mover. Remaining in synchronism means that all the
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generators electromagnetic torque is exactly balanced by the mechanical
torque. If in some generator the balance between electromagnetic and
mechanical torque is disturbed, due to disturbances in the system, then this
will lead to oscillations in the rotor angle.
Beyond certain point, the increase in the angular separation will
result in decrease of power transfer. This increases the
angular separation further and also may lead to instability
and synchronous generators fall out of synchronism. Hence, the transient
stability can be assessed by assuming the rotor angle deviation following a
fault.
5.3.3 Rotor speed oscillation
Rotor speed oscillation can also be utilized to assess the system
stability under various operating conditions. The following indicators are
used to quantify the rotor speed oscillations of the large generators:
Maximum rotor speed deviation, and
Oscillation duration
The maximum rotor speed deviation is defined as the maximum
rotor speed value achieved during the transient phenomenon. The
oscillation duration is defined as the time interval between the application
of the fault and the moment after which the rotor speed stays within a
bandwidth of 10-4
p.u. during a time interval longer than 2.5 seconds.
Figure 5.1 shows the typical allowable maximum rotor speed deviation and
oscillation duration.
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Figure 5.1 Typical allowable maximum Rotor speed deviation and
oscillation duration
5.4 TRANSIENT STABILITY IN THE PRESENCE OF WIND
TURBINE GENERATORS
Wind turbines use squirrel cage induction generators or
generators that are grid coupled via power electronic converters. These
generator types interact with the power system differently. The impact of
the generators on the transient stability of power system is investigated in
this section.
5.4.1 Fixed Speed Wind Turbine Generators
Fixed speed wind turbines use a directly grid coupled squirrel
cage induction generator to convert mechanical energy into electrical
power. Owing to the different operating speeds of the wind turbine rotor
and generator, a gearbox is connected to match the speeds.
In fixed speed SCIG, the terminal voltage drops after the
occurrence of a fault. Because of this only a small amount of electrical
power can be fed into the grid, as the generated electrical power is
proportional to the terminal voltage. However, the wind continues to supply
mechanical power. Due to the imbalance between supplied mechanical
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power and generated electrical power, the generator speeds up. Once the
fault is cleared, the SCIG draws large amount of reactive power from the
grid because of its high rotational speed. Because of this reactive power
consumption, it can happen that terminal voltage recovers quickly.
5.4.2 Variable Speed Wind Turbine Generators
The dynamic behavior of variable-speed wind turbines is
fundamentally different from that of fixed-speed wind turbines. Variable-
speed wind turbines use a power electronic converter to decouple
mechanical frequency and electrical grid frequency. This decoupling takes
place not only during normal operation but also during and after
disturbances.
In contrast to the case for directly grid coupled generators, for
variable speed wind turbines there are various degrees of freedom to switch
then ease to normal operation after the fault clearance. They are not
governed by the intrinsic behavior of the generator. It would be possible to
generate extra reactive power when the voltage starts to increase again in
order to accelerate voltage restoration.
5.4.2.1 Geared drive Wind Turbine Generators
The reactive-power capability of DFIG presents similarities to
the CSG capability. It depends on the active-power generated, the slip and
the limitations due to stator and rotor maximum-currents as well as the
maximum rotor voltage.
The asynchronous active power flows can aid in maintaining the
rotor angle stability of the system. However, the manner in which wind
generation injects reactive power into the system can be critical in
maintaining angular stability of the synchronous units. Utilizing wind
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generation to control voltage and reactive power in the system can ease the
reactive power burden on synchronous generators, and minimize angular
separation in the system following a contingency event and can provide a
significant level of support which will become increasingly important in
future power systems.
The implementation of appropriate control strategies in DFIGs,
particularly the implementation of terminal voltage control, can lessen the
reactive power requirements of CSGs and help mitigate large rotor angle
swings and aid conventional generation in damping the oscillatory signal
following a loss of generation event.
5.4.2.2 Direct drive wind turbine generators
With full decoupling capability between the converters of direct-
drive structure, in case of grid disturbance, the GSC is controlled so that it
can support the voltage recovery by supplying necessary reactive power to
maintain the transient stability.
During a severe contingency, the rotor angle between the
machines increases rapidly and may fall out of synchronism. DDSG with
controllers could support the voltage by injecting reactive power on the line
when the voltage is lower than the reference voltage. By increasing the
VAR output to the required value after fault clearing, the transient stability
can be enhanced.
However, the transient stability can be enhanced further by
temporarily increasing the voltage above the regulation reference for the
duration of the first acceleration period of the machine. The voltage
increased above its nominal value will increase the electric power
transmitted and thus will increase also the deceleration of the machine.
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The decoupling of mechanical rotor frequency and electrical grid
frequency in variable speed wind turbines also affects the response of
variable-speed wind turbines to changes in grid frequency. If the grid
frequency changes because of a mismatch between generation and load, the
mechanical frequency of a variable-speed wind turbine does not change.
Thus, no energy is stored in or withdrawn from the rotating mass and drawn
from or supplied to the system. The controllers of the power electronic
converters in variable speed system compensate changes in grid frequency,
and the mechanical rotor frequency is not affected. Using power electronic
control, the reactive current injected is controlled so as to obtain 1 p.u. rated
grid voltage.
5.5 SIMULATION RESULTS
This section presents the details of the simulation study carried
out on IEEE 9-bus system for analysis of transient stability using the
WTGs. Figure 5.2 shows the one-line diagram of IEEE 9-bus test system.
IEEE 9- bus system consists of 3 generator buses, 3 load buses, 3
transformers and 6 transmission lines. First the transient stability of the
system is analyzed with the CSGs alone. Next, wind power plant (WPP)
having 57 numbers of WTGs of capacity 1.75 MVA, 2.2kV, 50Hz is
connected at bus-1. The fixed speed SCIG and variable speed DFIG in
MATLAB /PSAT library are connected at bus-1 of IEEE 9-bus system.
The direct drive EESG and direct drive PMSG implemented in
MATLAB/SIMULINK and presented in chapter 3 are converted to
MATLAB coding and interconnected with the PSAT.
Parameters of CSG, fixed speed SCIG and variable speed DFIG
given in Table 4.1, Table 4.5 and Table 4.6 are also considered in transient
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stability analysis also. The stability analysis is done with line fault near bus
7 initiated at t=1 sec. in IEEE 9-bus test system.
Figure 5.2 One-line diagram of IEEE 9 bus system
5.5.1 Transient stability with CSGs alone
First, the system stability is analyzed with CSGs alone without
connecting any WTG. CSG has inbuilt Automatic voltage regulator (AVR)
which could maintain the voltage level within limit. A CSG has an inherent
tendency to remain in synchronism with the power system on which it
operates, due to the presence of synchronizing power. Since it has a
constant mechanical input power, if the rotor accelerates due to some
disturbance the load angle increases, resulting in an increase in electrical
power output. The extra output power is derived from the stored kinetic
energy of the rotor; consequently the rotor slows down as the rotor
mechanical energy is being extracted, and the generator will return to
synchronous operation.
Figures 5.3 (a-e) show the simulation results of transient stability
with CSG only. Simulation is carried out from 0 to 10 sec. time period.
Figure 5.3(a) shows the voltage at generator buses along with the CCT
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value. The CCT in this case is calculated as 0.250 sec. (12.5 cycles). With
AVR in CSGs, the magnitude of the rotor oscillations, subsequent to the
first swing after the fault, was reduced. Furthermore, the AVR helped to
return the terminal voltage of the CSG to its pre-fault level after the grid
fault.
