
Citation 
 Permanent Link:
 http://digital.auraria.edu/AA00000037/00001
Material Information
 Title:
 Application of thyristorcontrolled series reactor for fault current limitation and power system stability enhancement
 Creator:
 Kang, Bu Il
 Place of Publication:
 Denver, Colo.
 Publisher:
 University of Colorado Denver
 Publication Date:
 2013
 Language:
 English
 Physical Description:
 1 electronic file : ;
Thesis/Dissertation Information
 Degree:
 Master's ( Master of Science)
 Degree Grantor:
 University of Colorado Denver
 Degree Divisions:
 Department of Electrical Engineering, CU Denver
 Degree Disciplines:
 Electrical Engineering
 Committee Chair:
 Park, JaeDo
 Committee Members:
 MancillaDavid, Fernando
Deng, Yiming
Subjects
 Subjects / Keywords:
 Thyristors ( lcsh )
Electric power systems  Control ( lcsh ) Electric power systems  Control ( fast ) Thyristors ( fast )
 Genre:
 bibliography ( marcgt )
theses ( marcgt ) nonfiction ( marcgt )
Notes
 Review:
 Various types of Fault Current Limiters (FCLs) have been proposed and proven that they offer many advantages with respect to transmission losses, voltage quality, and power system stability. However, those including the SolidState Fault Current Limiters (SSFCL), the most advanced type of FCL, have been mainly focusing on the FCL system itself such as optimization of components, improving the efficiency and reducing the cost. Conventional ways such as splitting buses, replacing the switchgear, and installing permanentlyinserted series reactor are still used to avoid fault current problems, which impairs overall power system reliability. In this thesis, a ThyristorControlled Series Reactor (TCSR) is presented to limit the fault current and enhance the power system stability simultaneously. The influence of TCSR is analyzed from the perspective of voltage security enhancement and the feasibility of real power system application is assessed. The benefits of the TCSR are demonstrated with bulk power system simulation results from the voltage security and angle stability stand point.
 Thesis:
 Thesis (M.S.)University of Colorado Denver. Electrical engineering
 Bibliography:
 Includes bibliographical references.
 General Note:
 Department of Electrical Engineering
 Statement of Responsibility:
 by Bu Il Kang.
Record Information
 Source Institution:
 University of Colorado Denver
 Holding Location:
 Auraria Library
 Rights Management:
 All applicable rights reserved by the source institution and holding location.
 Resource Identifier:
 862973529 ( OCLC )
ocn862973529

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Full Text 
APPLICATION OF THYRISTORCONTROLLED SERIES REACTOR FOR
FAULT CURRENT LIMITATION AND POWER SYSTEM STABILITY
ENHANCEMENT
by
Bu II Kang
Bachelor of ScienceChonnam National University1994
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Science
Electrical Engineering
2013
This thesis for the Master of Science degree by
Bu II Kang
has been approved for the
Electrical Engineering Program
by
JaeDo Park, Chair
Fernando MancillaDavid
Yiming Deng
KangBu H (M.S.Electrical Engineering)
Application of ThyristorControlled Series Reactor for Fault Current Limitation and
Power System Stability Enhancement
Thesis directed by Assistant Professor JaeDo Park.
ABSTRACT
Various types of Fault Current Limiters (FCLs) have been proposed and proven
that they offer many advantages with respect to transmission losses, voltage quality, and
power system stability. However, those including the SolidState Fault Current Limiters
(SSFCL), the most advanced type of FCL, have been mainly focusing on the FCL system
itself such as optimization of components, improving the efficiency and reducing the cost.
Conventional ways such as splitting buses, replacing the switchgear, and installing
permanentlyinserted series reactor are still used to avoid fault current problems, which
impairs overall power system reliability. In this thesis, a ThyristorControlled Series
Reactor (TCSR) is presented to limit the fault current and enhance the power system
stability simultaneously. The influence of TCSR is analyzed from the perspective of
voltage security enhancement and the feasibility of real power system application is
assessed. The benefits of the TCSR are demonstrated with bulk power system simulation
results from the voltage security and angle stability stand point.
The form and content of this abstract are approved. I recommend its publication.
Approved: JaeDo Park
DEDICATION
I dedicate this work to Eungjeong, my lovely wife, who has always
believed and supported me by my side.
IV
ACKNOWLEDGMENTS
This thesis would not have been possible without the support of my company,
Korea Power Exchange (KPX).
TABLE OF CONTENTS
CHAPTER
I. INTRODUCTION.......................................................1
Introduction.....................................................1
II. FAULT CURRENT LIMITERS.............................................3
Fault Current Limitation by a Series Reactor.....................3
Bypass Switch....................................................4
Tuned LC Circuit Shunted by a Metal Oxide Varistor (MOV).........5
Series Compensator...............................................6
Power Electronic Switches.......................................11
III. POWER SYSTEM STABILITY...........................................13
Thyristor Controlled Series Compensator (TCSC)..................17
Short Circuit Current Limiter (SCCL)............................20
IV. DQ TRANSFORMATION................................................22
V. PROPOSED APPROACH.................................................29
Voltage Stabilizing Fault Current Limiter.......................29
Plant Model and Compensator Design..............................32
VI. COMPUTER SIMULATIONS..............................................37
Duty Control to Increase Output Voltage.........................37
Effects of TCSR on Different Fault Locations....................40
Effects of TCSR on Bulk Power System Voltage Stability..........44
Effects of TCSR on Bulk Power System Angle Stability............46
VII. CONCLUSION.......................................................51
vi
LIST OF TABLES
Table
VI.1 Simulation parameters................................................38
VI.2 Comparison results of the voltage and the fault current........45
VI.3 Fault current of the adjacent buses with respect to 4400 bus fault...48
VI.4 Fault current of critical buses(kA)..................................48
VI.5 Case summary(MW).....................................................48
VI.6 Critical Clearing Time(msec).........................................48
vii
Figure
LIST OF FIGURES
11.1 Fault current limiter application: it protects the entire bus or individual circuit.4
11.2 Relationship between system voltage drop, reactor shortcircuit voltage and power
factor................................................................................5
11.3 Fault current limiter with tuned impedance..........................................6
11.4 Fault current limiter using a tuned LC circuit shunted by a MOV.....................7
11.5 Power system network with SC.....................................................8
11.6 Power system network during the source side fault with compensation.................9
11.7 Network model and phasor diagram under the prefault condition.......................10
11.8 Network model and phasor diagram under the load side fault condition................10
11.9 FCL using power electronic switches (a) Short Circuit Current Limiter (SCCL), (b)
SolidState Fault Current Limiter (SSFCL)............................................12
111.1 Shunt compensation with a current source (aj Network configuration, (b) Phasor
diagram: Vr can be controlled Vr to Vr by compensating the reactive component of the
load current.........................................................................13
111.2 Series compensation with a voltage source (a) Network configurationb) Phasor
diagram: Vr can be controlled by inserting Vcomp and the appropriate magnitude control
of Vcomp.............................................................................14
111.3 Equivalent circuit of singlemachine infinite bus system: a generator delivers power
to an infinite bus through two transmission circuits.....................................17
111.4 Powerangel curve for Equal Area Criterion.....................................17
111.5 A practical configuration of TCSC..............................................18
111.6 Impedance characteristics of a TCSC with respect to firing angle...................19
111.7 The characteristics of SCCL and powerangle curve (a) During normal operation,
equivalent impedance is treated as zero and XL during the fault (b) Accelerating power is
decreased as much as the hatched area by inserting the series reactor................20
IV.1 Axes of reference frame.........................................................23
viii
IV.2 Voltage and current waveforms when duty ratio is 0 where the current flows only
through the series reactor, (a) Load voltage (b) Current...............27
IV. 3 Voltage and current waveforms when duty ratio is 1 where the current flows only
through the bypass switch, (a) Load voltage (b) Current..........................28
V. l Model for circuit analysis (a) Original circuit, (b) Equivalent circuit when switch is
off, (c) Equivalent circuit when switch is on....................................30
V. 2 PI regulator with negative feedback.........................................34
VI. 1 Step responses of the plant: Uncompensated model has a steady state error (0.4651),
which is eliminated by a PI controller where Kp=0.8, Ki=100......................38
VI.2 Overall model configuration and the output voltage responses: the output voltage
changes from about 245kV to 270kV based on the duty ratio which starts to increase
from 0.5sec.......................................................................39
VI.3 Typical power system model to investigate the effects of TCSR on fault currents
and voltage dips: faults can be occurred either near the TCSR or far away from it.40
VI.4 Simulation results for the fault near the TCSR: The TCSR is required to be operated
as fault current limiter and voltage restorer, (a) The bus voltage is operating in low level
when the series reactor is inserted, (b) The fault current is exceeding the nominal value
when the series reactor is bypassed, (c) Voltage is maintained higher and the fault current
is limited within nominal value when the control scheme is applied...............42
VI.5 Simulation results for the fault far away from the TCSR: The TCSR is required to be
operated as voltage restorer, (a) The bus voltage is operating in low level when the series
reactor is inserted, (b) The voltage is maintained higher and the fault current is in low
level when the series reactor is bypassed, (c) Voltage is maintained higher and no control
action is required to limit the fault current....................................43
VI.6 A 345kV transmission network for the voltage stability simulation: three substation
buses can be reconnected when the TCSR is installed..............................44
VI.7 PV curves during normal and contingent conditions: maximum incremental
transfer is increased from 300MW to 475MW when the TCSR is used..................45
VI.8 Power angle curve for Equal Area Criterion: power system synchronism can be
maintained when the accelerating power is smaller than the decelerating power and
inserting the series reactor decreases the accelerating power as much as the hatched area.
..................................................................................46
VI.9 Network configuration for the transient stability simulation: a FCL using
permanentlyinserted series reactor is installed on a substation and two contingency cases
(FI,F2) are studied to analyze the influences of the FCL on the power system angle
stability.........................................................................47
IX
VI.10 Simulation results on FI fault: the power system can maintain synchronism with
the TCSR (a) Machine electrical power [P.U.] (b) Bus voltage [P.U.].........49
VI.11 Simulation results on F2 fault: the power system can maintain synchronism with
the TCSR (a) Machine electrical power [P.U.] (b) Bus voltage [P.U.].........50
Equation
LIST OF EQUATIONS
III Equation for system voltage drop..............................................3
11.2 Equation for the current increase............................................5
11.3 Equation for the receiving end voltage.......................................7
11.4 Circuit equations.............................................................7
11.5 Injection voltage equation....................................................8
11.6 Current and voltage equations under the prefault condition....................9
11.7 Current and voltage equation during the fault.................................9
111.1 Voltage equation for simple AC circuit......................................15
111.2 Voltage equation for the series compensated AC system.......................15
111.3 Relationship between the rotor angle and the accelerating power.............16
111.4 Equivalent impedance of TCSC................................................19
IV.1 Transformation matrix........................................................22
IV.2 Column vector and transformation matrix......................................23
IV.3 Conversion variables in different reference frames...........................24
IV.4 Conversion variables in the stationary reference frames......................24
IV.5 Conversion variables in the synchronous reference frames.....................25
IV.6 Space vector represented by threephase components...........................25
IV.7 Space vector in the stationary reference frame...............................26
IV.8 Transformation to other reference frame......................................26
IV. 9 Individual variables fafbfc..............................................26
V. 1 Voltage and current equations in case the thyristor switches are open......29
V.2 Voltage and current equations in case the thyristor switches are close........31
xi
V.3 Averaged voltage and current dynamic equations.................................32
V.4 Linearized function.............................................................32
V.5 Dynamic model including steadystate term and linear small signal term.........33
V.6 Linearized small signal dynamic model...........................................33
V.7 Control transfer functions......................................................34
V.8 Control transfer function for the plant model..................................35
V.9 A PI compensator model..........................................................35
V.10 Closedloop transfer function..................................................35
xii
CHAPTER I
INTRODUCTION
Introduction
Demand on electricity has been increasing tremendously and many countries
invest significant amount of money for reliable power supply. More generation plants and
transmission lines were constructed and the power systems became more complex. Major
transmission lines tend to be longdistance and generation sites are largescaled. Load
concentration requires more transmission lines to be interconnected. However, those
characteristics of power systems have been causing problems related to fault currents and
system stabilities.
