Optimum Location of TCSC by Sensitivity Factor Analysis for Congestion Management

International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169
Volume: 5 Issue: 7 851 – 857
_______________________________________________________________________________________________
851
IJRITCC | July 2017, Available @ http://www.ijritcc.org
_______________________________________________________________________________________
Optimum Location of TCSC by Sensitivity Factor Analysis for Congestion
Management
Mr. Sonu Gurra
Assistant Professor in Dept. of Electrical and Electronics
Engineering
YMCA University of Science and Technology
Faridabad, Haryana (INDIA)
sonu.gurra444@gmail.com
Dr. Poonam Singhal
Associate Professor in Dept. of Electrical Engineering
YMCA University of Science and Technology
Faridabad, Haryana (INDIA)
ymcapoonamsinghal@gmail.com
Abstract—Due to deregulation of electric market transmission congestion occurs due insufficient transmission capacity to accommodate all
constraints for transmission of a line. FACTS devices such as Gate Controlled Series Capacitor and Thyristor Control Series Compensator can
help to reduce the flow in heavily loaded lines by controlling the power flow in the network. It increases the load ability of the network and
reduces the cost of production. Congestion management using series connected FACTS devices can be done in two steps. First, find the optimal
location of FACTS device and second, optimize the setting of the control parameter of FACTS device. Three methods to determine the optimal
location of series connected FACTS device are discussed in this paper. The approach is based on sensitivity of line loss, total system loss and
real power flow performance index. The proposed method has been demonstrated on 9-bus system in MATLAB programming as well as
SIMULINK.
Keywords— Congestion management, TCSC, Sensitivity factor analysis.
__________________________________________________*****_________________________________________________
I. INTRODUCTION
The increasing industries and change of life style has led to
increase the dependency on the electrical energy. This has
resulted into surge of power systems. This increase in power
systems has resulted into few uncertainties. Power interruption
and power outages are one of the main problems and affects the
economy of a country. In contrast to the fast changes in
technologies and the power demanded by these technologies,
transmission systems are force to operate closer to their
stability limits and reaching their thermal limits, because the
power delivering through the line is increased. If the power
exchanges are not controlled, any line located between any two
areas may become overloaded, this phenomenon is called
congestion. The main problems faced by power industries to
match the supply and demand required are:
 Transmission & Distribution; supply the electric
demand keeping the line within the thermal limit.
 In large power system, stability problems causing
power interruptions and blackouts which leads to huge
losses.
These constraints affect the quality of power supplied.
However, these constraints can be suppressed by improving the
power system control. Congestion may be removed through
different ways. Among the technical solutions, we have system
reconfiguration, system re-dispatch, operation of FACTS
devices, out-aging of congested lines, and operation of
transformer tap changers [10][17].
The issue of transmission congestion is more important in the
case of deregulated markets and competitive markets and it
needs a very special analysis. In these conditions, independent
system operator (ISO) has to remove the congestion, so that
the system remains in secure state. To remove the congestion
ISO can use followings methodologies [16],
 Out-ageing of overloaded lines
 Operation of on load tap changer transformer or
operation of phase shifters [9]
 Use of FACTS devices mainly series devices such as
GCSC, SSSC or TCSC
 Change of the generation amounts. By using this
method, some generators reduce while others increase
their output. The effect of change of generation means
generators will no longer run at equal incremental
costs as it did in case of economic load dispatch..
 Removal of loads and the operation of load
interruption options [13]
FACTS devices are used as one of those technologies
which can relieve the transmission congestion and hence leads
to better utilization of the existing grid infrastructure.
Furthermore, using FACTS devices gives more freedom to ISO
[16].
Thyristor Controlled Series Capacitor (TCSC) is a device
which is connected in series of a transmission line and its
impedance can be varied by varying its firing angle and hence
it can increase the power transfer capability, increase the
transient stability, decrease the transmission losses and improve
the transient stability [6].
This paper deals with the location of the series FACTS
devices, especially to manage congestion and to minimize the
losses after removal of congestion in the deregulated electricity
markets. The location of FACTS devices can be found on the
basis of the static performance or dynamic/transient
performance of the system. Sensitivity factor analysis methods
are used to determine the optimal location for FACTS devices
[1-4] and the results are compared with IEEE 9-Bus Model’s
MATLAB programming results.
This paper presents the comparative analysis of approaches
based on line loss sensitivity indices, real power Performance