Figure 5.3 (a) Voltage at generator buses with CCT with only CSGs
Figure 5.3(b) shows the rotor angle deviation at bus-2 and bus-3.
Figure 5.3(b) Rotor angle deviation at generator bus-2 and bus-3 with
only CSGs
From Figure 5.3(b), it is found that rotor angle swing, after
disturbance has reached a maximum of 900 and settled around 87
0 with
CSGs.
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Figure 5.3(c) shows the rotor speed oscillations at bus-2 and bus-
3 with only CSGs.
Figure 5.3(c)(i) Rotor speed oscillation at generator bus-2 and bus-3
with only CSGs
From Figure 5.3(c) (i), it is found that rotor speed oscillation
varies between 0.995 p.u. and 1.025 p.u. and the bandwidth is 0.03 p.u. To
analyze the rotor speed oscillation duration, simulation is done upto 30 sec.
time period and the response is shown in Figure 5.3(c) (ii). From the graph
it is found that, the rotor oscillation settled at 23 sec. and the duration of
oscillation is 22 sec.
Figure 5.3(c) (ii) Rotor speed oscillation at generator bus-2 and bus-3
with only CSGs
Figures 5.3(d) (i) & (ii) show the real power generation from all
the three generators.
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Figure 5.3(d)(i) Real power at generator buses with only
CSGs
Since the real power of generators get not settled down upto 10
sec. time period, to note down the settling of real power, simulation is done
upto 30 sec. time period and the response is shown in Figure 5.3(d)(ii).
Figure 5.3(d) (ii) Real power at generator buses with only CSGs
From Figures 5.3(d)(i) & (ii), it is observed that real power from
one generator bus before disturbance is at 1.2p.u. and after fault clearance
real power settled at 1.2 p.u. Real power from other two generators is 0.69
p.u. and after fault clearance real power settled at 0.69 p.u.
Figure 5.3(e) shows the reactive power at all generator buses.
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Figure 5.3(e) Reactive power at generator buses with only CSGs
From Figure 5.3(e), it is observed that one generator is with
positive reactive power ie above zero p.u. which shows that it supplied
reactive power and two generators are below zero p.u. which shows, they
consumed reactive power from other generators.
5.5.2 Impact of WTGs on transient stability
Next, the transient stability of the system was analysed with
WTG. Fixed speed SCIG, variable speed DFIG with standard control in
PSAT library and the variable speed direct drive EESG and PMSG with
modified controllers modeled and simulated in chapter 3 are connected at
bus-1 of IEEE 9- bus system. As in the previous case a line fault was
simulated near bus 7 at t= 1 sec. The voltage at all generator buses, CCT,
rotor angle deviation, rotor speed oscillations, active and reactive power
support are measured and plotted and the results are presented in the
following sections.
5.5.2.1 Impact of SCIGs on transient stability
Here the CSGs at Bus-1 of IEEE 9-bus system is replaced with
standard SCIGs and the voltage at generator buses along with CCT is
measured. Figures 5.4(a-e) represent the voltage at generator buses along
with CCT, rotor angle deviation, rotor speed oscillations, active and
reactive power support with SCIGs.
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Figures 5.4(a) (i) shows the voltage at generator buses along
with CCT values in the presence of SCIGs.
Figure 5.4(a) Voltage at generator buses with CCT with SCIGs
The CCT in this case is 0.11 sec.(5.5 cycles). When compared
with the system with only CSGs, CCT has decreased when SCIGs are
connected at bus-1. It can also be noted that, with SCIGs, the voltage
dropped during disturbance and remains at 0.73 p.u.
The rotor angle deviation at generator bus-2 and bus-3 are also
analyzed. with SCIGs connected at generator bus-1. Figure 5.4(b) shows the
rotor angle deviation at generator bus-2 and bus-3 in the presence of SCIGs.
Figure 5.4(b) Rotor angle deviation at generator bus-2 and bus-3 with
SCIGs
From Figure 5.4(b), it is found that rotor angle swing after
disturbance is indefinite with SCIGs which shows the transient instability in
the system.
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Figures 5.4(c) (i) & (ii) show the rotor speed oscillation at
generator bus-2 and bus-3 with SCIGs.
Figure 5.4(c) (i)Rotor speed oscillation at generator bus-2 and bus-3
with SCIGs
Figure 5.4(c) (ii) Rotor speed oscillation at generator bus-2 and bus
with SCIGs
From Figure 5.4(c) (i), it is found that rotor speed oscillation
varies from 0.985 p.u. to 1.03 p.u. and its bandwidth is 0.045 p.u. Also from
Figure 5.4(a) (ii), it is found that, rotor speed oscillation has not settled
even upto 30 sec.
Actually, IGs have no provision of providing damper windings
and therefore rotor oscillations exist for more period compared to
synchronous generators.
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The real power at generator buses with SCIGs was also analysed.
Figure 5.4(d) (i) & (ii) show the real power at generator buses with SCIGs.
Figure 5.4(d) (i) Real power at generator buses with SCIGs
Figure 5.4(d) (i) Real power at generator buses with SCIGs
From Figures 5.4(d) (i) & (ii), it is observed that, before
disturbance real power is 0.85 p .u. and after fault clearance it reaches a
value of 0.72 p.u. Active power production from all turbines has reduced
due to the reduction of their corresponding bus voltages.
Figure 5.4(e) shows the reactive power at generator buses with SCIGs.
Figure 5.4(e) Reactive power at generator buses with SCIGs
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From Figure 5.4(e), it is observed that, it has no reactive power
injection capability.
5.5.2.2 Impact of DFIGs on transient stability
Here the CSGs at Bus-1 of IEEE 9-bus system is replaced with
standard DFIGs and the voltage at generator buses along with CCT is
measured. Figures 5.5(a-e) show the voltage at generator buses along with
CCT, rotor angle deviation, rotor speed oscillations, active and reactive
power support with DFIGs.
Figures 5.5(a) shows the voltage at generator buses along with
CCT values in the presence of DFIGs.
Figure 5.5(a) Voltage at generator buses with CCT with DFIGs
As indicated in Figures 5.5(a), the value of CCT in this case is
0.225 sec.(11.25 cycles). When compared with the system with only CSGs,
CCT has decreased in this case. It can also be noted that, with DFIGs, the
voltage dropped during disturbance but regained its value at 0.96 p. u.
The rotor angle deviation at generator bus-2 and bus-3 are also
analyzed with DFIGs connected at generator bus-1. Figure 5.5(b) shows the
rotor angle deviation at generator bus-2 and bus-3 in the presence of
DFIGs.
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Figure 5.5(b) Rotor angle deviation at generator bus-2 and bus-3 with
DFIGs
From Figure 5.5(b), it is found that rotor angle swing after
disturbance reached a maximum of 950 and settled around 85
0.
Figures 5.5(c) (i) & (ii) show the rotor speed oscillation at
generator bus-2 and bus-3 with DFIGs.
Figure 5.5(c)(i) Rotor speed oscillation at generator bus-2 and bus-3
with DFIGs
Figure 5.5(c) (ii) Rotor speed oscillation at generator bus-2 and bus-3
with DFIGs
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From Figure 5.5(c) (i), it is found that rotor speed oscillation
varies from 0.985 p.u. to 1.015 p.u. and its bandwidth is 0.035 p.u. Also
from Figure 5.5(a) (ii), it is found that, rotor speed oscillation duration is
24 sec.
The real power at generator buses with DFIGs is also analyzed.
Figures 5.5(d) (i) & (ii) show the real power at generator buses with
DFIGs.