Several approaches to cope with the fault current problems are being used in
distribution and transmission areas. Permanentlyinserted series reactors, uprating and
replacement of switchgear, splitting buses or transmission lines are the most commonly
used techniques to limit the fault current in power systems, which are regarded as cost
effective and more secure measures for the operational reliability of power system
facilities. However, uprating and replacement of switchgear can be very expensive and
shortcircuit current duty may not be reduced. Network splitting can deteriorate the
power system security. Permanentlyinserted currentlimiting series reactors introduce a
voltage drop, active and reactive power losses and also adversely affect the power system
stability. In spite of these drawbacks, a lot of power systems are still divided into several
subsystems to solve fault current problems.
For the power system stability enhancement, on the other hand, the following has
been used as countermeasures in general:(1)Constructing more interconnection lines2)
1
Installing dynamic reactive resources, (3) Constraining power transfers, and (4) Using
Special Protection Schemes (SPS).
So far, fault current and stability analysis has been studied separately, since
network configuration influences in an opposite way to those problems. When
transmission systems are fully meshed, they tend to yield fault current problems, rather
than stability problems. On the other hand, when powers are delivered through high
impedance transmission lines, stability issues may arise instead of fault current problems.
However, as the power systems become more complex with the meshed transmission
networks which are interconnected with longdistance, highpower transfer transmission
lines, those two problems become coexistent. Consequently, countermeasures to deal
with the fault current impact more on the power system stability than before.
In this work, prior researches related to fault currents limitation and power system
stability enhancement are reviewed and a TCSR that limits the fault current and improves
the stability simultaneously is presented. The influence of the TCSR from the perspective
of voltage security enhancement is shown with a theoretical analysis, and to assess the
feasibility of the TCSR to real power systems, the benefits of the TCSR are demonstrated
with bulk power system simulation results.
2
CHAPTER II
FAULT CURRENT LIMITERS
Fault current limiters can be applied in a variety of distribution and transmission
areas. Those can be used for the protection of entire bus or individual circuit as in Figure
II.1.For the last 20 years, superconductive FCLs have been studied and suggested to
limit the fault current, but they have not been used widely in the field because of the cost
problem. Reactors, high impedance transformers, circuit breaker upgrades and splitting
buses or transmission lines are still widely used. Because of the fault current problem,
many power system operators are sacrificing their system reliability by splitting the
network into many subsystems. However, comparing to the Superconductive FCL, these
methods have many disadvantages with respect to transmission losses and system
reliability. Many alternative ways to overcome those problems have been suggested.
Fault Current Limitation by a Series Reactor
Most commonly used FCLs are permanentlyinserted series reactor type fault
current limiters. As this type of fault current limiter does not require replacement of
switchgear and more economical than others, it is commonly used in power systems. The
fault current driven by the voltage source is reduced by the impedance of the reactor.
AV 1
=1
^jl + 1cos2 0 +Vk
Equation 11.1 Equation for system voltage drop.
3
Figure 11.1 Fault current limiter application: it protects the entire bus or individual
circuit.
However, it may cause severe voltage drop during contingent state, while the system
voltage drop may not represent a particular problem during normal operating conditions
[1].The system voltage drop can be calculated using the following equation and Figure
11.2 shows the relationship between system voltage drop, reactor shortcircuit voltage Vk,
and power factor.
Bypass Switch
In the 1980s, most power systems were operating with splitting network topology
such as splitting buses or opening transmission lines at normal operating conditions to
limit the fault current. A tunedcircuit impedance method was proposed to limit the fault
current by Electric Power Research Institute (EPRI) [2]. Figure 11.3 shows the basic
configuration of this circuit. Under normal operating conditions, the switch is opened and
transmission line has zero net impedance if they are tuned properly. When a fault occurs,
the switch is closed and the equivalent impedance becomes where X is the impedance
4
of the reactive components, which results in fault current reduction. Although it requires
high initial cost, its zero net impedance during normal operating conditions can reduce
the operating cost such as transmission loss; besides, the system voltage recovers to its
prefault level after clearing the fault.
AV
0
cos^>=0.6
cos =0.7
cos =0.8
cos<5>=0.9
cosO=0.95
cos=l
Vk[%i
5 10 15 20 25
Figure 11.2 Relationship between system voltage drop, reactor shortcircuit
voltage and power factor.
Tuned LC Circuit Shunted by a Metal Oxide Varistor (MOV)
This type of i^uL was developed for the fault current limitation and power quality
improvement [3]. It consists of a series LC circuit tuned at the system frequency and a
MOV in parallel with the capacitor as shown in Figure 11.4. Since the LC circuit is well
tuned, it is almost transparent during normal operation. When there is a fault in the
downstream of the FCL, it forces a gradual increase of the current, which is justified by
the following equations.
i(t) = VP[sin(wt + 6 8) +~sinSsinwt + ~wtsin(wt + 0)]
Equation 11.2 Equation for the current increase.
5
WhereVp: magnitude of the source voltagephase angle of the source voltageZ: the
magnitude of the load impedance, 8:load angle.
Figure 11.3 Fault current limiter with tuned impedance.
This shows that the higher the L, the slower the current increase, which reduces the
voltage sag during the fault. However, since the voltage on the L and C will increase
during the fault, additional device to limit the overvoltage is required. MOV is
connected in parallel with the capacitor, and it absorbs the excessive energy in case its
protection level is reached. However, long cooldown time of the MOV and possibility of
SubSynchronous Resonance (SSR) [4] are the drawback to be solved.
Series Compensator
Dynamic voltage restorer (DVR) using energy storage device and a series
compensator (SC) shown in Figure 11.5 was proposed to limit the fault current and
improve the voltage quality of the power system [5, 6]. By controlling the amplitude and
6
phase angle, they control the real and reactive power between the controller and the
power system.
Figure 11.4 Fault current limiter using a tuned LC circuit shunted by a MOV.
During normal operating conditions where the receiving end voltage Vl is given
by
rL= vsjxsrL
Equation 11.3 Equation for the receiving end voltage.
,the SC does not operate. However, when there is a fault in the network, it compensates
the voltage by injecting a lagging or leading voltage in quadrature with the load (fault)
current to restore the line voltage and limit the fault current. Considering a fault at the
source side, the voltage of the source will be dropped, and the circuit equation becomes
Without compensation VPF = VfL = VSAG jXsVL
With compensation VL = VSAG jXsIL + Vsc
Equation 11.4 Circuit equations.
7
Where VfL> /^and VPF are the load side voltage, line current, and SC side voltage vector
during the fault respectively.
Figure 11.5 Power system network with SC.
To enhance the voltage drop, the SC injects a lagging voltage Vsc until the load side
voltage is restored to its prefault level VL as shown in Figure 11.6. Since VSAG jXsIL is
the voltage on the source side of the SC and if we set VL = VP, then the injection voltage
Vsc becomes
Equation 11.5 Injection voltage equation.
: measured voltage on the source side of the Series Compensator (SC). By injecting
a lagging voltage, we allow the DVR to restore the load side voltage to its predefined
8
level under normal and contingency conditions. On the other hand, if the fault occurs at
the load side, the SC should act as a fault current limiter.
Figure 11.6 Power system network during the source side fault with compensation.
The current and voltage equations under the prefault condition can be expressed as
%%jXsTL = Q
VpVpjxTL = o
r %%
L_ jXS
Equation 11.6 Current and voltage equations under the prefault condition.
,and the system model is shown in Figure 11.7. During the fault where the VF = 0, those
equations become
vsvPFjxsrL =
v^F ]XTF = o
^5 ^PF
Equation 11.7 Current and voltage equation during the fault.
9
From the comparison between equation 11.6 and equation 11.7, we see that the fault
current can be limited to the load current when VPF is restored to VP. The SC injects a
> > >
leading voltage Vsc until VPF is restored into its prefault level VP as shown in Figure 11.8.
Figure 11.7 Network model and phasor diagram under the prefault condition.
Figure 11.8 Network model and phasor diagram under the load side fault condition.
10
Power Electronic Switches
A great deal of power electronics based FCLs have been proposed for fault
current limitation and power system stability enhancement. With the development of
power electronic devices and control technologies, a large number of Flexible AC
Transmission Systems (FACTS) devices have been developed and are in operation
extensively for the security enhancement of power systems [7]. FCLs using solidstate
devices such as Insulated Gate Bipolar Transistor (IGBT), Silicon Controlled Rectifier
(SCR), and Gate Turnoff Thyristor (GTO) can be classified into (1)Series Switch type
FCL, (2) Bridge type FCL, and (3) Resonant FCL [8]. The basic operational principle of
SSFCLs is almost same in that currents flow through zero impedance path in steadystate
and they are switched into the fault current limiting reactor in case of shortcircuit
conditions. However, the configuration of SSFCLs can be different based on their
application purpose. Different types of Series Switch type FCLs were described [9] and
an application of a ThyristorControlled Series Reactor was presented to reduce furnace
arc flicker [10]. Bridgetype FCLs using different types of switching device were also
proposed [11, 12], and the influence of this type of FCL was investigated in terms of
power system transient stability [13]. Another application using FACTS based Short
Circuit Current Limiter (SCCL) was suggested in [14], where thyristor Protected Series
Compensator (TPSC) combined with an external reactor showed the benefits for fault
current limitation and SSR mitigation. Transient stability was also evaluated with this
type of series capacitor compensated FCL in [15]. Basic configurations for those FCLs
are illustrated in Figure 11.9.
11
SCCL
SSFCL
Figure 11.9 FCL using power electronic switches (a) Short Circuit Current Limiter
(SCCL), (b) SolidState Fault Current Limiter (SSFCL).
12
CHAPTER III
POWER SYSTEM STABILITY
For the voltage and reactive power compensation, we usually use reactive power
compensator such as static condensers, shunt reactors which are static reactive sources
being used for steady state voltage regulations and thyristor controlled series condensers,
thyristor controlled reactors which are dynamic reactive sources being used for transient
stability enhancement.
Figure 111.1 Shunt compensation with a current source (a) Network configuration,
(b) Phasor diagram: Vr can be controlled Vr to V^by compensating the
reactive component of the load current.
13
Figure 111.2 Series compensation with a voltage source (a) Network configuration,
(b) Phasor diagram: VR can be controlled by inserting Vcomp and the
appropriate magnitude control of Vcomp.
They can be connected to the system in series or in shunt. To reduce transmission losses
and improve the voltage regulation and stability, we normally compensate reactive
powers near the load. By injecting the reactive component of the current near the load, a
compensator can control the current from the generator resulting in voltage regulation
improvement in the load side. Considering leading compensation, we can increase the
14
load side voltage to Vr with the same source voltage Vs. In additionwe can reduce
relatively large amount of reactive losses compare to uncompensated system. Therefore,
this kind of compensation is usually used for voltage stability enhancement. Figure III.1
shows the principle of shunt reactive power compensation in a simple AC circuit which
can be represented as
Vs = VR + IP(R+jX)
Equation 111.1 Voltage equation for simple AC circuit.
Based on the compensation types required, inductors or capacitors can be used. For
independent control with the voltage at the connection point, current source or voltage
source compensator can be used [16]. Var compensation can also be realized using series
compensator. Typical series compensation is made by series capacitors and Figure 111.2
shows the principles of series compensation in a radial AC system which can be
represented as
Vs = VfR + IP(R+jX)VC0MP
Equation 111.2 Voltage equation for the series compensated AC system.
The voltage angle of Vr can be changed by inserting Vcomp between the line and the
load. With the appropriate magnitude control of Vcomp, Vr can be controlled. This kind
of series compensation gives three main benefits to the transmission system.(1)Increase
angular stability of the system (2) Improve voltage stability of the system (3) Optimize
power sharing between parallel circuits. Equal Area Criterion is generally used to
understand basic factors that influence the transient stability of power systems [17]. It
basically uses the relationship between the rotor angle and the accelerating power.
15
^ = ^(PMPE)
Equation 111.3 Relationship between the rotor angle and the accelerating power.