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Index, reduction of total system VAR power losses and
MATLAB programming results of IEEE 9-Bus Model for
proper location of TCSC for congestion management in power
system.
II. FLEXIBLE AC TRANSMISSION SYSTEM (FACTS)
The FACTS is a concept based on power-electronic
controllers, which increase the value of transmission networks
by increasing their capacity. As the operation of these
controllers is very fast, they increase the safe operating limits
of a transmission system without reducing stability. The era of
the FACTS is started with the development of new solid-state
high power electrical switching devices. The use of the
FACTS has improved the new controllable systems.
FACTS devices are divided in three categories based on the
connection of these devices to the transmission line: -
A. Series FACTS devices
Series FACTS device consists of series connected capacitor
or a series connected current source are used to partially
compensate the effects of the series inductances of lines. Series
compensation increases the maximum power-transmission
capacity of the line. Some of the series connected FACTS
devices are: -
 Gate Controlled Series Compensator (GCSC)
 Thyristor Controlled Series Capacitor (TCSC)
 Static Synchronous Series Compensator (SSSC)
 Thyristor Switched Series Reactor (TSSC)
 Thyristor Controlled Power Angle Regulator
(TCPAR)
B. Shunt FACTS devices
Shunt devices may be connected permanently or through
semiconductor switch. Shunt reactors provide compensation for
the line capacitance and due to the reason they control over
voltages at no loads or light loads, they are always connected
permanently in the line, not to the bus. Shunt capacitors are
used to increase the power-transfer capacity and to compensate
for the reactive-voltage drop in the line. Some of the Shunt
connected FACTS devices are: -
 Static Synchronous Series Compensator (STATCOM)
 Static Var Compensator (SVC)
 Thyristor Controlled Reactor (TCR)
 Thyristor Switched Capacitor (TSC)
C. Series-Shunt FACTS Devices
These are the FACTS devices which are connected in series as
well as parallel of the transmission line. The principle of these
devices is to inject the current into the system with shunt part
and voltage with the series part.
 Unified Power Flow Controller (UPFC)
 Interline Power Flow Controller (IPFC)
 Thyristor Controlled Phase Shifter (TCPS)
III. THYRISTOR CONTROLLED SERIES COMPENSATOR
(TCSC)
The concept of TCSC is an extremely simple main circuit.
In TCSC the capacitor is inserted directly in the series of a
transmission line and the Thyristor-controlled inductor is
connected in parallel with that capacitor. So there is no
requirement of interfacing equipments like high voltage
transformers (HVT) are required. Due to this reason TCSC is
quiet economic than many of other competing FACTS devices.
Hence it makes TCSC simple and easy to understand the
construction and operation [2].
Fig. 1 Diagram of TCSC
A. Operation of TCSC
The operation of a TCSC can be easily explained from
electrical circuit analysis. It consists of a series capacitor (for
compensation) having a Thyristor controlled reactor (TCR) in
parallel. TCR is nothing but a variable inductive reactor whose
inductive reactance XL can controlled by firing angle α.
variation of XL w.r.t. α can be shown as Fig. 2.
Fig. 2 Equivalent circuit of TCR
By varying α from 0 to 90, XL(α) start from actual reactance XL
and vary up to infinity. This controlled reactor is connected in
parallel of the series capacitor, so that the variable capacitive
reactance (fig. 3) is possible across the TCSC to modify the
transmission line impedance.
Fig. 3 Equivalent Circuit to TCSC
Where
CL
LC
TCSC
XX
XX
X


)(
)(
)(



(1)



sin2
)(

 LL XX
(2)
α is the firing angle, XL is the reactance off the inductor and
XL(α) is the reactance of the inductor (effective reactance) at
firing angle α and is limited thus: XL ≤ XL(α) ≤ ∞.
B. TCSC impedance characteristics
Fig. 4 TCSC impedance characteristics

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Here the TCSC thus behave like a tunable parallel LC circuit in
the line current that is behaving like a constant AC (alternating
current) source. As XL(α), the impedance of the controlled
reactor, is varied from its maximum value (infinity) to its
minimum value (ωL), the TCSC changes (increases) its
minimum capacitive impedance, XTCSC,min = XC = 1/ωC until the
parallel resonance is established at XC = XL(α) and XTCSC,max
becomes infinite theoretically. Further decreasing XL(α), the
impedance of the TCSC, which is XTCSC(α) becomes inductive
and reaches its lowest value of XLXC/(XL – XC) at α = 0, where
the capacitor is in bypassed by the TCR. Hence, with the
ordinary TCSC arrangement in which the impedance of the
TCR reactor, XL, is lower than that of the capacitor, XC, the
TCSC has two operating ranges around its internal circuit
resonance which occurs at XC = XL(α): first is the αClim ≤ α ≤
π/2 range, where XTCSC(α) is capacitive, and the second is the 0
≤ α ≤ αClim range, where XTCSC(α) is inductive, as illustrated in
Fig. 4.
C. Static Modeling of TCSC
The Fig.5 shows a simple transmission line which is
represented by its lumped equivalent parameters in pi model
connected between two buses, bus -i and bus-j. Let the complex
voltages at bus-i and bus-j are Vi < δi and Vj < δj respectively.
The reactive and real power flow from bus-i to bus-j can be
written as
]sincos[2
ijijijijjiijiij BGVVGVP  
(3)
]cossin[)(2
ijijijijjishijiij BGVVBBVQ  
(4)
Where δij = δi – δj, similarly the real and reactive power
flow from bus-j to bus-i is;
]sincos[2
ijijijijjiijjji BGVVGVP  
(5)
]cossin[)(2
ijijijijjishijjji BGVVBBVQ  
(6)