Figure 5.5(d)(i) Real power at generator buses with DFIGs
Figure 5.5(d) (ii) Real power at generator buses with DFIGs
From Figures 5.5(d) (i) & (ii), it is observed that, before
disturbance real power from one generator is 1 p .u. and after fault
clearance it remained at 1 p.u. Real power from other two generators
remained at 0.69p.u. due to the reduction in the corresponding bus voltages.
Figure 5.5(e) shows the reactive power at generator buses with
DFIGs. From Figure 5.4(e), it is observed that, one generator bus with
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reactive power and two generators are with negative reactive power which
shows they consumed reactive power from the other generators.
Figure 5.5(e) Reactive power at generator buses with DFIGs
5.5.2.3 Impact of EESGs on transient stability
The CSGs at Bus-1 of IEEE 9-bus system is replaced with
EESGs in this case and the voltage at generator buses along with CCT is
measured. Figures 5.6(a-e) show the voltage at generator buses along with
CCT, rotor angle deviation, rotor speed oscillations, active and reactive
power support in the presence of EESGs.
Figure 5.6(a) shows the voltage at generator buses along with CCT
values in the presence of EESGs.
Figure 5.6(a) Voltage at generator buses with CCT with EESGs
The CCT in this case is 0.255 sec.(12.75 cycles).When compared
to the system with only CSGs, CCT has increased when EESGs are
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connected at bus-1. It can also be noted that, with EESGs, the voltage has
dropped during disturbance and after fault clearance it has reached a value
of 1.01 p.u.
The rotor angle deviation at generator bus-2 and bus-3 are also
analyzed. with EESGs connected at generator bus-1. Figure 5.6(b) shows
the rotor angle deviation at generator bus-2 and bus-3 in the presence of
EESGs.
Figure 5.6(b) Rotor angle deviation at generator bus-2 and bus-3 with
EESGs
From Figure 5.6(b), it is found that rotor angle swing after
disturbance has reached a maximum of 870 and settled around 80
0 which
shows the transient stability of the system.
Figures 5.6(c) (i) & (ii) show the rotor speed oscillation at
generator bus-2 and bus-3 with EESGs.
Figure 5.6(c)(i) Rotor speed oscillation at generator bus-2 and bus-3
with EESGs
128
Figure 5.6(c)(ii) Rotor speed oscillation at generator bus-2 and bus-3
with EESGs
From Figure 5.6(c) (i), it is found that rotor speed oscillation
varies from 0.995 p.u. to 1.01 p.u. and its bandwidth is 0.015 p.u. Also from
Figure 5.6(a) (ii), it is found that, rotor speed oscillation duration is 20 sec.
Compared to CSGs, oscillation deviation is lesser in direct drive EESGs.
The real power at generator buses with EESGs is also measured.
Figures 5.6 (d) (i) & (ii) show the real power at generator buses with
EESGs.
Figure 5.6(d) (i) Real power at generator buses with EESGs
129
Figure 5.6(d) (ii) Real power at generator buses with EESGs
From Figures 5.6(d) (i) & (ii), it is observed that, before
disturbance real power is 1.35 p .u. and after fault clearance it reaches a
value of 1.35 p.u. at one bus and from other two generators, active power
production increased to 0.8 p.u. Active power production from all turbines
has increased due to the increase of their corresponding bus voltages.
Figure 5.6(e) shows the reactive power at generator buses with EESGs
The reactive power at generator buses with EESGs is also
monitored. Figure 5.6 (e) shows the reactive power at generator buses with
EESGs with modified control. It is observed that reactive power from two
generators is around 0.25 p.u. and from one generator it is -0.1p.u. which
shows it consumed reactive power from other generators.
Figure 5.6(e) Reactive power at generator buses with EESGs
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5.5.2.4 Impact of PMSGs on transient stability
In this case, the CSGs at bus-1 of IEEE 9-bus system is replaced
with PMSGs and the voltage at generator buses along with CCT is
measured. Figures 5.7(a-e) show the voltage at generator buses along with
CCT, rotor angle deviation, rotor speed oscillations, active and reactive
power support with PMSGs.
Figure 5.7(a) shows the voltage at generator buses along with
CCT values in the presence of PMSGs in the system..
Figure 5.7(a) Voltage at generator buses with CCT with PMSGs
The value of CCT in this case is 0.260 sec. (13 cycles). When
compared with the system with only CSGs, CCT has increased when
PMSGs are connected at bus-1. It can also be noted that, with PMSGs, the
voltage has dropped during the disturbance and after fault clearance it has
improved to1.01 p.u. similar to EESGs.
The rotor angle deviation at generator bus-2 and bus-3 are also
analyzed with PMSGs connected at generator bus-1. Figure 5.7(b) shows
the rotor angle deviation at generator bus-2 and bus-3 in the presence of
PMSGs.
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Figure 5.7(b) Rotor angle deviation at generator bus-2 and bus-3 with
PMSGs
From Figure 5.7(b), it is found that rotor angle swing after
disturbance has reached a maximum of 870 and settled around 78
0 which
shows the transient stability possessed by the system in the presence of
WECS with PMSGs.
Figures 5.7(c) (i) & (ii) show the rotor speed oscillation at
generator bus-2 and bus-3 with PMSGs.
Figure 5.7(c)(i) Rotor speed oscillation at generator bus-2 and bus-3
with PMSGs
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Figure 5.7(c) (ii) Rotor speed oscillation at generator bus-2 and bus-3
with PMSGs
From Figure 5.7(c) (i), it is found that, with PMSGs, rotor speed
oscillation varies from 0.995 p.u. to 1.01 p.u. and its bandwidth is 0.015
p.u. Also from figure 5.7(c) (ii), it is found that, rotor speed oscillation
duration is 20 sec. Compared to CSGs, oscillation deviation is lesser in,
direct drive PMSGs.
CSGs, direct drive EESGs and PMSGs are provided with damper
windings. The damper winding consists of short circuited copper bars
embedded in the face of the rotor poles. By this, hunting can be suppressed.
Since , rotors of IGs are of slot and tooth arrangement, damper windings
cannot be provided.
When there is a change in load, excitation or change in other
conditions of the systems, rotor of the synchronous generators will oscillate
to and fro about an equilibrium position. At times, if these rotor oscillations
are not suppressed by damper windings, rotor oscillations becomes more
violent and resulting in loss of synchronism of the synchronous generators
and comes to halt.
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The real power at generator buses with PMSGs is also analysed.
Figures 5.7(d) (i) & (ii) show the real power at generator buses with
PMSGs.
Figure 5.7(d) (i) Real power at generator buses with PMSGs
Figure 5.7(d) (ii) Real power at generator buses with PMSGs
From Figures 5.7(d) (i) & (ii), with PMSGs, it is observed that,
before disturbance real power is 1.35p.u. and after fault clearance also it
remained at 1.35 p.u. at one generator and from other two generators, active
power production increased to 0.8 p.u. Active power production from all
turbines has increased due to the increase of their corresponding bus
voltages.
Also analysed the reactive power at generator buses with PMSGs.
Figure 5.7 (e) shows the reactive power at generator buses with modeled
PMSGs with modified control. . It is observed that reactive power from two
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generators is around 0.25 p.u. and from one generator it is -0.1p.u. which
shows it consumes reactive power from other generators.
Figure 5.7(e) Reactive power at generator buses with PMSGs
Table 5.1 shows the comparison of transient stability
performance of the system with CSGs,and fixed and variable speed WTGs.