Where, Pm mechanical power, PE: electrical power, 8: rotor angle, in electrical radian, H:
inertia constant, in MWs/MVA. Let us consider the response of singlemachine infinite
bus system to a threephase fault on transmission line2, as shown in Figure 111.3. Network
conditions can be represented as:(1)Prefault (both circuits in service), (2) During a
threephase fault, (3) Postfault (circuit 2 out of service) and those are illustrated with P8
plots in Figure 111.4. Initially, the system is operating where Pm = Pe When the fault
occurs, Pe goes down to b. At this point, since Pm is greater than PE, the rotor starts to
accelerate until the fault is cleared. When the fault is cleared, the operating point shifts to
d based on the line condition. However, since the rotor speed is greater than the
synchronous speed, it continues to increase until the kinetic energy gained during the
acceleration period is exhausted. The operating point moves to e, where the accelerating
power is equal to the decelerating power. At point e, the rotor speed is equal to the
synchronous speedbut Pe is greater than Pm. Thereforethe rotor starts to decrease the
speed following the P8 curve for the single circuit condition. In the presence of any
source of damping, the rotor finally gets to a new stable operating point. With a delayed
fault clearing, acceleration power is greater than deceleration power, leading to loss of
synchronism.
16
eb^o
Figure 111.3 Equivalent circuit of singlemachine infinite bus system: a generator
delivers power to an infinite bus through two transmission circuits.
Generator
output Po^ er
Figure 111.4 Powerangel curve for Equal Area criterion.
Thyristor Controlled Series Compensator (TCSC)
A typical TCSC consists of a Fixed Series Capacitor (FC) in parallel with a
Thyristor Controlled Reactor (TCR). The bidirectional thyristor valves are red with a
phase angle ranging between 90 and 180 with respect to the capacitor voltage. A Metal
17
Oxide Varistor (MOV) is used to prevent the overvoltage across the capacitor. A circuit
breaker is installed across the capacitor and it bypasses the capacitor when severe faults
or equipmentmalfunction events occur. Conduction losses of the TCSC valves can be
minimized by installing an UltraHighSpeed Contact (UHSC) across the valve. It is
closed shortly after the thyristor valve is turned on, and opened shortly before the valve is
turned off. During a sudden overload of the valve and fault conditions, the metallic
contact is closed to alleviate the stress on the valve [18].
Figure 111.5 A practical configuration of TCSC.
Figure 111.5 shows a practical configuration of TCSC. The main capabilities of the TCSC
can be achieved by changing the impedance of the line where it is connected, which can
be done by controlling the firing angle of the thyristors. Variation of XL with respect to
firing angle and the equivalent impedance of the TCSC are given as the following
equations
&=A
71
n 2a 2sin2a
AS A
18
XTCScla) = Xc
^xa^ + J^xgs!(g)xktan(^)tan(^)
XC XL
n
Xc XL 2 1
n
Equation 111.4 Equivalent impedance of TCSC.
Whereo = 2(:ra) is the conduction angle of TCSCand k =
is the compensation
ratio. Figure 111.4 shows the impedance characteristics of a TCSC.
The followings represent the main functions of a TCSC.(1)Damping of the power
swings from local and interarea oscillations, (2) Suppression of sub synchronous
oscillations, (3) Voltage support, and (4) Reduction of the shortcircuit current.
Z
Figure 111.6 Impedance characteristics of a TCSC with respect to firing angle.
19
Short Circuit Current Limiter (SCCL)
SCCL is developed from the series compensation which normally uses a capacitor
to compensate the inductor used as a fault current limiter, thus the line is regarded as
shortcircuited. During normal operation, the FCL compensated with series capacitor
increases the steady state stability limit. When a shortcircuit fault occurs, the FCL can
reduce the accelerating power at the initial stage of the fault and provide additional
decelerating power at the fault clearing stage [15].
Generator
output Power
(b)
Figure 111.7 The characteristics of SCCL and powerangle curve (a) During normal
operation, equivalent impedance is treated as zero and XL during the fault (b)
Accelerating power is decreased as much as the hatched area by inserting the
series reactor.
20
Figure 111.7 shows an example of a single line fault where double circuit transmission line
becomes single circuit transmission line. The accelerating power will be decreased as
much as the hatched area and power system synchronism can be maintained if the
resultant accelerating power is smaller than the decelerating power.
21
CHAPTER IV
DQ TRANSFORMATION
We transform timevarying voltage, current differential equations into time
invariant differential equations. As it is not only easy to solve but also easy to understand
and control. A, B, C phase variables in three phase AC system are transformed into
orthogonal d, q, n axes variables [21].Direct axis d represents the axis where excitation
flux (or main flux) is and quadrature axis is 90 degree in electrical angle ahead to d axis
in positive rotational direction and neutral axis is orthogonal to dq axes in three
dimensional spaces. Figure IV.1 represents axes of reference frames, where superscript s
denotes stationary reference framee synchronous reference framew arbitrary rotating
speed and 0 is defined as
0 =  w(d^ + 0(0) = J w(d^
The transformation matrix can be derived as
faqn = Tmabc
Equation IV.1 Transformation matrix.
The column vectors of variables are given as
fW fW fw fWiT
J dqn U d Jq Jn 1
ac = [fafbfc]T
22
2
COS0 COS (q Tl'j COS(0+:TI
2
r(0) = sinQ sin ^0 sin ^0 + ti !
Ill
a/2 a/2 V2
Equation IV.2 Column vector and transformation matrix.
imaginary axis
real axis
Figure IV.1 Axes of reference frame.
The variables in the threephases axis can be converted both to the variables in the
stationary reference frame and to the variables in the arbitrary reference frame as
fdqn ~ T(jy)fabc
faqn = Tmabc = Rmmabc = Rmiqn
23
i ~2 ~2
n)= 2 0 V3 V3
3 T 1 T 1
1 Vf Vf Vf
COS sin 0
: = sin cos 0
0 0 iJ
r(0) = /?(0) r()
Equation IV.3 Conversion variables in different reference frames.
If the system is balancedthat is fa + fb + fc = 0, and convert the variables in the three
phase axis to the variables in the stationary reference framethen
fdqn ~ T(jy)fabc
71 2  1 1 1 ~2 ~2 a/3 a/3 'fa
Us O 0 2 2 111 V2 V2 V2  fb
[fn\ o fc
fd
(fa 2_ ~^fc) fa
fqs
fb ~ fc
V3
fn ^
Equation IV.4 Conversion variables in the stationary reference frames.
Likewise, the variables in the synchronous reference frame can be converted with respect
to the stationary reference frame as
24
fdqn = (0e)/i
qn
fqe =
[fn\ fi
cos0e sin0e 0
sin0e cos0e 0
0 0 1
m
fqS
In.
fd = fd cosQe + fqSinQe
fq = fd sinQe + fqscosQe
Equation IV.5 Conversion variables in the synchronous reference frames.
As a result, when the space vector by threephase components can be represented as the
equation IV.7, threephase variables can be represented by only two orthogonal
components of a complex vector.
2
fabc ~ 3 + afb + a fc)
/n =/a + / + /c)
,2 2 2 1 a/3
a = = cosn + isinTi =h /
3 J 3 2 J 2
Equation IV.6 Space vector represented by threephase components.
The real part of fabc equals to (/a /c) which is correspondent to fsd and the
imaginary part of fabc equals to (/fc) which is correspondent to fsq.
Consequently, the equation to transform a space vector fabc to the space vector in dq
axes which are stationary can be expressed as
fdq = fd +)fq = fabc
fi = real(fabc)
25
fqs = imag(fabc)
Equation IV.7 Space vector in the stationary reference frame.
Likewise, from the previous relationship between the synchronous reference
frame and stationary reference frame, and using Euler equation and basic vector
modificationwe can derive the transformation to other reference frame as
f!q = n +jfqe = fiqejQe = fabce^
Equation IV.8 Transformation to other reference frame.
Inverselywe can extract the individual variables fafbfc from the space vector fabc.
2 ? 2 1 1
real(fabc) = ^(fa + ah + a Jc) = ^fa ~ ^fb ~ ^fc
2, 9 , 12 1
reaKa Jabc) ~ Ja + fb + afc) ~ ~~fa +~fb ~~fc
2 112
real(afabc) = + a fb + fc) ~^a 3^ + 3^c
/n = 2 ^ + fb+ fc)
fa realQfabc) fn
fb = real{a2fahc) + fn
fc reoKjxfabc) fn
Equation IV.9 Individual variables fa, fb, fc.
This approacn is demonstrated with a specific RL circuit shown in Figure V.l(a) and
parameters used in Table VI.1.Following figures are the voltage and current responses
with respect to different duty ratios.
26
x IQ5 Three phase signals
2
0
2
0.1 0.12 0.14 0.16 0.18 0.2
0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2
0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2
Three phase signals
5000
0
5000
0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2
0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2
6000
4000
2000
0
2000
0.1 0.12 0.14 0.16 0.18 0.2
synchronousfec fram
I 
L_LLi ^ ^ j Ide Iqe
i
i
(b)
Figure IV.2 Voltage and current waveforms when duty ratio is 0 where the current
flows only through the series reactor, (a) Load voltage (b) Current.
27
x IQ5 Three phase signals
^ l \. y mrt L.\. / \ i Vds1 ^ Vqs 1
\\ l \V / wy \\ / \\j\i ^\i \i f\ \
\> KJ ^^
0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2
0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2
Three phase signals
8000
6000
4000
2000
O
2000
0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2
synchronous reference frame
< =
. r i Ide
 Iqe
] j
I f i
5
(b)
Figure IV.3 Voltage and current waveforms when duty ratio is 1 where the current
flows only through the bypass switch, (a) Load voltage (b) Current.
28
CHAPTER V
PROPOSED APPROACH
In order to demonstrate the advantages of the TCSR, especially from the voltage
point of view, a simple RL circuit shown in Figure V.l(a) is used. The receivingend
voltage is controlled by changing the equivalent impedance of FCL. To achieve this goal,
following approach is proposed. A statespace model is constructed and averaged using
dq transformation method. Since the input (duty) and output (vr) variables feature
nonlinear relationships, linearization technique is applied to the averaged statespace
model to obtain a system transfer function. A PI controller is designed to get a better
dynamic response and zero steadystate error.
Voltage Stabilizing Fault Current Limiter
When the thyristor switch is open, the network in Figure V.l (a) becomes as
shown in Figure V.1(b) and the voltage and current dynamic equations are given as
dij _ dij
hj RtIlLfcl
1 dt 1 L tLL dt
RJl
dif _R +)w{Lt + Lfcl)s vs
dt (Lt + Lfcl) 1 (Lt + Lfcl)
k = rJi
Equation V.l Voltage and current equations in case the thyristor switches are open.
xe = xe~Jwtf R = RL + Rt, and the superscript e denotes synchronous reference frame.
When the switch is closed, the network becomes like Figure V.1(c) and the voltage and
current dynamic equations become
29
Rl
Figure V.l Model for circuit analysis (a) Original circuit, (b) Equivalent circuit
when switch is off, (c) Equivalent circuit when switch is on.
30
dt
= RLh
v!
vi =
Equation V.2 Voltage and current equations in case the thyristor switches are close.
LEq = LFclLtcr/(Lfcl+Ltcr). These equations can be arranged into a set of state
equations as
Where, x: state variable, u: input variable, y: output variable.
As the average behavior of the system is dependent on the conduction time of the
thyristors [19]if we define the conduction and offconduction time as Tt and Tb
respectively, we can rewrite the previous equations into two sets of state equations
depending on the different conduction stages
Where Ts = Tt + Tb: switching timeand subscript T and B denote ON and OFF
respectively. The averaged model for the system can be expressed as the following set of
state equations
x = Ax + Bu
y = Cx + Du
Xj1
xB = (Abx + Bbu)Tb
x = (ATdT + ABdB)x + (BTdT + BBdB)u
Aj'X + Bj'U + i4^)x + B^u
y CT(1d)x + dCBx
31
dT = Tt/Ts =1d, dB = Tb/Ts = d
Applying this relationship into the system model equations V.l, V.2, then,
dieL _R+ jw(LT + Lfcl) f v + R + jw(LT + Lfcl)
dt (Lr + Lfcl) 1 (Lr + Lfcl) (Lr + Lfcl)
R + 7*w(Lr + LEQy
Vl + d{~
1
{lt + LEq^ (Lr + L(Lt + Lfcl)
Vr = RLil
K
Equation V.3 Averaged voltage and current dynamic equations.