Table 5.1 Transient stability assessment with CSGs and fixed and
variable speed WTGs
Type of
generators
CCT Rotor angle
deviation in
degrees
Rotor speed oscillation
Bandwidth in
p.u.
Duration in
sec.
CSG 0.250 87 0.03 22
SCIG 0.110 indefinite 0.045 Nearly 30
DFIG 0.225 85 0.035 24
EESG 0.255 80 0.015 20
PMSG 0.260 78 0.015 20
From the table it is observed that, the variable speed direct drive
EESG and PMSG with modified controllers could increase the CCT,
decrease rotor angle deviation, suppress rotor speed oscillations, maintain
the voltage magnitude, provide real and reactive power support during fault
condition and thus improve the transient stability of the system.
135
Compared to DFIG, EESGs with excitation control could
generate the required reactive power and thus can maintain the voltage at all
times. PMSGs are more efficient than the CSGs and simpler because no
exciter is needed. Compared to DFIG, the diameter of direct drive EESGs
and PMSGs are more. This increases the vibrations of rotor and thus
increased oscillations occur. But these are suppressed by providing damper
windings.
5.6 SUMMARY
In this chapter, the effect of fixed speed SCIGs, variable speed
DFIGs with standard control and variable speed direct drive EESGs and
PMSGs with modified control on the transient stability of power system has
been investigated. The performance of above WTGs is compared with
CSGs by connecting them at bus-1 of IEEE 9- bus test system. From the
simulation results it is observed that, fixed speed SCIGs with capacitor
bank arrangement could not contribute to transient stability improvement.
The variable speed WTG systems DFIG, EESG and PMSG
could contribute to the transient stability enhancement. EESG and PMSG
with modified controllers perform better than DFIG with standard control
with respect to increase of CCT, rotor angle swing and rotor speed
deviation, capability of active and reactive power support and maintaining
voltage magnitude of all generator buses.
And EESG and PMSG with modified controllers could perform
better than CSGs. It can thus be concluded from these investigations that
variable speed wind generators with modified controllers have a more
favourable impact on the transient stability of the power network and thus
would bring an additional value to the installation.
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CHAPTER 6
SUMMARY OF FINDINGS AND CONCLUSION
6.1 INTRODUCTION
In the preceding chapters, a research study carried out on the
impact of fixed speed and variable speed WTGs on voltage stability and
transient stability of power system is presented. The purpose of this
concluding chapter is:
1. To give a summary of the findings of the research study.
2. To list out the major contributions of the study
3. To suggest possible extensions for future work in this area of
research.
6.2 SUMMARY OF THE RESEARCH FINDINGS
The main objective of the research work is to model and simulate
the various WTGs with different power electronic topologies and control
strategies and to evaluate their impact on power system with respect to voltage
stability and transient stability. The summary of findings is given below:
Modeling and simulation of WECS is very important for analyzing
its performance when integrating it in power systems. First, fixed speed SCIG
with capacitor bank and DFIG with AC/DC/AC IGBT-based PWM converter
with standard rotor speed control and voltage control are considered. Next, a
variable speed direct drive EESG with passive rectifier and d-q current
controlled VSC is modeled. The d-q current control scheme of a VSC
decouples the real and reactive components and enabled the real power and
reactive power to be separately controlled.
137
Also, a variable speed direct drive PMSG with passive rectifier,
MPPT controlled dc-to-dc boost converter and adaptive hysteresis band
current controlled VSC to maintain constant dc link voltage is simulated.
A step and search MPPT control strategy which senses the VDC alone and
controls the same is utilized. This MPPT control strategy maintained the DC
link voltage constant under variable wind speeds. The adaptive hysteresis band
current controller adjusts the hysteresis bandwidth, according to the measured
line current of the grid connected inverter. This technique maintained the DC
link voltage constant under transient grid currents.
Tests were carried out on IEEE 14-bus test system to study the
effect of WTGs on voltage stability by computing loading margin, bus voltage
magnitude and reactive power delivered by the WTGs. It is found that, SCIGs
cannot delay or prevent a voltage collapse event, also is incapable of
supplying reactive power and thus unable to maintain the voltage magnitude.
DFIGs, EESGs and PMSGs increased the loading margin, assisted the grid to
delay or prevent a voltage collapse event, maintained the voltage magnitude
due to the capability to supply reactive power. EESGs and PMSGs with
modified controllers could perform even better than DFIGs with standard
control and CSGs.
To analyse the impact of WTGs on transient stability, a line fault is
applied near bus-7 of IEEE 9-bus test system and the rotor angle swing, rotor
speed deviation and oscillation, CCT, voltage magnitude, active power support
and reactive power support by the WTGs are calculated. It is found that, with
SCIGs, rotor angle swing increased indefinitely, rotor speed deviation is more
and oscillation duration is more. Further, it is not capable of increasing the
CCT. In addition, the voltage magnitude is below the allowable limit. With
variable speed WTGs, the rotor angle swing is lower, rotor speed deviation
and oscillation are lesser, and CCT has increased. In addition, the voltage
138
magnitude is maintained within limit and full active power is supplied because
of reactive power injection capability. Compared to DFIGs with standard
control, EESGs and PMSGs with modified controllers performed better. It is
found that DDSGs with modified controllers could bring an additional value to
the installation.
6.3 SIGNIFICANT RESEARCH CONTRIBUTION
The major contributions of this research work are presented below:
In this thesis, a variable speed direct drive EESG with d-q current controlled
VSC is modeled and simulated. The performance of the WTG is evaluated
under different operating conditions.
Also, a variable speed direct drive PMSG with MPPT controlled
DC-DC boost converter and adaptive hysteresis band current controlled VSC
is modeled. The suitability of the adaptive hysteresis band algorithm for the
control of VSC in WECS to maintain a constant DC link voltage is
demonstrated through simulation.
Further the effect of fixed speed SCIG, variable speed DFIG with
standard control, variable speed direct drive EESG and PMSG with modified
controllers on voltage stability has been evaluated on IEEE 14- bus test
system.
In addition, the impact of fixed speed SCIG, variable speed DFIG
with standard control, variable speed direct drive EESG and PMSG with
modified controllers on transient stability has been investigated and the
simulation results are presented.
139
6.4 CONCLUSION OF THE THESIS
This research work has focused on modeling and simulation of
variable speed direct drive WTGs and analyzed the impact of fixed and
variable speed WTGs on voltage stability and transient stability.
The variable speed direct drive EESG has been modeled with d-q
current controlled VSC. The variable speed direct drive PMSG has been
modeled with MPPT controlled DC-DC boost converter and adaptive
hysteresis band current controlled VSC.
The voltage stability of the system is analyzed under base case
and severe line outage conditions in IEEE 14 bus test system. Fixed speed
SCIGs are incapable of avoiding a voltage collapse event. The variable speed
DFIGs with standard control and direct drive EESGs and PMSGs with
modified controllers could assist the grid to delay or prevent a voltage collapse
event. The improvement of voltage stability of a system when WTGs are
connected with modified controllers is high compared to the system with only
CSGs and variable speed DFIGs with standard control. The instability is
completely avoided with variable speed direct drive WTGs with modified
controllers.
To evaluate the impact on transient stability, simulation has been
carried out on IEEE 9 bus test system. From the simulation results, it is
observed that fixed speed SCIGs with standard capacitor bank arrangement
could not contribute to transient stability improvement. The EESGs and
PMSGs with modified controllers performed better than DFIGs with respect to
increase of CCT, rotor angle swing and rotor speed deviation, capability of
active and reactive power support and maintaining voltage magnitude of all
generator buses. The variable speed direct drive EESG and PMSG with
140
modified control could increase the CCT, maintain the voltage, produce real
and reactive power, decrease rotor angle deviation during fault condition and
thus leads to improvement in transient stability.
6.5 SUGGESTIONS FOR FUTURE WORK
The present work can be extended in the following directions:
Fuzzy adaptive control for VSC
Fuzzy adaptive control can be applied in the VSC of variable speed
direct drive WTGs.
Evaluating the impact on small signal stability
The impact of fixed and variable speed WTGs on small signal
stability analysis can be evaluated.
Usage of matrix converters
AC-AC matrix converter capable of multilevel switching can be
applied in the variable speed direct drive WTGs.
140
APPENDIX 1
CONTINUATION POWER FLOW
The Jacobian matrix of power flow equations becomes singular at
the voltage stability limit. Continuation power flow overcomes this problem.
Continuation power flow finds successive load flow solutions according to a
load scenario. It consists of prediction and correction steps. From a known
base solution, a tangent predictor is used so as to estimate next solution for a
specified pattern of load increase. The corrector step then determines the exact
solution using Newton-Raphson technique employed by a conventional power
flow. After that a new prediction is made for a specified increase in load based
upon the new tangent vector. Then corrector step is applied. This process goes
until critical point is reached. The critical point is the point where the tangent
vector is zero. The illustration of predictor-corrector scheme is depicted in
Figure A1.1.
Figure A1.1 Illustration of prediction-correction steps
141
In continuation load flow, first power flow equations are
reformulated by inserting a load parameter into the equations.
1.1 MATHEMATICAL REFORMULATION
Injected powers can be written for the ith
bus of an n-bus system as
follows:
n
kikBikikGikVkViPi
1)sincos( (A1.1)
(A1.2)
(A1.3)
where, the subscripts G and D denote generation and load demand respectively
on the related bus. In order to simulate a load change, a load parameter is
inserted into demand powers and .
(A1.4)
(A1.5)
and are original load demands on ith
bus whereas
and are given quantities of powers chosen to scale W appropriately.
After substituting new demand powers in Equations (A1.4) and (A1.5) to
Equation (A1.3), new set of equations can be represented as:
(A1.6)
where, denotes the vector of bus voltage angles and V denotes the vector of
bus voltage magnitudes. The base solution for is found via a power
flow. Then, the continuation and parameterization processes are applied.
1.2 PREDICTION STEP
In this step, a linear approximation is used by taking an
appropriately sized step in a direction tangent to the solution path. Therefore,
the derivative of both sides of Equation (A1.5) is taken.
142
(A1.7)
=0 (A1.8)
In order to solve Equations (A1.7) and (A1.8), one more equation is
needed since an unknown variable is added to load flow equations. This can
be satisfied by setting one of the tangent vector components to +1 or -1 which
is also called continuation parameter. Setting one of the tangent vector
components +1 or -1 imposes a non-zero value on the tangent vector and
makes Jacobian nonsingular at the critical point. As a result Equation (A1.8)
becomes
(A1.9)
where is the appropriate row vector with all elements equal to zero except
the kth
element equals 1. At first step is chosen as the continuation
parameter.As the process continues, the state variable with the greatest rate of
change is selected as continuation parameter due to nature of parameterization.
By solving Equation (A1.9), the tangent vector can be found. Then, the
prediction can be made as follows:
(A1.10)
where, the subscript denotes the next predicted solution. The step size
is chosen so that the predicted solution is within the radius of convergence
of the corrector. If it is not satisfied, a smaller step size is chosen.
143
1.3 CORRECTION STEP
In correction step, the predicted solution is corrected by using local
parameterization. The original set of equation is increased by one equation that
specifies the value of state variable chosen and it results in:
(A1.11)
where, is the state variable chosen as continuation parameter and is the
predicted value of this state variable. Equation (A1.11) can be solved by
using a slightly modified Newton-Raphson power flow method.
1.4 PARAMETERIZATION
Selection of continuation parameter is important in continuation
power flow. Continuation parameter is the state variable with the greatest rate
of change. Initially, is selected as continuation parameter since at first steps
there are small changes in bus voltages and angles due to light load. When the
load increases after a few steps the solution approaches the critical point and
the rate of change of bus voltages and angles increase. Therefore, selection of
continuation parameter is checked after each corrector step. The variable with
the largest change is chosen as continuation parameter. If the parameter is
increasing +1 is used, if it is decreasing -1 is used in the tangent vector in
Equation (A1.9).In order to summarize the whole continuation power flow
process, a flow chart is presented in Figure A1.2.
144
Figure A1.2 Flow chart for Continuation power flow
The continuation power flow is stopped when critical point is
reached as it is seen in the flow chart. Critical point is the point where the
loading has maximum value. After this point it starts to decrease. The tangent
component of is zero at the critical point and negative beyond this point.
Therefore, the sign of shows whether the critical point is reached or not.
145
APPENDIX 2
SIMULTANEOUS IMPLICIT METHOD
In simultaneous implicit approach, the state variables and the
network variables are solved simultaneously. Trapezoidal rule is illustrated
here. Equation (5.1) which is the general form of representing a set of first
order differential equations.
.x =f(x,V) (5.1)
Let x be the state variables and V be the network variables With x=xn and
V=Vn at t=tn, the solution of x at t= tn+1= tn+Δt is given by
Δ
(5.2)
From a set of algebraic equations
(5.3)
Where I be the current injection vector
From eq.(5.3) the solution of V at t=tn+1 is
(5.4)
The vectors xn+1 and Vn+1 are unknown . Let
Δ
(5.5)
And
(5.6)
At solution ,
(5.7)
(5.8)
146
Equations (5.7) and (5.8) are both nonlinear algebraic equations.
Thus the differential equations have been made algebraic by using an implicit
formula. These equations are very sparse; for computational efficiency it is
necessary to take advantage of their special structure. Applying the Newton
method to solve equations (5.19) and (5.20), we may write for the (k+1)st
iteration
Δ
Δ
(5.9)
The following equation is solved to obtain Δ andΔ
:
Δ
Δ
(5.10)
The Jacobian in the above equation is computed at and
.
It has the following structure:
(5.11)
The matrices , , and are associated with the models for
the dynamic devices and non-linear static loads.
The solutions of equations (5.19) and (5.20) are given as
Δ Δ
Δ
(5.12)
Δ Δ
Δ
(5.13)
In the above equations, k is the iteration counter and good starting
values are established by extrapolation. Also and
are the residue
vectors of the states and current injections, respectively.
147
From equation (5.12), Δ can be expressed as a function ofΔ
:
Δ
Δ
(5.14)
Substitution of equation (5.14)into equation (5.13)yields
Δ
(5.15)
Now Δ and Δ
can be calculated by solving equations (5.14) and
(5.15). Then and
are obtained from equation (5.9).
Treatment of discontinuities:
Equations (5.12) and (5.13) are valid only when the functions given
by equations (5.5) and (5.6) are continuous and differentiable. At points of
discontinuity, such as network switching or limits on state variables, the exact
formulation by the Newton method or any method requiring derivatives would
be complicated. This problem is dealt as follows:
For large network discontinuities, such as a network fault or switching
operations, the integration method is temporarily changed to the fourth
order Runge-Kutta method for one step at the point of discontinuity.
This time step has a zero step size and is used only for the calculation
of the post-fault network conditions (the state vector is not updated).
After this, the normal trapezoidal integration is resumed.