As a result, the voltage drop on the fault current limiting reactor can be limited by the
following factor and controlled by duty d.
R + jw{lT + LFCl) +7*w(Lr + LÂ£(?)1
1(LT + Lfcl) (Lt + Leq) \Lt + Leq)
1
(Lt + Lfcl)
Plant Model and Compensator Design
However, the system model is nonlinear because the duty is also a function of
time. Therefore, we need to linearize the nonlinear equation to solve. Considering non
linear function F(Z) and applying Taylor formula at Z = Z, the linearized function can
be approximated as
F(Z)^ F(Z)+ (ZZ)
Equation V.4 Linearized function.
For the controller design, we define state variable, input, and output vector as
^ = Ihl
u =
Vs
dY
y = [vr]
32
,then the state equations can be written as
x = F(il, vs, d)
y = G(Jl%d)
If we apply linearization method at an operating point where steady state values are II, Vs,
D, Vr, X, U, the dynamic model can be expressed with steadystate terms and linear
small signal terms as
d dF dF dF
lL = F(X,U)+ (il /l) + ^ (1^5 ^) + ^ (rf D)
v = G(X,U)+ (Tl
dG
dG
Equation V.5 Dynamic model including steadystate term and linear small signal
term.
From these equations, we get the following linearized small signal dynamic model of the
system.
d dF dF dF ^
It If H17c? Hd
dt 1 diL 1 dvs 5 dd
_dG ^ ^ dG ^ ^dG ^
h, = rL + Tl,v^ = + %, d = d + D
Equation V.6 Linearized small signal dynamic model.
Rewriting the equations leads to the following form as
5 = i+
vR = CiL + Dvsvs + Dda
,and applying superposition mle gives the following control transfer functions (vs = 0).
33
h_
d
(sZi)1^
C(sZi)1^
R(D 1) RD 1
j tr W
{Lt + LFcl) [Lt + LEq)
R(D 1) RD
W ; 7^
(Lt + Lfcl) (^Lj + L^q).
Bd =
R R ]
(Lt + Lfcl) (Lr + Leq^j
R R 
(Lt + Lfcl) (Lr + Leq^j LQ
\Rl
w
w
Rl.
Equation V.7 Control transfer functions.
d Gvd(s)
J i
V,
Figure V.2 PI regulator with negative feedback.
In the synchronous dq reference frameAU quantities can be treated as DC. In addition
by aligning the voltage vector to the daxis, the output voltage of the qaxis can be set to
zero. Therefore, substituting the equation V.7 with the derived values A, Bd,C, we obtain
the following transfer function.
34
=
VRd K2RiJlDS KiKzRiJLD + K2R[JlQW
d 5^ 2/C^5 + K^ +
R
Lt + Lfcl
+ RD(
1
1
Lt + Lfcl Lt + LEq
k2 =
/?(
1
1
Lt + Lfcl Lt + LEq
Equation V.8 Control transfer function for the plant model.
Our plant and compensator transfer function can be expressed with Gvd(s) and Gc(s) in
Figure V.2. To improve lowfrequency loop gain and regulation, a PI compensator is
designed.
Kr
Gc(s) = KP +7
Equation V.9 A PI compensator model.
The closedloop transfer function is given as
VR T
Vref ~ 1 + T
Equation V.10 Closedloop transfer function.
The loop gain T = Gc(s).Gvd(s)+
Routh's Stability Criterion can be used to determine the ranges of coefficients of
polynomials for stability [20]. Considering the characteristic equation of an nth order
system, the Routh array can be arranged as the following form
35
H(s) = n i n1 =s + ais + a2S "+ + anis + an
Row n sn 1 a2 a4 "
Row n1 s111 ai a3 a5
Row n2 Sn_2 bi b2 b3
Row n3 sn_3 Cl C2 c3
Row 2 s2 .
Row 1 s1 .
Row 0 s .
a1a2 a3
i=b2
Cll
_ a5
^ b1a3 a1b2 ^ bas
A necessary and sufficient condition for stability is that all the elements in the first
column of the Routh array are positive and it is shown that it is true for equation V.8 and
V.9.
36
CHAPTER VI
COMPUTER SIMULATIONS
Duty Control to Increase Output Voltage
This approach is demonstrated with the RL circuit shown in Figure V.1 and
parameters used for the simulation are shown in Table VI.1.The transfer function of the
plant model can be derived from V.8, which is given as
12045 + 1.261 X 106
^vd (*^)
d
s2 + 20945 + 1.096 X 106
It has a constant steady state error, because the plant model has a small value when s = 0.
To eliminate the steady state error, we have designed PI compensator, which gives the
openloop transfer function as
T =
(Kp +
12045 + 1.261 x 106
52 + 20945 + 1.096 X 106
The characteristic equation of the closeloop transfer function as
1 + T = 53 + (2094 + 1204KP)s2 + (1.261 X 10eKP + 1204^ + 1.096 X 106)s
+ 1.261 x 10%
Applying Routh's Stability Criterion to the characteristic equation of the closeloop
transfer function gives Kp = 0.8 and Ki =100. As a resultthe PI compensated transfer
function becomes
T = Gc(s)Gvd(s)=
963.552 + 1.129 x 1065 + 1.261 x 108
s3 + 2094s2 + 1.096 x 106s
Steady state error is eliminated and the bus voltage can be enhanced by controlling the
duty ratio of the TCSR. The output voltages are controlled from 245kV to 270kV based
37
on the duty ratio which starts to increase from 0.5sec. The step responses of the system
and the output voltage responses with respect to different duty ratios are shown in Figures
VI.1 and VI.2. Simulations are done with MATLAB.
Table VI.l Simulation oarameters__________________________________________________
Vs Rt Rl Lt Lfcl Ltcr
345kV 0.82H 41.06n 0.015H 0.025H 0.00025H
Figure VI.1 Step responses of the plant: Uncompensated model has a steady state
error (0.4651), which is eliminated by a PI controller where Kp=0.8, Ki=100.
38
e
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
i'ime [sec]
(b)
Figure VI.2 Overall model configuration and the output voltage responses: the
output voltage changes from about 245kV to 270kV based on the duty ratio
which starts to increase from 0.5sec.
39
Effects of TCSR on Different Fault Locations
Because the network is more complex than the simple RL circuit in Figure V.l
(a)we need to consider faults that occur at different locationse.g.near or far from the
TCSR. When the fault occurs near the TCSR, the fault current will be high and the
voltage will be low. Then the TCSR is required to operate as a fault current limiter and
voltage restorer. On the other hand, when the fault occurs at a location far away from the
TCSR, both the fault current and the voltage will be low. Then it does not need to act as a
fault current limiter, but as a voltage restorer. This has been shown by PSCAD/EMTDC
model shown in Figure VI. 3.
Figure VI.3 Typical power system model to investigate the effects of TCSR on fault
currents and voltage dips: faults can be occurred either near the TCSR or far
away from it.
The fault current is confined within nominal shortcircuit current level with the series
reactors and voltage drop due to the series reactor is around 4% which can be derived
from the following equation [1].
AV
VN
l + 2Vk^lcos20 +Vk
40
,where, _: system voltage drop, Vk reactor shortcircuit voltage, and cosO: power
V
factor. In this system, possible issues are fault current problems in case the faults occur
near the TCSR and undervoltage problems when the faults occur far away from the
TCSR. Control actions of the TCSR enhance the voltages and limit the fault currents
within nominal ranges. It can be seen that the fault currents for the near fault are limited
within 40kA, which is the nominal shortcircuit current, and the voltages are maintained
higher in both cases. Figures VI.4, VI.5 and Table VI.2 show the simulation results.
so
175
130
12s
.8
f 0
^11
41
0.900 G.9SO 1.000 1.05D 1100 1.15D 1.230
Figure VI.4 Simulation results for the fault near the TCSR: The TCSR is required
to be operated as fault current 111111ter and voltage restorer, (a) The bus voltage
is operating in low level when the series reactor is inserted, (b) The fault current
is exceeding the nominal value when the series reactor is bypassed, (c) Voltage is
maintained higher and the fault current is limited within nominal value when
the control scheme is applied.
FALLT FAR
1Z5 
iao
Â§
i
3
aeo ago 1.00 1.10 1^0 1.30 1.40
(a)
gaeesA
gaeelpA gi51
42
"VrrrK L CWl
FALLT
Figure VI.5 Simulation results for the fault far away from the TCSR: The TCSR is
required to be operated as voltage restorer, (a) The bus voltage is operating in
low level when the series reactor is inserted, (b) The voltage is maintained higher
and the fault current is in low level when the series reactor is bypassed, (c)
Voltage is maintained higher and no control action is required to limit the fault
current.
Q8D
0.90
Too"
1.10
\.2D
.30
1.40
(b)
FALLT FAR
195.0
190.0
185.0
100.0
175.0
170.0
1G5.0
1600
1550
150.0
i D^n
fpA
00000000000l05r550Â£51015i0r5(
9&9Qs5l8a7sseQ5&5Q45L1a1z.?z5L;J
gaeesA
43
Effects of TCSR on Bulk Power System Voltage Stability
To assess the benefits of the TCSR from the stability point of view, computer
simulations have been performed with a bulk power system where the total demand is
73,000MW. A typical power system shown in Figure VI.6 is used for the voltage stability
assessment.
Figure VI.6 A 345kV transmission network for the voltage stability simulation:
three substation buses can be reconnected when the TCSR is installed.
To deal with the possible fault currents and voltage stability problems, the network is
operated by splitting buses and interchange flow on some transmission lines is
constrained. For the voltage stability assessment, a fault is applied far away from the
TCSR. In this case, it does not need to operate as a fault current limiter, because fault
currents cannot propagate farther as shown in Table VI.3. It can be seen that the fault
currents of other buses far away from 4400 bus are considerably reduced. With the
benefit of proposed control actions of the TCSR, we can expect that the voltage will be
44
maintained higher, and accordingly the voltage stability can be maintained with less
dynamic reactive reserves. The interchange flows are increased to 300MW and 475MW,
so the available transfer capability of 175MW is achieved. Fault currents are limited
within nominal ratings resulting in the reconnection of three split 345kV buses. In
addition, this reduces the transmission losses by 3MW at normal operating conditions.
The simulation results are summarized in Tables VI.4, VI.5 ana Figure VI.7 shows the P
V Curves on a special contingent case.
Figure VI.7 PV curves during normal and contingent conditions: maximum
incremental transfer is increased from 300MW to 475MW when the TCSR is
used.
Table VI.2 Comparison results of the voltase and the fault current
Fault Location Condition Prefault Voltage(kV) During the fault Postfault Fault Current(kA)
Without TCSR 186.38 148.5 186.38 9.5
FAR
With TCSR 193.9 176.2 193.9 11.2
Without TCSR 186.38 0 186.38 37.1
NEAR
With TCSR 193.9 0 193.9 38.5
45
Effects of TCSR on Bulk Power System Angle Stability
On the other hand, if the fault occurs near the place where the TCSR is installed,
e.g.a generation siteit should act both as a fault current limiter and a voltage restorer.
Fault current limitation and voltage restoration are controlled by a process of changing
the impedance of the TCSR, and angle stability is highly related to the impedance behind
the machine. Therefore, the power system angle stability can be enhanced by changing
the impedance of the TCSR. Based on the concept of Equal Area Criterion [17], power
system synchronism can be maintained under the condition where the accelerating power
is smaller than the decelerating power.
Generator
output Power
Figure VI.8 Power angle curve for Equal Area Criterion: power system
synchronism can be maintained when the accelerating power is smaller than the
decelerating power and inserting the series reactor decreases the accelerating
power as much as the hatched area.
46
Considering a Single Machine Infinite Bus (SMIB) system where double circuit
transmission line is connected in parallel, network conditions can be represented as:(1)
Prefault (both circuits in service), (2) During a threephase fault, (3) Postfault (circuit 2
out of service) and those are illustrated with P8 plots in Figure VI.8. When a short
circuit fault occurs, the TCSR reduces the accelerating power as much as the hatched area
by inserting the series reactor at the initial stage of the fault.