For local non- differentiable functions, such as limits associated with
controllers, the device Jacobians are computed by neglecting their
effect. This is acceptable since they have only local impact and the
overall convergence will not be significantly affected.
148
APPENDIX 3
TRANSMISSION LINE PARAMETERS OF
IEEE 14 BUS TEST SYSTEM
Table A3.1 shows the transmission line parameters of IEEE 14 bus
test system.
Table A3.1 Transmission line parameters of IEEE 14 bus test system
Sending
end Bus
Receiving
end Bus
Resistan
ce p.u.
Reactance
p.u.
Half
Susceptance
p.u.
Tranformer
tap
1 2 0.01938 0.05917 0.0264 1
2 3 0.04699 0.19797 0.0219 1
2 4 0.05811 0.17632 0.0187 1
1 5 0.05403 0.22304 0.0246 1
2 5 0.05695 0.17388 0.017 1
3 4 0.06701 0.17103 0.0173 1
4 5 0.01335 0.04211 0.0064 1
5 6 0 0.25202 0 0.932
4 7 0 0.20912 0 0.978
7 8 0 0.17615 0 1
4 9 0 0.55618 0 0.969
7 9 0 0.11001 0 1
9 10 0.03181 0.0845 0 1
6 11 0.09498 0.1989 0 1
6 12 0.12291 0.25581 0 1
6 13 0.06615 0.13027 0 1
9 14 0.12711 0.27038 0 1
10 11 0.08205 0.19207 0 1
12 13 0.22092 0.19988 0 1
13 14 0.17093 0.34802 0 1
149
APPENDIX 4
THREE-PHASE DIODE BRIDGE RECTIFIER
In the analysis of three-phase diode bridge rectifier, it is assumed
that the impedances of the supply lines are low enough to be neglected, and
that the load current is constant in time. , , are the phase voltages.
The amplitude of the phase voltage is
(A4.1)
where, is the root-mean-square (RMS) value of the phase voltage.
Assuming that is strictly greater than zero during the whole period, in
each time point two diodes of the diode bridge conduct. The first conducting
diode is from the group of odd-indexed diodes , and it is
connected by its anode to the highest of the phase voltages at the time point
considered. The second conducting diode is from the group of even-indexed
diodes , and it is connected by its cathode to the lowest of the
phase voltages. The DC component of the output voltage is given by
(A4.2)
The input currents have the same RMS value, given by
(A4.3)
The output power of the rectifier is
(A4.4)
150
and it is the same as the input power , since losses in the rectifier diodes
are neglected in the analysis.
150
REFERENCES
1. Aarti Gupta, D.K Jain and Surender Dahiya, (2012) “Some
Investigations on Recent Advances in Wind Energy Conversion
Systems,” IPCSIT, vol. 28 , IACSIT Press, Singapore, pp.47-52.
2. American Wind Energy Association "20% Wind Energy by 2030" 2009.
3. Andreas Binder, Tobias Schneder, (2005) “Permanent magnet
synchronous generators for regenerative energy conversion- a survey,”
European Conference on Power Electronics and Applications,EPE-2005,
10 pp.10.
4. Andreas Petersson, “Analysis, Modeling and Control of Doubly-Fed
Induction Generators for Wind Turbines”, Thesis For The Degree Of
Doctor Of Philosophy Division of Electric Power Engineering
Department of Energy and Environment, Chalmers University Of
Technology, G¨oteborg, Sweden 2005
5. Bob Erickson, “Future Directions in Wind Power Conversion
Electronics,” Colorado Power Electronics Center, University of
Colorado, Boulder.
6. Camm E.H, Behnke M. R, Bolado O, Bollen M, Bradt M, Brooks C,
Dilling W, Edds M , Hejdak W. J, Houseman D, Klein S, Li F, Li J,
Maibach P, Nicolai T, Patiño J., Pasupulati S. V, Samaan N, Saylors S.,
Siebert T, Smith T, Starke M, Walling R, (2009)“Characteristics of Wind
Turbine Generators for Wind Power Plants,” IEEE PES Wind Plant
Collector System Design Working Group.
7. Chen Z ,E. Spooner,( 2001) “Grid power quality with variable speed
wind turbines,” IEEE Trans. Energy Convers., vol. 16, No. 2, pp. 148–
154.
8. Chinchilla M , S. Arnalte, J.C. Burgos and J.L.Rodríguez,(2005) “Power
limits of grid-connected modern wind energy systems,” Renewable
Energy,vol.31, No. 9, pp.1455-1470.
9. Conroy J, Watson R, (2009) "Aggregate modelling of wind farms
containing full-converter wind turbine generators with permanent magnet
synchronous machines: transient stability studies”, IET Renewable
Power Generation, Volume: 3 , Issue: 1 ,pp. 39 – 52.
151
10. Cultura A.B, Z.M. Salameh,( 2011) "Modeling and simulation of a wind
turbine-generator system”, IEEE Power and Energy Society General
Meeting, pp 1-7.
11. Cutsem T. V ,C. Vournas, (1998)Voltage Stability of Electric Power
Systems. Boston, MA: Kluwer.
12. De Rijcke S, H.Ergun, D. Van Hertem and J.Driesen ,( 2012) “Grid
Impact of Voltage Control and Reactive Power Support by Wind
Turbines Equipped With Direct-Drive Synchronous Machines,” IEEE
Transactions on Sustainable Energy, vol. 3 , No. 4 , pp. 890 – 898.
13. Devaraj D , J. Preetha Roselyn, (2010) “Genetic algorithm based reactive
power dispatch for voltage stability improvement,” Electrical Power and
Energy Systems, vol.32, No. 10,pp. 1151–1156.
14. Devaraj D, R. Jeevajyothi , (2011) "Impact of fixed and variable speed
wind turbine systems on power system voltage stability enhancement,”
IET Conference on Renewable Power Generation, RPG-11,pp.1-9.
15. Djemai NAIMI, Tarek Bouktir,( 2008) “ Impact of Wind Power on the
Angular Stability of a Power System”, Leonardo Electronic Journal of
Practices and Technologies, No. 12, pp. 83-94.
16. Durga Gautam ,(2010) “Impact of Increased Penetration of DFIG Based
Wind Turbine Generators on Rotor Angle Stability of Power Systems,”
Ph.D Dissertation , Arizona State University.
17. Ekanayake J.B, Holdsworth, Lee, XueGuang Wu and Jenkins N ,( 2003)
“Dynamic modeling of doubly fed induction generator wind turbines,”
IEEE Transactions on Power Systems, vol. 18 , No.2 , pp. 803 – 809.
18. Eleschova Z, M.Smitkova and A. Belan, (2010) “Evaluation of Power
System Transient Stability and Definition of the Basic Criterion,”
International Journal of Energy, vol.4,No.1, pp.9-16.
19. Errami Y, M. Ouassaid and M. Maaroufi, (2013) “Control of a PMSG
based Wind Energy Generation System for Power Maximization and
Grid Fault Conditions,” Proceedings of the International Conference on
Mediterranean Green Energy Forum, MGEF-13, pp. 220–229.
152
20. Feltes C, S. Engelhardt, J. Kretschmann,J. Fortmann, F. Koch and I.
Erlich, (2009) “Comparison of the Grid Support Capability of DFIG-
based Wind Farms and Conventional Power Plants with Synchronous
Generators,” IEEE Power & Energy Society General Meeting, PES-09,
pp.1-7.
21. Folly K.A., S. Sheetekela,( 2009) “Impact of fixed and variable speed
wind generators on the transient stability of a power system network,”
IEEE Proceedings of Power Systems Conference and Exposition, PSCE-
0, pp.1-7 .
22. Giraldo E, A Garces., (2014) “An Adaptive Control Strategy for a Wind
Energy Conversion System Based on PWM-CSC and PMSG,” IEEE
Transactions on Power Systems, vol.29 , No.3 ,pp. 1446 - 1453 .
23. Haiying Dong, Shuaibing Li, Lixin Cao, Hongwei Li, (2013) “Voltage
and Reactive Power Control of Front-end Speed Controlled Wind
Turbine via H∞ Strategy,” TELKOMNIKA, vol. 11, No. 8, pp. 4190-
4199.
24. Hasnaoui O B K, J. belhadj, M. Elleuch,( 2006) “Low voltage ride
through performances of direct drive permanent magnet synchronous
generator wind turbine, “ CERE- 06, Hammamet, TUNISIA.
25. Henk Polinder, F.A. Frank van der Pijl, Gert-Jan de Vilder and Peter
Tavner,(2005) “Comparison of Direct-Drive and Geared Generator
Concepts for Wind Turbines”, IEEE International Conference on Electric
Machines and Drives, EMDC-05 , pp.543 – 550.
26. Hosaka N, Kumano T , (2008) “Evaluation of voltage fluctuation in
electric power system with wind power generators”, IEEE Power and
Energy Society General Meeting - Conversion and Delivery of Electrical
Energy in the 21st Century, pp.1-6.
27. Hossain M.J, H.R. Pota, M.A. Mahmud and R. A. Ramos,(2011)
"Impacts of large-scale wind generators penetration on the voltage
stability of power systems," IEEE Power and Energy Society General
Meeting, pp 1-8.
153
28. Jagdeep Singh Lather, Sukhwinder Singh and Sanjay Marwaha, (2013)
“Dynamic modeling, analysis and simulation of grid connected Doubly
fed induction generator based wind power under different operating
conditions,” International Journal of Electrical and Electronics
Engineering Research, vol. 3, No. 2, pp.29-40.
29. Jamal A. Baroudi, Venkata Dinavahi and Andrew M. Knight, (2007) “A
review of power converter topologies for wind generators,” Renewable
Energy, 32, pp.2369–2385.
30. Jan Machowski, Janusz Bialek and Jim Bumby, (2008)Power System
Dynamics: Stability and Control, 2nd Edition.
31. Jianzhong Zhang, Ming Cheng, Zhe Chen and Xiaofan Fu, (2008)
“Pitch Angle Control for Variable Speed Wind Turbines,” Proceedings
of the 3rd International Conference on Electric Utility Deregulation and
Restructuring and Power Technologies, DRPT 2008, pp.1-6.
32. Jogendra Singh Thongam and Mohand Ouhrouche (2011). MPPT
Control Methods in Wind Energy Conversion Systems, Fundamental and
Advanced Topics in Wind Power, Dr. Rupp Carriveau (Ed.)
33. Johansson S, (1998) “Long-term voltage stability in power systems”
Ph.D. dissertation, School Electr. Comput. Eng., Chalmers Univ.
Technol., Goteborg, Sweden.
34. Junfei Chen, Hongbin Wu, Ming Sun, Weinan Jiang, Liang Cai and
Caiyun Guo, (2012) "Modeling and simulation of directly driven wind
turbine with permanent magnet synchronous generator”, IEEE
Innovative Smart Grid Technologies - Asia (ISGT Asia), pp. 1 – 5.
35. Kawale Y.M, S.Dutt , (2009) “Comparative Study of Converter
Topologies Used for PMSG Based Wind Power Generation”, Second
International Conference on Computer and Electrical Engineering,
ICCEE-09, pp. 367 – 371.
36. Kesraoui M , N. Korichi , A. Belkadi, (2011) “Maximum power point
tracker of wind energy conversion system”, Renewable Energy,vol.36,
No.10, pp.2655–2662.
37. Kundur P, (1994) “Power System Stability and Control”, McGraw-Hill.
154
38. Londero R.R, C.M. Affonso , J.P.A.Vieira,( 2014 ) "Long-Term Voltage
Stability Analysis of Variable Speed Wind Generators,” IEEE
Transactions on Power Systems, vol. PP , No. 99 , pp. 1 – 9.
39. M. R. Patel, Wind and Solar Power Systems. USA: CRC Press, 1999,pp.
82–83.
40. Machowski J, J. W. Bialek and J. R. Bumby, (1997)Power System
Dynamics and Stability. New York: Wiley.
41. Md Rabiul Islam, Youguang Guo, Jianguo Zhu , “ Power converters for
wind turbines: Current and future development ,“ Materials and
processes for energy: Communicating current research and
developments, FORMATEX 2013.
42. Mihet-Popa L , Blaabjerg F, (2004) “Wind turbine Generator modeling
and Simulation where rotational speed is the controlled variable”, IEEE
Transactions on Industry Applications, vol. 40 , No.1 ,pp.3 – 10.
43. Milano, F. “PSAT, Matlab-based Power System Analysis Toolbox”,
2002, available at http://thunderbox.uwaterloo.ca/_fmilano.
44. Ming Yin, Gengyin Li, Ming Zhou, Chengyong Zhao, "Modeling of the
Wind Turbine with a Permanent Magnet Synchronous Generator for
Integration”, IEEE Power Engineering Society General Meeting, 24-28
June 2007, pp.1 – 6.
45. Mokui H.T, M.A.S. Masoum, M.Mohseni and M. Moghbel, (2012)
“Power system transient stability enhancement using direct drive wind
generators,” IEEE Power and Energy Society General Meeting,pp.1-6.
46. Muljadi E, T. B. Nguyen and M.A. Pai , (2008)” Impact of Wind Power
Plants on Voltage and Transient Stability of Power Systems,” IEEE
Energy 2030, Atlanta, Georgia, USA.
47. Muljadi E,C. P. Butterfield, (2001) “Pitch-controlled variable-speed
wind turbine generation,” IEEE Trans. Ind. Appl., vol. 37, no. 1,
pp. 240–246.
48. Murat Kale, Engin Ozdemir, (2005) “An adaptive hysteresis band current
controller for shunt active power filter,” Electric Power Systems
Research, vol.73, No.1, pp.113–119.
155
49. Muyeen S. M , M H Ali , R Takahashi , T Murata , J Tamura , Y
Tomaki , A Sakahara and E Sasano ,(2007) “Comparative study on
transient stability analysis of wind turbine generator system using
different drive train models,” IET Renewable Power Generation, vol. 1 ,
No. 2 , pp.131 – 141.
50. Nanou S, G.Tsourakis, C.D.Vournas, (2011)"Full-converter wind
generator modelling for transient stability studies,” IEEE Trondheim
PowerTech, pp.1 – 7.
51. Nayeem Rahmat Ullah, (2006) “Grid Reinforcing Wind Generation,
“Thesis for the degree of licentiate of engineering, Department of Energy
and Environment, Chalmers university of Technology, Goteborg,
Sweden.
52. Nayeem Rahmat Ullah, Torbjorn Thiringer, (2007) “Variable Speed
Wind Turbines for Power System Stability Enhancement,” IEEE
Transactions on Energy Conversion, vol. 22, No. 1, pp.52-60.
53. Pejovic P, “Three phase diode rectifiers with low harmonics current
injection methods,” Chapter 2,Three-phase diode bridge rectifier.
54. Rahimi M, M. Parniani, (2010) “Coordinated Control Approaches for
Low-Voltage Ride-Through Enhancement in Wind Turbines With
Doubly Fed Induction Generators, “IEEE Transactions on Energy
Conversion, vol. 25, No.3 , pp. 873 – 883.