Figure VI.9 Network configuration for the transient stability simulation: a FCL
using permanentlyinserted series reactor is installed on a substation and two
contingency cases (FI,F2) are studied to analyze the influences of the FCL on
the power system angle stability.
To assess an impact of the TCSR on the bulk power system angle stability, another fault
is applied near the TCSR as shown in Figure VI.9. A permanently inserted series reactor
was installed to limit the shortcircuit current and a Special Protection Scheme (SPS)
such as transfertrip of some loads and generators, etc. has being applied. In this specific
case, simulation shows that the critical clearing time can be increased more than 50msec.
47
Table VI.3 Fault current of the adjacent buses with respect to 4400 bus fault
Table VI.4 Fault current of critical buses(kA)
Bus number Without TCSR With TCSR Rating
1400 43.08 35.34 40
1500 43.94 36.67 40
2500 51.05 48.25 50
Table VI.5 Case summary(MW)
Division Transmission loss Max. Incremental Transfer
Without TCSR 1070 300
With TCSR 1067 475
Table VI.6 Critical Clearing Time(msec)
Fault Location Without TCSR With TCSR Difference
FI 70 160 90
F2 50 100 50
Furthermore, considering circuit breaker braking time, we can reduce the number of
generators to be tripped when some generators should be tripped with SPS. Figures VI.10,
VI.11 and Table VI.6 show the simulation results using PSS/E. With the control action of
48
With TCSR
Without TCSR
a h
0123456739 10 [SEC]
(b)
Figure VI.10 Simulation results on FI fault: the power system can maintain
synchronism with the TCSR (a) Machine electrical power [P.U.] (b) Bus voltage
[P.U.l.
01^3456739 10 [SEC]
(a)
the TCSR, the output power of the machine and the system voltage can get to a new
stable operating point.
CPSi"K
nl' isl,?u,,r*'1u t*='
________jgg 1_HI________________
MM mjmf'ltrl u
1sIf.% t.............................* 
*3MITrl i;
49
(b)
Figure VI.11 Simulation results on F2 fault: the power system can maintain
synchronism with the TCSR (a) Machine electrical power [P.U.] (b) Bus voltage
[P.U.l.
seeker g
nv*1mfr mnMXv,lff,j7 t t..'I
ML lg3"5 aw 5 G
i
1
t i tit Is (111 I^
50
CHAPTER VII
CONCLUSION
Various kinds of Fault current limiters (FCLs) are being applied in a distribution
and transmission network. However, because of the disadvantages on power system
operations, such as transmission losses and inferior system stability, their usage has been
limitedwhich has adversely resulted in more investments on constructing transmission
lines, replacement of switchgear and degrading the system reliability. However, as the
transmission network is meshed and more generations are interconnected to the grid, a
capability to deal with both fault current and power system stability is required. This
paper has shown that fault currents and stability problems can be managed with the
TCSR and a PI controller. It has also been shown that the TCSR can maintain the voltage
higher during the fault situation. For the bulk power system, the proposed approach can
enhance the system reliability by reducing the number of split buses and increase the
available transfer capability and critical clearing time. The validity of the proposed
control scheme has been verified with computer simulation using Matlab,
PSCAD/EMTDC and PSS/E. The proposed method can be a viable option for the power
system planners and operators to make countermeasures to cope with fault current and
stability problems.
51
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Full Text 
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APPLICATION OF THYRISTOR CONTROLLED SERIES REACTOR FOR FAULT CURRENT LIMITATION AND POWER SYSTEM STABILITY ENHANCEMENT by B u I l K ang Bachelor of Science, Chonnam National University, 1994 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Master of Science Electrical Engin e ering 2013
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ii This thesis for the Master of Science degree by B u I l K ang has been approved for the Electrical Engineering Program b y Jae Do Park Chair Fernando Mancilla David Yiming Deng April 16, 2013
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iii K ang B u I l (M .S., Electrical Engineering) Application of Thyristor Controlled Series Reactor for Fault Current Limitation and Power System Stability Enhancement Thesis dire cted by Assistant Professor Jae Do Park ABSTRACT Various types of Fault Current Limiters (FCLs) have been proposed and proven that they offer many advantages with respect to transmission losses, voltage quality, and power system stability. However, those including the Solid State Fault Current Limiters (SSFCL), the most advanced type of FCL, have been mainly focusing on the FCL system itself such as optimization of components, improving the efficiency and reducing the cost. Conventional ways such as split ting buses, replacing the switchgear, and installing permanently inserted series reactor are still used to avoid fault current problems, which impairs overall power system reliability. In this thesis, a Thyristor Controlled Series Reactor (TCSR) is present ed to limit the fault current and enhance the power system stability simultaneously. The influence of TCSR is analyzed from the perspective of voltage security enhancement and the feasibility of real power system application is assessed. The benefits of th e TCSR are demonstrated with bulk power system simulation results from the voltage security and angle stability stand point. The form and content of this abstract are approved. I recommend its publication. Approved: Jae Do Park
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iv DEDICATION I dedicat e this work to Eungjeong, my lovely wife, who has always believed and supported me by my side.
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v ACKNOWLEDGMENTS This thesis would not have been possible without the support of my company, Korea Power Exchange (KPX).
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vi TABLE OF CONTENTS CHAPTER I. INTRODUCTION ................................ ................................ ................................ ....... 1 Introduction ................................ ................................ ................................ ............. 1 II. FAULT CURRENT LIMITERS ................................ ................................ ................. 3 Fault C urrent L imitation by a S eries R eactor ................................ ......................... 3 Bypass S witch ................................ ................................ ................................ ......... 4 Tuned LC C ircuit S hunted by a Metal Oxide Varistor (MOV) .............................. 5 Series C ompensator ................................ ................................ ................................ 6 Power E lectronic S witches ................................ ................................ ................... 11 III. POWER SYSTEM STABILITY ................................ ................................ ............... 13 Thyristor Controlled Series Compensator (TCSC) ................................ ............... 17 Short Circuit Current Limiter (SCC L) ................................ ................................ .. 20 IV. D Q TRANSFORMATION ................................ ................................ ...................... 22 V. PROPOSED APPROACH ................................ ................................ ......................... 29 Voltage Sta bilizing Fault Current Limiter ................................ ............................ 29 Plant Model and Compensator Design ................................ ................................ 32 VI. COMPUTER SIMULATIONS ................................ ................................ ................. 37 Duty C ontrol to I ncrease O utput V oltage ................................ ............................. 37 Effects of TCSR on D ifferent F ault L ocations ................................ ..................... 40 Effect s of TCSR on B ulk P ower S ystem V oltage S tability ................................ .. 44 Effects of TCSR on B ulk P ower S ystem A ngle S tability ................................ ..... 46 VII. CONCLUSION ................................ ................................ ................................ .......... 51
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vii LIST OF TABLES T able VI.1 Simulation parameters ................................ ................................ ............................. 38 VI.2 Comparison results of the voltage and the fault current ................................ .......... 45 VI.3 Fault current of the adjacent buses with respect to 4400 bus fault .......................... 48 VI.4 Fault current of critical buses(kA) ................................ ................................ ........... 48 VI.5 Case summary(MW) ................................ ................................ ................................ 48 VI.6 Critical Clearing Time(msec) ................................ ................................ .................. 48
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viii LIST OF FIGURES Figure II.1 Fault current limiter application: it protects the entire bus or individual circuit. ........ 4 II.2 Relationship between system voltage drop reactor short circuit voltage and power factor. ................................ ................................ ................................ ................................ .. 5 II.3 Fault current limiter with tuned impedance. ................................ ................................ 6 II.4 Fault current limiter using a tuned LC circuit shunted by a MOV ............................ 7 II.5 Power system network with SC ................................ ................................ ................. 8 II.6 Power system network during the source s ide fault with compensation .................... 9 II.7 Network model and phasor diagram under the prefault condition ........................... 10 II.8 Network model and pha sor diagram under the load side fault condition ................. 10 II.9 FCL using power electronic switches (a) Short Circuit Current Limiter (SCCL), (b) Solid State Fault Current Limiter (SSFCL) ................................ ................................ ..... 12 III.1 Shunt compensation with a current source (a) Network configuration, (b) Phasor diagram: V R can be controlled V R R by compensating the reactive component of the load current ................................ ................................ ................................ ...................... 13 III.2 Series compensation with a voltage source (a) Network configuration, (b) Phasor diagram: V R can be controlled by inserting V COMP and the appropriate magnitude control of V COMP ................................ ................................ ................................ ........................... 14 III.3 Equivalent circuit of single machine infinite bus system: a generator delivers power to an infinite bus through two transmission circuits ................................ ........................ 17 III.4 Power angel curve for Equal Area Criterion. ................................ .......................... 17 III.5 A practical configuration of TCSC. ................................ ................................ ......... 18 III.6 Impedance characterist ics of a TCSC with respect to firing angle. ......................... 19 III.7 The characteristics of SCCL and power angle curve (a) During normal operation, equivalent impedance is treated as zero and XL during the fau lt (b) Accelerating power is decreased as much as the hatched area by inserting the series reactor ............................ 20 IV.1 Axes of reference frame ................................ ................................ .......................... 23
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ix IV.2 Voltage and current waveforms when duty ratio is 0 where the current flows only through the series reactor (a) Load voltage (b) Current. ................................ .................. 27 IV.3 Voltage and current waveforms whe n duty ratio is 1 where the current flows only through the bypass switch (a) Load voltage (b) Current. ................................ ................. 28 V.1 Model for circuit analysis (a) Original circuit, (b) Equivalent circuit when switc h is off, (c) Equivalent circuit when switch is on ................................ ................................ ... 30 V.2 PI regulator with negative feedback ................................ ................................ .......... 34 VI.1 Step responses of the plan t: Uncompensated model has a steady state error (0.4651), which is eliminated by a PI controller where K P =0.8, K I =100 ................................ ........ 38 VI.2 Overall model configuration and the output voltage responses: the output voltage changes from about 245kV to 270kV based on the duty ratio which starts to increase from 0.5sec ................................ ................................ ................................ ....................... 39 VI.3 Typical power system model to investigate the effects of TCSR on fault cu rrents and voltage dips: faults can be occurred either near the TCSR or far away from it ........ 40 VI.4 Simulation results for the fault near the TCSR: The TCSR is required to be operated as fault cu rrent limiter and voltage restorer. (a) The bus voltage is operating in low level when the series reactor is inserted. (b) The fault current is exceeding the nominal value when the series reactor is bypassed. (c) Voltage is maintained higher and the fault current is limited within nominal value when the control scheme is applied. .............................. 42 VI.5 Simulation results for the fault far away from the TCSR: The TCSR is required to be operated as voltage resto rer. (a) The bus voltage is operating in low level when the series reactor is inserted. (b) The voltage is maintained higher and the fault current is in low level when the series reactor is bypassed. (c) Voltage is maintained higher and no control action i s required to limit the fault current. ................................ ................................ ....... 43 VI.6 A 345kV transmission network for the voltage stability simulation: three substation buses can be reconnected when the TCSR is installed ................................ .................... 44 VI.7 P V curves during normal and contingent conditions: maximum incremental transfer is increased from 300MW to 475MW when the TCSR is used ......................... 45 VI.8 Power angle curve for Equal Area Criterion: power system synchronism can be maintained when the accelerating power is smaller than the decelerating power and inserting the series reactor decreases the accelerating power as much as the hatc hed area ................................ ................................ ................................ ................................ ........... 46 VI.9 Network configuration for the transient stability simulation: a FCL using permanently inserted series reactor is installed on a substation and two contingency cases (F1, F2) are studied to analyze the influences of the FCL on the power system angle stability ................................ ................................ ................................ ............................. 47
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x VI.10 Simulation results on F1 fault: the power system can maintain synchronism with the TCSR (a) Machi ne electrical power [P.U.] (b) Bus voltage [P.U.] ........................... 49 VI.11 Simulation results on F2 fault: the power system can maintain synchronism with the TCSR (a) Machine electrical power [P.U.] (b) Bus voltage [P.U.] ........................... 50
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xi LIST OF EQUATIONS Equation II.1 Equation for system voltage drop. ................................ ................................ ................ 3 II.2 Equation for the current increase. ................................ ................................ ................ 5 II.3 Equation for the receiving end voltage. ................................ ................................ ....... 7 II.4 Circuit equations ................................ ................................ ................................ ......... 7 II.5 Injection voltage equation ................................ ................................ .......................... 8 II.6 Current and voltage equations under the prefault condition ................................ ....... 9 II.7 Current and voltage equation during the fault ................................ ............................. 9 III.1 Voltage equation for simple AC circuit ................................ ................................ ... 15 III.2 Voltage equation for the series compensated AC system ................................ ........ 15 III.3 Relationship between the rotor angle and the accelerating power ........................... 16 III.4 Equivalent impedance of TCSC ................................ ................................ ............... 19 IV.1 Transformation matrix ................................ ................................ ............................. 22 IV.2 Column vector and transformation matrix ................................ ............................... 23 IV.3 Conversion variables in different reference frames ................................ ................. 24 IV.4 Conversion variables in the stationary reference frames ................................ ......... 24 IV.5 Conversion variables in the synchronous reference frames ................................ .... 25 IV.6 Space vector represented by three phase components ................................ ............. 25 IV.7 Space vector in the stationary reference frame ................................ ........................ 26 IV.8 Transformation to other reference frame ................................ ................................ 26 IV.9 Individual variables f a f b f c ................................ ................................ ..................... 26 V.1 Voltage and current equations in case the thyristor switches are open ..................... 29 V.2 Voltage and current equations in case the thyristor switches are close .................... 31
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xii V.3 Averaged voltage and current dynamic equations ................................ .................... 32 V.4 Linearized function ................................ ................................ ................................ ... 32 V.5 Dynamic model including steady state term and linear small signal term ............... 33 V.6 Linearized small signal dynamic model ................................ ................................ ... 33 V.7 Control transfer functions ................................ ................................ ........................ 34 V.8 Control transfer function for the plant model ................................ .......................... 35 V.9 A PI compensator model ................................ ................................ .......................... 35 V.10 Closed loop transfer function ................................ ................................ ................. 35
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1 CHAPTER I INT RODUCTION Introduction Demand on electricity has been increasing tremendously and many countries invest significant amount of money for reliable power supply. More generation plants and transmission lines were constructed and the power systems became more complex. Major transmission lines tend to be long distance and generation sites are large scaled. Load concentration requires more transmission lines to be interconnected. However, those characteristics of power systems have been causing problems related t o fault currents and system stabilities. Several approaches to cope with the fault current problems are being used in distribution and transmission areas. Permanently inserted series reactors, up rating and replacement of switchgear, splitting buses or tra nsmission lines are the most commonly used techniques to limit the fault current in power systems, which are regarded as cost effective and more secure measures for the operational reliability of power system facilities. However, up rating and replacement of switchgear can be very expensive and short circuit current duty may not be reduced. Network splitting can deteriorate the power system security. Permanently inserted current limiting series reactors introduce a voltage drop, active and reactive power lo sses and also adversely affect the power system stability. In spite of these drawbacks, a lot of power systems are still divided into several subsystems to solve fault current problems. For the power system stability enhancement, on the other hand, the fol lowing has been used as countermeasures in general: (1) Constructing more interconnection lines, (2)
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2 Installing dynamic reactive resources, (3) Constraining power transfers, and (4) Using Special Protection Schemes (SPS). So far, fault current and stabilit y analysis has been studied separately, since network configuration influences in an opposite way to those problems. When transmission systems are fully meshed, they tend to yield fault current problems, rather than stability problems. On the other hand, w hen powers are delivered through high impedance transmission lines, stability issues may arise instead of fault current problems. However, as the power systems become more complex with the meshed transmission networks which are interconnected with long dis tance, high power transfer transmission lines, those two problems become co existent. Consequently, countermeasures to deal with the fault current impact more on the power system stability than before. In this work, prior researches related to fault curren ts limitation and power system stability enhancement are reviewed and a TCSR that limits the fault current and improves the stability simultaneously is presented. The influence of the TCSR from the perspective of voltage security enhancement is shown with a theoretical analysis, and to assess the feasibility of the TCSR to real power systems, the benefits of the TCSR are demonstrated with bulk power system simulation results.
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3 CHAPTER II FAULT CURRENT LIMITERS Fault current limiters can be applied in a va riety of distribution and trans mission areas. Those can be used for the protection of entire bus or individual circuit as in Fig ure II.1. For the last 20 years, s uper conductive FCLs have been studied and suggested to limit the fault current, but they have not been used widely in the fie ld because of the cost problem. Reactors, high impedance transformers, circuit breaker upgrades and splitting buses or transmission lines are still widely used. Because of the fault current problem, many power system ope rators are sacri fi cing their system reliability by splitting the network into many sub systems. However, comparing to the Superconductive FCL, these methods have many disadvantages with respect to transmission losses and system reliability. Many alternativ e ways to overcome those problems have been suggested. Fault C urrent L imitation by a S eries R eactor Most commonly used FCLs are permanently inserted series reactor type fault current limiters. As this type of fault current limiter does not require replacem ent of switchgear and more economical than others, it is commonly used in power systems. The fault current driven by the voltage source is reduced by the impedance of the reactor. Equation II 1 Equation for system voltage drop.
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4 Figure II 1 Fault current limiter application: it protects the entire bus or individual circuit. However, it may cau se severe voltage drop during contingent state, while the system voltage drop may not represent a particular problem during normal operating conditions [1]. The system voltage drop can be calculated using the following equation and Fig ure II .2 shows the re lationship between system voltage drop, reactor short circuit voltage V k and power factor. Bypass S witch In the 1980s, most power systems were operating with splitting network topology such as splitting buses or opening transmission lines at normal operat ing conditions to limit the fault current. A tuned circuit impedance method was proposed to limit the fault current by Electric Power Research Institute (EPRI) [2]. Fig ure II .3 shows the basic configuration of this circuit. Under normal operating condition s, the switch is opened and transmission line has zero net impedance if they are tuned properly. When a fault occurs, the switch is closed and the equivalent impedance becomes where X is the impedance
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5 of the reactive components, which results i n fault current reduction. Although it requires high initial cost, its zero net impedance during normal operating conditions can reduce the operating cost such as transmission loss; besides, the system voltage recovers to its prefault level after clearing the fault. Figure II 2 Relationship between system voltage drop, reactor short circuit voltage and power factor. Tuned LC C ircuit S hunted by a Metal Oxide Varistor (MOV) This type of FCL was developed for th e fault current limitation and power quality improvement [3]. It consists of a series LC circuit tuned at the system frequency and a MOV in parallel with the capacitor as shown in Fig ure II .4. Since the LC circuit is well tuned, it is almost transparent du ring normal operation. When there is a fault in the downstream of the FCL, it forces a gradual increase of the current, which is justified by the following equations. Equation II 2 Equation for the current increase.
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6 W here, V P : magnitude of the source voltage, : phase angle of the sou rce voltage, Z: the magnitude of the load impedance, : load angle. Figure II 3 Fault current limiter with tuned impedance. This shows that the higher the L, the slower the current increase, which reduces th e voltage sag during the fault. However, since the voltage on the L and C will increase during the fault, additional device to limit the over voltage is required. MOV is connected in parallel with the capacitor, and it absorbs the excessive energy in case its protection level is reached. However, long cool down time of the MOV and possibility of Sub Synchronous Resonance (SSR) [4] are the drawback to be solved Series C ompensator Dynamic voltage restorer (DVR) using energy storage device and a series compen sator (SC) shown in Fig ure II .5 was proposed to limit the fault current and improve the voltage quality of the power system [5, 6]. By controlling the amplitude and
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7 phase angle, they control the real and reactive power between the controller and the power system. Figure II 4 Fault current limiter using a tuned LC circuit shunted by a MOV During normal operating conditions where the receiving end voltage V L is given by Equation II 3 Equation for the receiving end voltage. the SC does not operate. However, when there is a fault in the network, it compensates the voltage by injecting a lagging or leading voltage in quadrature with the load (fault) current to restore the line voltage and limit the fault current. Considering a fault at the source side, the voltage of the source will be dropped, and the circuit equation becomes Equation II 4 Circuit equations
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8 W here and are the load side voltage, line current, and SC side voltage vector during the fault respectively. Figure II 5 Power system network with SC To enhance the voltage drop, the SC injects a lagging voltag e until the load side voltage is restored to its prefault level as shown in Fig ure II .6. Since is the voltage on the sour ce side of the SC and if we set then the injection voltage becomes Equation II 5 Injection voltage equation : measured voltage on the source side of the Series Compensator (SC) By injecting a lagging vol tage, we allow the DVR to restore the load side voltage to its pre de fi ned
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9 level under normal and contingency conditions. On the other hand, if the fault occurs at the load side, the SC should act as a fault current limiter. Figure II 6 Power system network during the source side fault with compensation The current and voltage equations under the prefault condition can be expressed as Equation II 6 Current and voltage equations under the prefault condition and the syst em model is shown in Fig ure II .7. During the fault where the = 0, those equations become Equation II 7 Current and voltage equation during the fault
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10 From the comparison between equation II.6 and equation II.7 we see that the fault current can be limited to the load current when is restored to The SC injects a leading voltage until is restored into its prefault level as shown in Fig ure II 8 Figure II 7 Network model and phasor diagram under the prefault condition Figure II 8 Network model and phasor diagram under the load side fault condition
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11 Power E lectronic S witches A great deal of power electronics based FCLs have been proposed for fault current limitation and power sy stem stability enhancement. With the development of power electronic devices and control technologies, a large number of Flexible AC Transmission Systems (FACTS) devices have been developed and are in operation extensively for the security enhancement of p ower systems [7]. FCLs using solid state devices such as Insulated Gate Bipolar Transistor (IGBT), Silicon Controlled Rectifier (SCR), and Gate Turn off Thyristor (GTO) can be classified into (1) Series Switch type FCL, (2) Bridge type FCL, and (3) Resonan t FCL [8]. The basic operational principle of SSFCLs is almost same in that currents flow through zero impedance path in steady state and they are switched into the fault current limiting reactor in case of short circuit c onditions. However, the configurat ion of SSFCLs can be di ff erent based on their application purpose. Different types of Series Switch type FCLs were described [9] and an application of a Thyristor Controlled Series Reactor was presented to reduce furnace arc flicker [10]. Bridge type FCLs using different types of switching device were also proposed [11, 12], and the influence of this type of FCL was investigated in terms of power system transient stability [13]. Another application using FACTS based Short Circuit Current Limiter (SCCL) was suggested in [14], where thyristor Protected Series Compensator (TPSC) combined with an external reactor showed the benefits for fault current limitation and SSR mitigation. Transient stability was also evaluated with this type of series capacitor compensa ted FCL in [15]. Basic configurations for those FCLs are illustrated in Fig ure II .9.
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12 (a) (b) Figure II 9 FCL using power electronic switches (a) Short Circuit Current Limiter (SCCL), (b) Solid State Faul t Current Limiter (SSFCL)
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13 CHAPTER III POWER SYSTEM STABILITY For the voltage and reactive power compensation, we usually use reactive power compensator such as static condensers, shunt reactors which are static reactive sources being used for steady sta te voltage regulations and thyristor controlled series condensers, thyristor controlled reactors which are dynamic reactive sources being used for transient stability enhancement. (a) (b) Figure III 1 Shu nt compensation with a current source (a) Network configuration, (b) Phasor diagram: V R can be controlled V R to V R by compensating the reactive component of the load current
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14 (a) (b) Figure III 2 Series compensation with a voltage source (a) Network configuration, (b) Phasor diagram: V R can be controlled by inserting V COMP and the appropriate magnitude control of V COMP They can be connected to the system in series or in shunt. To reduce transmission lo sses and improve the voltage regulation and stability, we normally compensate reactive powers near the load. By injecting the reactive component of the current near the load, a compensator can control the current from the generator resulting in voltage reg ulation improvement in the load side. Considering leading compensation, we can increase the
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15 load side voltage to V R with the same source voltage V S In addition, we can reduce relatively large amount of reactive losses compare to uncompensated system. The refore, this kind of compensation is usually used for voltage stability enhancement. Fig ure III .1 shows the principle of shunt reactive power compensation in a simple AC circuit which can be represented as Equation III 1 V oltage equation for simple AC circuit Based on the compensation types required, inductors or capacitors can be used. For independent control with the voltage at the connection point, current source or volt age source compensator can be used [16]. Var compensation can also be realized using series compensator. Typical series compensation is made by series capacitors and Fig ure III .2 shows the principles of series compensation in a radial AC system which can b e represented as Equation III 2 Voltage equation for the series compensated AC system The voltage angle of V R can be changed by inserting V COMP between the line and the load. With the appropriate magnitude control of V COMP V R can be controlled. This kind of series compensation gives three main benefits to the transmission system. (1) Increase angular stability of the system (2) Improve voltage stability of t he system (3) Optimize power sharing between parallel circuits. Equal Area Criterion is generally used to understand basic factors that influence the transient stability of power systems [17]. It basically uses the relationship between the rotor angle and the accelerating power.