55. Revel G, A.E.Leon, D.M.Alonso, and J.L. Moiola,(2014)" Dynamics
and Stability Analysis of a Power System With a PMSG-Based Wind
Farm Performing Ancillary Services” IEEE Transactions on Circuits and
Systems I, vol. PP, No.99 , pp. 2182 – 2193.
56. Rolan, A., Luna A, Vazquez G and Aguilar D,(2009) “Modeling of a
variable speed wind turbine with a Permanent Magnet Synchronous
Generator”, International Symposium on Industrial Electronics, ISIE
2009, pp.734 – 739.
57. Sachin Khajuria, Jaspreet Kaur, “Implementation of Pitch Control Of
wind Turbine Using Simulink (Matlab),” International Journal of
Advanced Research in Computer Engineering & Technology vol.1, No.4,
June 2012.
156
58. Seul-ki Kim and Eung-Sang Kim,( 2007) ”PSCAD/EMTDC based
modeling and analysis of a gearless variable speed wind turbine” ,IEEE
Trans,, Energy Convers.,vol.22,No.2,pp.421-430.
59. Shu J, B.H. Zhang , C.G. Wang and Z.Q.Bo,( 2009) “Investigation of
control for grid integrated doubly fed induction wind generator,”IEEE
Power & Energy Society General Meeting, PES-09 ,pp.1-7.
60. Slootweg J. G, de Haan S. W. H, Polinde, H and Kling W. L, “General
model for representing variable speed wind turbines in power system
dynamics simulations,” IEEE Transactions on power systems, vol. 18,
No. 1, February 2003.
61. Slootweg J.G, Polinder H, Kling W.L, (2001)“Dynamic modelling of a
wind turbine with doubly fed induction generator,” Power Engineering
Society Summer Meeting, vol. 1,pp. 644 - 649 .
62. Taylor C. W, (1994)Power System Voltage Stability, McGraw-Hill.
63. Thomas Ackermann, (2005)”Wind Power in Power Systems”.Royal
Institute of Technology. Stockholm, Sweden.
64. Vittal, Eknath O'Malley, Mark, Keane and Andrew, (2012)“Rotor angle
stability with high penetrations of wind generation”, IEEE Transactions
on Power Systems, vol.27,No.1pp. 353-362.
65. Wei Qiao , Harley R.G and Venayagamoorthy G.K ,( 2007) “Dynamic
Modeling of Wind Farms with Fixed-Speed Wind Turbine Generator,”
IEEE Power Engineering Society General Meeting, pp.1 – 8.
66. www.mathworks.in/help/physmod/powersys/.../synchronousmachine.
htm.
67. Yazhou Lei, Mullane A, Lightbody G and Yacamini, R,
(2006)"Modeling of the wind turbine with a doubly fed induction
generator for grid integration studies,” IEEE Transactions on Energy
Conversion, Vol. 21 , No.1, pp. 257 – 264.
68. Ziping Wu, Wenzhong Gao ,Daye Yang and Yan Shi ,(2012)
"Comprehensive modeling and analysis of Permanent Magnet
Synchronous Generator-Wind Turbine system with enhanced Low
Voltage Ride Through Capability,” IEEE Energy Conversion Congress
and Exposition, ECCE- 2012 , pp. 2091 – 2098.
157
LIST OF PUBLICATIONS
Journals
1. Jeevajothi R, D. Devaraj. (2011) “Impact of Variable Speed Wind Turbine
driven Synchronous Generators in Transient Stability of Power Systems”,
International Journal of Innovative Technology and Creative Engineering, Vol.1
,No.2,pp.54-60.
2. Jeevajothi, R, D. Devaraj, (2012) “Modeling of a Grid compatible Variable
Speed Wind Turbine with direct drive Synchronous Generator”, International
Journal of Engineering Science and Technology, Vol.2, No.5, pp.603-608.
3. Jeevajothi, R, D. Devaraj, (2012) “Voltage Stability Enhancement using VSWT
with direct drive Synchronous Generators”,International Journal of Energy
Engineering, Vol.1,No.1,pp.259-265.
4. Jeevajothi, R, D. Devaraj, (2012) “Transient Stability Enhancement using
Variable Speed Wind Turbine with Direct Drive Synchronous Generators”,
International Journal of Computer and Electrical Engineering, Vol.4, No.2,
pp.231-235.
5. Jeevajothi, R, D. Devaraj, (2014) “Voltage stability enhancement using
adaptive hysteresis controlled variable speed wind turbine driven EESG with
MPPT,” Journal of Energy ,South Africa, May.2014,pp.48-60(Impact factor-
0.214).
6. Jeevajothi, R, D. Devaraj, “A new approach for constant DC link voltage in a
direct drive Variable Speed Wind Energy Conversion System”, International
Journal of Electrical Engineering and Technology. (Revised and submitted)
International Conferences
1. Jeevajothi R, D.Devaraj, “MATLAB/ Simulink based Modeling and Simulation
of Variable Speed Wind Turbine driven Synchronous Generator”, International
Conference on Power, Control, Signals and Computation-EPSCICON’2010,
Vidya Academy of Science & Technology, 4th
to 6th
, January 2010.
2. R.Jeevajothi, D.Devaraj, “Impact of Variable Speed Wind Turbine driven
Synchronous Generators in Transient Stability of Power Systems”, IEEE
International Conference on Electrical Energy and Networks-ICEEN’2011,
IACSIT, 7th
to 9th
,January 2011.
158
3. R.Jeevajothi, D.Devaraj, Impact of Wind Turbine Systems on Power System
Voltage Stability”, IEEE sponsored International Conference on Computer,
Communication and Electrical Technology - ICCCET 2011, 18th
& 19th
,
February 2011. Cited in IEEE explore.
4. Jeevajothi R, D. Devaraj, “Impact of fixed and variable speed wind turbine
systems on power system voltage stability enhancement”, IEEE sponsored
International Conference on IET Renewable Power Generation Conference
2011-RPG 2011, 6th
to 8th
September 2011. Cited in IEEE explore.
5. Jeevajothi R, D. Devaraj, S.Thilaka, “Step and search control method of
tracking maximum power using variable speed wind turbine driven synchronous
generator”, International Conference on Computing Techniques, Embedded
Systems and Drives-ICCTESD 2011, 7th
to 9th
, March 2012.
159
CURRICULAM VITAE
R.Jeevajothi was born at Nagercoil, Kanyakumari District, located
in the Southern part of Tamilnadu, India on 25th
June, 1970. She obtained her
B.E. Degree in Electrical and Electronics Engineering in the year 1990 from
Shanmugha College of Engineering, Thirumalaisamudram, Thanjavur District.
She received the Master’s degree in Marketing Management from Indira
Gandhi National Open University in 1998 and Master’s degree in Energy
Engineering from Arulmigu Kalasalingam College of Engineering,
Virudhunagar District, affiliated to Anna University in 2006.
She has published papers in 6 International Journals and presented papers
in 5 International conferences and 3 National conferences. She has organized 2
workshops. Her research interests include wind energy conversion systems, modeling
of wind turbine generators, analyzing the impact of wind energy conversion systems
on voltage stability and transient stability. She is a life member of Indian Society for
Technical Education (ISTE).
Since 1991, she has been working in reputed Engineering Colleges in
Tamilnadu, India. Currently she is working as an Asst. Professor in the Department
of Electrical and Electronics Engineering in Kalasalingam University, Virudhunagar
Dt., Tamilnadu, India.