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16 Equation III 3 Relationship between the rotor angle and the accelerating power W here, P M : mechanical power, P E : electrical power, : rotor angle, in electrical radian, H: inertia constant, in MWs/MVA. Let us consider the response of single machine infinite bus system to a three phase fault on transmission line2, as shown in Fig ure III .3. Network conditions can be represented as: (1) Pr efault (both circuits in service), (2) During a three phase fault, (3) Postfault (circuit 2 out of service) and those are illustrated with P plots in Fig ure III .4. Initially, the system is operating where P M = P E When the fault occurs, P E goes down to b. At this point, since P M is greater than P E the rotor starts to accelerate until the fault is cleared. When the fault is cleared, the opera ting point shifts to d based on the line condition. However, since the rotor speed is greater than the synchronous speed, it continues to increase until the kinetic energy gained during the acceleration period is exhausted. The operating point moves to e, where the accelerating power is equal to the decelerating power. At point e, the rotor speed is equal to the synchronous speed, but P E is greater than P M Therefore, the rotor starts to decrease the speed following the P curve for the single circuit condition. In the presence of any source of damping, the rotor finally gets to a new stable operating point. With a delayed fault clearing, acceleration power is greater than deceleration power, leading to loss of synchronism
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17 Figure III 3 Equivalent circuit of single machine infinite bus system: a generator delivers power to an infinite bus through two transmission circuits Figure III 4 Power angel curve for Equal Area Criterion. Thyristor Controlled Series Compensator (TCSC) A typical TCSC consists of a Fixed Series Capacitor (FC) in parallel with a Thyristor Controlled Reactor (TCR). The bi directional thyristor valves are red with a phase angle ranging between 90 and 180 with respect to the capacitor voltage. A Metal
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18 Oxide Varistor (MOV) is used to prevent the over voltage across the capacitor. A circuit breaker is installed across the capacitor and it bypasses the capacitor w hen severe faults or equipment malfunction events occur. Conduction losses of the TCSC valves can be minimized by installing an Ultra High Speed Contact (UHSC) across the valve. It is closed shortly after the thyristor valve is turned on, and opened shortl y before the valve is turned o ff. During a sudden overload of the valve and fault conditions, the metallic contact is closed to alleviate the stress on the valve [18]. Figure III 5 A practical configuration of TCSC. Fig ure III .5 shows a practical con fi guration of TCSC. The main capabilities of the TCSC can be achieved by changing the impedance of the line where it is connected, which can be done by controlling the fi ring angle of the thyristors. Variation of X L with respect to fi ring angle and the equivalent impedance of the TCSC are given as the following equations
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19 Equation III 4 Equivalent impedance of TCSC W here, = 2( ) is the conduction angle of TCSC and k = is the c ompensation ratio F ig ure III .4 shows the impedance characteristics of a TCSC The followings represent the main functions of a TCSC. (1) Damping of the power swings from local and inter area oscillations, (2) Suppression of subsynchronous oscillations, ( 3) Voltage support, and (4) Reduction of the short circuit current. Figure III 6 Impedance characteristics of a TCSC with respect to firing angle.
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20 Short Circuit Current Limiter ( SCCL ) SCCL is developed fro m the series compensation which normally uses a capacitor to compensate the inductor used as a fault current limiter, thus the line is regarded as short circuited. During normal operation, the FCL compensated with series capacitor increases the steady stat e stability limit. When a short circuit fault occurs, the FCL can reduce the accelerating power at the initial stage of the fault and provide additional decelerating power at the fault clearing stage [15]. (a) (b) Figure III 7 The characteristics of SCCL and power angle curve (a) During normal operation, equivalent impedance is treated as zero and XL during the fault (b) Accelerating power is decreased as much as the hatched area by inserting the series rea ctor
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21 Fig ure III .7 shows an example of a single line fault where double circuit transmission line becomes single circuit transmission line. The accelerating power will be decreased as much as the hatched area and power system synchronism can be maintained if the resultant accelerating power is smaller than the decelerating power.
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22 CHAPTER IV D Q TRANSFORMATION We transform time varying voltage, current di ff erential equations into time i nvariant di ff erential equations. As it is not only ea sy to solve but also easy to understand and control. A, B, C phase variables in three phase AC system are transformed into orthogonal d, q, n axes variables [21]. Direct axis d represents the axis where excitation fl ux (or main fl ux) is and quadrature axis is 90 degree in electrical angle ahead to d axis in positive rotational direction and neutral axis is orthogonal to d q axes in three dimensional space s Fig ure IV .1 represents axes of reference frames, where superscript s denotes stationary reference fra me, e synchronous reference frame, w arbitrary rotating speed and is de fin ed as T he transformation matrix can be derived as Equation IV 1 Transformation matrix T he column vectors of variable s are given as
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23 Equation IV 2 Column vector and transformation matrix Figure IV 1 Axes of reference frame The variables in the thre e phases axis can be converted both to the variables in the stationary reference frame and to the variables in the arbitrary reference frame as
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24 Equation IV 3 Conversion variables in different reference frames If the system is balanced, that is f a + f b + f c = 0, and convert the variables in the three p hase axis to the variables in the stationary reference frame, then Equation IV 4 Conversion variables in the stationary reference frames Likewise, the variables in the synchronous reference frame can be converted with respect to the stationary reference frame as
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25 Equation IV 5 Conversion variables in the synchronous reference frames As a result, when the space vector by three phase components can be represented as the equation IV.7, t hree phase variables can be represented by only two orthogonal co mponents of a complex vector. Equation IV 6 Space vector represented by three phase comp onents The real part of f abc equals to which is correspondent to f s d and the imaginary part of f abc equals to which is correspondent to f s q Consequently, the equation to tra nsform a space vector fabc to the space vector in d q axes which are stationary can be expressed as
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26 Equation IV 7 Space vector in the stationary reference frame Likewise, from the previous relationship between the synchronous reference frame and stationary reference frame and using Euler equation and basic vector modi fi cation, we can derive th e t ransformation to other reference frame as Equation IV 8 Transformation to other reference frame Inversely, we can extract the individual variables fa, fb, fc from the space vector f abc Equation IV 9 Individual variables f a f b f c This approach is demonstrated with a speci fi c R L circuit shown in Fig ure V .1 (a) and parameters used in Table VI .1. Following fi gures are the voltage and current respon ses with respect to di ff erent duty ratios.
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27 (a) (b) Figure IV 2 Voltage and current waveforms when duty ratio is 0 where the current flows only through the series reactor (a) Load voltage (b) Current.
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28 (a) (b) Figure IV 3 Voltage and current waveforms when duty ratio is 1 where the current flows only through the bypass switch (a) Load voltage (b) Current.
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29 CHAPTER V PROPOSED APPROACH In order to demon strate the advantages of the TCSR, especially from the voltage point of view, a simple R L circuit shown in Fig ure V .1 (a) is used. The receiving end voltage is controlled by changing the equivalent impedance of FCL. To achieve this goal, following approac h is proposed. A state space model is constructed and averaged using d q transformation method. Since the input (duty) and output (v R ) variables feature nonlinear relationships, linearization technique is applied to the averaged state space model to obtain a system transfer function. A PI controller is designed to get a better dynamic response and zero steady state error. Voltage Stabilizing Fault Current Limiter When the thyristor switch is open, the network in Fig ure V .1 (a) becomes as shown in Fig ure V .1 (b) and the voltage and current dynamic equations are given as Equation V 1 Voltage and current equations in case the thyristor switches are open and the superscript e denotes synchronous reference frame. When the switch is closed, the network becomes like Fig ure V .1 (c) and the voltage and current dynamic equations become
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30 (a) (b) (c) Figure V 1 Model f or circuit analysis (a) Original circuit, (b) Equivalent circuit when switch is off, ( c ) Equivalent circuit when switch is on
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31 Equation V 2 Voltage and current equations in case the thyristor switches are close L EQ = L FCL L TCR / (L FCL +L TCR ). These equations can be arranged into a set of state equations as W here, x: state variable, u: input variable, y: output variable. As the average behavior of the system is dependent on the conduction time of the thyristors [19], if we define the conduction and off conduction time as T T and T B respectively, we can rewrite the p revious equations into two sets of state equations depending on the different conduction stages W here T S = T T + T B : switching time, and subscript T and B denote ON and OFF, respectively. The averaged model for the system can be expressed as the following set of state equation s
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32 = T T /T S = 1 d, = T B /T S = d Applying this relationship into the s ystem model equations V.1, V.2, then, Equation V 3 Averaged voltage and current dynamic equations As a result, the vol tage drop on the fault current limiting reactor can be limited by the following factor and controlled by duty d. Plant Model and Compensator Design However, the system model is nonlinear because the duty is also a function of time. Therefore, we need to linearize the non linear equation to solve. C onsidering non linear functio n and applying Taylor formula at Z = Z 0 the linearized function can be approximated as Equation V 4 Linearized function For the controller design, we de fi ne state variable, input, and output vector as
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33 then the state equations can be written as If we apply linearization method at a n operati ng point where steady state values are I L V S D V R X U, the dynamic model can be expressed with steady state terms and linear small signal terms as Equation V 5 Dynamic model including steady state term and linear small signal term From these equations, we get the following linearized small signal dynamic model of the system. Equation V 6 Linearized small signal dynamic model Rewriting the equations leads to the following form as and applying superposition rule gives the following control transfer functions ( = 0).
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34 Equation V 7 Co ntrol transfer functions Figure V 2 PI regulator with negative feedback In the synchronous d q reference frame, AC quantities can be treated as DC. In addition, by aligning the voltage vector to the d axis, the output voltage of the q axis can be set to zero. Therefore, substituting the equation V.7 with the derived values we obtain the following transfer function.
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35 Equation V 8 Control transfer function for the plant model Our plant and compensator transfer fu nction can be expressed with G vd (s) and G c (s) in Fig ure V .2. To improve low frequency loop gain and regulation, a PI compensator is designed. Equation V 9 A PI compensator model The closed loop transfer function is given as Equation V 10 Closed loop transfer function T he loop gain T = G c (s) G vd (s) Routh's Stability Criterion can be used to determine the ranges of coe ffi cients of polynomials for stability [20]. Considering the characteristic equation of an nth order system, the Routh array can be arranged as the following form
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36 H(s) = s n + a 1 s n 1 + a 2 s n 2 + + a n 1s + a n Row n s n : 1 a 2 a 4 Row n 1 s n 1 : a 1 a 3 a 5 Row n 2 s n 2 : b 1 b 2 b 3 Row n 3 s n 3 : c 1 c 2 c 3 : : : : : : Row 2 s 2 : Row 1 s 1 : Row 0 s 0 : A necessary and sufficient condition for stability is that all the elements in the first column of the Routh array are positive and it is shown that it is true for equation V.8 and V.9
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3 7 CHAPTER VI COMPUTER SIMULATIONS Duty C ontrol to I ncrease O utput V oltage This approach is demonstrated with the R L circuit shown in Fig ure V .1 and parameters use d for the simulation are shown in Table VI .1. The transfer function of the plant model can be derived from V.8 which is given as It has a constant steady state error, because the plant model has a small value when s = 0. To eliminate the steady state error, we have designed PI compensator, which gi ves the open loop transfer function as T he characteristic equation of the close loop transfer function as Applying Routh's Stability Criterion to the characteristic equation of the close loop transfer function gives K P = 0 8 and K I = 100. As a result, the PI compensated transfer function becomes Steady state error is eliminated and the bus voltage can be enhanced by controlling the duty ratio of the TCSR. The output voltages are controlled from 245kV to 270kV based
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38 on the duty rat io which starts to increase from 0.5sec. The step responses of the system and the output voltage responses with respect to different duty ratios are shown in Fig ures VI .1 and VI .2. Simulations are done with MATLAB. Table VI 1 Simulation parameters V S R T R L L T L FCL L TCR 345kV 0.82 41.06 0.015H 0.025H 0.00025H Figure VI 1 Step responses of the plant: Uncompensated model has a steady state error (0.4651), which is eliminated by a PI controller where K P =0.8, K I =100
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39 (a) (b) F igure VI 2 Overall model configuration and the output voltage responses: the output voltage changes from about 245kV to 270kV based on the duty ratio which starts to increase from 0.5sec
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40 Effects of TCSR on D ifferent F ault L ocations Because the network is more complex than the simple R L circuit in Fig ure V .1 (a), we need to consider faults that occur at different locations, e.g., near or far from the TCSR. When the fault occurs near the TCSR, the fault curre nt will be high and the voltage will be low. Then the TCSR is required to operate as a fault current limiter and voltage restorer. On the other hand, when the fault occurs at a location far away from the TCSR, both the fault current and the voltage will be low. Then it does not need to act as a fault current limiter, but as a voltage restorer. This has been shown by PSCAD/EMTDC model shown in Fig ure VI .3. Figure VI 3 Typical power system model to investigat e the effects of TCSR on fault currents and voltage dips: faults can be occurred either near the TCSR or far away from it The fault current is confined within nominal short circuit current level with the series reactors and voltage drop due to the serie s reactor is around 4% which can be derived from the following equation [1].
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41 where : system voltage drop, V k : reactor short circuit voltage, and cos : power factor. In this system, possible issues are fault current problems in case the faults occur near the TCSR and under voltage problems when the faults occur far away from the TCSR. Control actions of the TCSR enhance the voltages and limit the fault currents within nominal ranges. It can be seen that the fault currents for the near fault are limited wit hin 40kA, which is the nominal short circuit current, and the voltages are maintained higher in both cases. Fig ure s VI .4 VI .5 and Table VI .2 show the simulation results. (a) (b)
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42 (c) Figure VI 4 Simulati on results for the fault near the TCSR: The TCSR is required to be operated as fault current limiter and voltage restorer. (a) The bus voltage is operating in low level when the series reactor is inserted. (b) The fault current is exceeding the nominal val ue when the series reactor is bypassed. (c) Voltage is maintained higher and the fault current is limited within nominal value when the control scheme is applied. (a)
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43 (b) (c) Figure VI 5 Simulation res ults for the fault far away from the TCSR: The TCSR is required to be operated as voltage restorer. (a) The bus voltage is operating in low level when the series reactor is inserted. (b) The voltage is maintained higher and the fault current is in low leve l when the series reactor is bypassed. (c) Voltage is maintained higher and no control action is required to limit the fault current
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44 Effects of TCSR on B ulk P ower S ystem V oltage S tability To assess the benefits of the TCSR from the stability point of vie w, computer simulations have been performed with a bulk power system where the total demand is 73,000MW. A typical power system shown in Fig ure VI .6 is used for the voltage stability assessment. Figure VI 6 A 345kV transmission network for the voltage stability simulation: three substation buses can be reconnected when the TCSR is installed To deal with the possible fault currents and voltage stability problems, the network is operated by splitting buses and inter change flow on some transmission lines is constrained. For the voltage stability assessment, a fault is applied far away from the TCSR. In this case, it does not need to operate as a fault current limiter, because fault currents cannot propagate farther as shown in Table VI .3. It can be seen that the fault currents of other buses far away from 4400 bus are considerably reduced. With the benefit of proposed control actions of the TCSR, we can expect that the voltage will be
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45 maintained higher, and accordingly the voltage stability can be maintained with less dynamic reactive reserves. The interchange flows are increased to 300MW and 475MW so the available transfer capability of 175MW is achieved. Fault currents are limited within nominal ratings re sulting in the reconnection of three split 345kV buses. In addition, this reduces the transmission losses by 3MW at normal operating conditions. The simulation results are summarized in Tables VI .4, VI .5 and Fig ure VI .7 shows the P V Curves on a special co ntingent case. Figure VI 7 P V curves during normal and contingent conditions: maximum incremental transfer is increased from 300MW to 475MW when the TCSR is used Table VI 2 Comparison results of the voltage and the fault current Fault Location Condition Voltage(kV) Fault Current(kA) Prefault During the fault Postfault FAR Without TCSR 186.38 148.5 186.38 9.5 With TCSR 193.9 176.2 193.9 11.2 NEAR With out TCSR 186.38 0 186.38 37.1 With TCSR 193.9 0 193.9 38.5
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46 Effects of TCSR on B ulk P ower S ystem A ngle S tability On the other hand, if the fault occurs near the place where the TCSR is installed, e.g., a generation site, it should act both as a fault cu rrent limiter and a voltage restorer. Fault current limitation and voltage restoration are controlled by a process of changing the impedance of the TCSR, and angle stability is highly related to the impedance behind the machine. Therefore, the power system angle stability can be enhanced by changing the impedance of the TCSR. Based on the concept of Equal Area Criterion [17], power system synchronism can be maintained under the condition where the accelerating power is smaller than the decelerating power. Figure VI 8 Power angle curve for Equal Area Criterion: power system s ynchronism can be maintained when the accelerating power is smaller than the decelerating power and inserting the series reactor decreas es the accelerating power as much as the hatched area
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47 Considering a Single Machine Infinite Bus (SMIB) system where double circuit transmission line is connected in parallel, network conditions can be represented as: (1) Prefault (both circuits in servic e), (2) During a three phase fault, (3) Postfault (circuit 2 out of service) and those are illustrated with P lots in Fig ure VI .8. When a short circuit fault occurs, the TCSR reduces the accelerating power as much as the hatched area by inserting the series reactor at the initial stage of the fault. Figure VI 9 Network configuration for the transient stability simulation: a FCL using permanently inserted series reactor is installed on a substation and two contingency cases (F1, F2) are studied to analyze the influences of the FCL on the power system angle stabil ity To assess an impact of the TCSR on the bulk power system angle stability, another fault is applied near the TCSR as shown in Fig ure VI .9. A permanently inserted series reactor was installed to limit the short circuit current and a Special Protection Scheme (SPS) such as transfer trip of some loads and generators, etc. has being applied. In this specific case, simulation shows that the critical clearing time can be increased more than 50msec.
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48 Table VI 3 F ault current of the adjacent buses with respect to 4400 bus fault Level Faulted bus Adjacent bus 4400 4600 6950 2400 4450 2600 3250 0 55.4 49.7 50.5 34.8 34.8 31.0 47.5 1 4600 34.7 15.0 6950 29.5 21.0 2 2400 10.2 24.6 4450 16.0 1 8.8 3 2600 1.2 29.8 3250 17.3 30.2 Table VI 4 Fault current of critical buses(kA) Bus number Without TCSR With TCSR Rating 1400 43.08 35.34 40 1500 43.94 36.67 40 2500 51.05 48.25 50 Tabl e VI 5 Case summary(MW) Division Transmission loss Max. Incremental Transfer Without TCSR 1070 300 With TCSR 1067 475 Table VI 6 Critical Clearing Time(msec) Fault Location Without TCSR With TCSR Difference F1 70 160 90 F2 50 100 50 Furthermore, considering circuit breaker braking time, we can reduce the number of generators to be tripped when some generators should be tripped with SPS. Fig ure s VI .10 VI .11 and Table VI .6 show the simulation results using PSS/E. With the control action of
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49 the TCSR, the output power of the machine and the system voltage can get to a new stable operating point. (a) (b) Figure VI 10 Simulation results on F1 fault: the power system can maintain synchronism with the TCSR (a) Machine electrical power [P.U.] (b) Bus voltage [P.U.]
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50 (a) (b) Figure VI 11 Simulation results on F2 fa ult: the power system can maintain synchronism with the TCSR (a) Machine electrical power [P.U.] (b) Bus voltage [P.U.]
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51 CHAPTER VII CONCLUSION Various kinds of Fault current limiters (FCLs) are being applied in a distribution and transmission network. However, because of the disadvantages on power system operations, such as transmission losses and inferior system stability, their usage has been limited, which has adversely resulted in more investments on constructing transmission lines, replacement of switchgear and degrading the system reliability. However, as the transmission network is meshed and more generations are interconnected to the grid, a capability to deal with both fault current and power system stability is required. This paper has shown t hat fault currents and stability problems can be managed with the TCSR and a PI controller. It has also been shown that the TCSR can maintain the voltage higher during the fault situation. For the bulk power system, the proposed approach can enhance the sy stem reliability by reducing the number of split buses and increase the available transfer capability and critical clearing time. The validity of the proposed control scheme has been verified with computer simulation using Matlab, PSCAD/EMTDC and PSS/E. Th e proposed method can be a viable option for the power system planners and operators to make countermeasures to cope with fault current and stability problems.
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52 REFERENCES circuit current limitation by series reactors," 2009. [ Power Apparatus and Systems, IEEE Transactions on, vol. PAS 99, no. 5, pp. 1964 1969, sept. 1980. t limitation," Power Delivery, IEEE Transactions on, vol. 16, no. 1, pp. 12 17, jan 2001. and Systems, IEEE Transactions on, vol. PAS 99, no. 2, pp. 506 511, march 1980. based dynamic voltage restorer," Power Delivery, IEEE Transactions on, vol. 14, no. 3, pp. 1181 1186, jul 1999. fault current limiting function," Power Delivery, IEEE Transactions on, vol. 20, no. 3, pp. 2248 2256, july 2005. performance improvement," in CEPSI Conference, 2006 Exhibition, No vember 2006. state fault current limiters," Power Electronics, IEEE Transactions on, vol. 27, no. 6, pp. 2770 2782, june 2012. current limiter for medium voltage systems, in Applied Power Electronics Conference and Exposition 2004, APEC '04 Nineteenth Annual IEEE, vol. 3, 2004, pp. 1825 1831 Vol.3 controlled series reactor to reduce arc furnace flicker in ELEKTROTEHNISKI VESTNIK 78 2011, pp. 112 117 [11] Z.Lu, D.Jiang, and Z.Wu, A new topology of fault current limiter and its p arameter s optimization" in Power Electronics Specialist Conference, 2003 PESC '03 2003 IEEE 34th Annual, vol. 1 june 2003, pp. 462 465 vol.1. [12] W. Fei, Y. Zhang, and Z. Lu, Novel bridge type fcl based on self turno devices for three phase pow er systems," Power Delivery, IEEE Transactions on, vol. 23, no. 4, pp. 2068 2078, oct. 2008.
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53 [13] A. Fereidouni, B. Vahidi, T. Hoseini Mehr, and M. Garmroodi Doiran, Enhancement of power system transient stability and power quality using a novel solid st ate fault current limiter," Journal of Electrical Engineering & Technology, vol. 6, no. 4, pp. 474 483, 2011. [14] V. Gor, D. Povh, L. Yichuan, E. Lerch, and D. Retzmann, S CCL a new type of FACTS based short circuit current limiter for application in hig h voltage systems," in CIGRE, Session 2004, B4 209, 2004. [15] S. Sugimoto, J. Kida, H. Arita, C. Fukui, and T. Yamagiwa, Principle and characteristics of a fault current limiter with series compensation," Power Delivery, IEEE Transactions on, vol. 11, n o. 2, pp. 842 847, apr 1996. [16] J. Dixon, L. Moran, J. Rodriguez, and R. Domke, pensation technologies: State of the art review," Proceedings of the IEEE, vol. 93, no. 12, pp. 2144 2164, dec. 2005. [17] P.Kundur, Power system stabil ity and control," 1994. [18] C.Vatsal J.Patel, Simulation and analysis for real and reactive power control with series type FACTS controller," 2012. [19] D. M. Robert W. Erickson, Fundamentals of power electronics," 2001. [20] A. E.N. Gene F.Franklin J.David Powell, Feedback control of dynamic systems," 1995. [21] S.K. Sul, Control of electric machine drive systems" 2011.