Fig. 5 Model of Transmission line
The model of transmission line with a TCSC connected
between bus -i and bus-j is shown in Fig.5. In the steady state
conditions, the TCSC can be considered equivalent to a static
reactance –jXC. The reactive power and real power flow to
bus-j from bus-i, and to bus-i from bus-j of a transmission line
which have a series impedance and a series reactance are,
]sincos[ '''2
ijijijijjiiji
c
ij BGVVGVP  
(7)
]cossin[)( '''2
ijijijijjishiji
c
ij BGVVBBVQ  
(8)
]sincos[ '''2
ijijijijjiijj
c
ji BGVVGVP  
(9)
]cossin[)( '''2
ijijijijjishijj
c
ji BGVVBBVQ  
(10)
Fig. 6
The reactive power loss and real power loss in the transmission
line consisting TCSC can be written as,
ij
'
ij
2
j
2
i
2
j
2
i
'
ij
c
ji
c
ijLK cosGV2V-)V+(VG=P+P=P 
(11)
ij
'
ij
2
j
2
ish
'
ij
2
j
2
i
c
ji
c
ijL cosBV2V-)B)(BV+(V=Q+Q=Q 
(12)
Where,
)(
)(
)( 2
'
2
'
'
cijij
cij
ij
cijij
ij
ij
xxr
xx
Band
xxr
r
G





Due to series capacitance the change in the line flow can be
represented as a transmission line without any series
capacitance with power injected at both the receiving and
sending ends of the line as represented in Fig.7.
Fig.7. Injection Model of TCSC
]sinB+cosG[VV-GV=P ijijijijjiij
2
iic  
(13)
]sinB-cosG[VV-GV=P ijijijijjiij
2
jjc  
(14)
]cB-sinG[VV-B-V=Q ijijijijjiij
2
iic  os
(15)
]cBsinG[VVB-V=Q ijijijijjiij
2
jjc  os
(16)
Where,
))()((
)(
))()((
)2(
2222
22
2222
'
cijijijij
ijcijijc
ij
cijijijij
ijcijc
ij
xxrxr
xxxrx
B
xxrxr
xxrx
G






The above Model of TCSC is used to change the parameters of
transmission line properly with the TCSC for optimal location
in system.
IV. METHODS FOR OPTIMAL LOCATION OF TCSC
This paper utilizes static considerations based on the
following objectives:
 Reduction in real power loss of a particular line-k
(PLK)
Yij = Gij + jBij Bus - jBus - i
jBsh jBsh
Zij = rij + jxij Bus - jBus - i
jBsh jBsh
-jxc
Zij = rij + jxij Bus - jBus - i
Sic
Sjc

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 Reduction in the total system power loss (PLT)
 Reduction in the real power flow performance index
(PI).
Using a FACTS device to reduce the real power loss in a
particular line as suggested in [5] as an objective of device
location may, however, increase the total system loss may
increase the overloading of the lines elsewhere. Reduction in
the total system active power loss will decrease or eliminate the
undesirable loop flows but it doesn’t give any guarantee that
lines will not be overloaded but this is unlikely when there is
no congestion.
A. Line Loss Sensitivity Indices (Method – I)
Define the sensitivity ak
c
of transmission loss (PLK) on a
series compensated line-k with respective series capacitive
reactance (xck), as follows:
ck
LKc
k
x
P
a



= line loss sensitivity with respect to TCSC placed in line-
k (k = 1,….Nl)
Hence from equation (11), at base load flow
ijijijjiji
ck
c
LKc
k BGVVVV
x
P
a ]cos2[2 22




(17)
B. Total System Loss Sensitivity Indices (Method-2)
The exact loss formula of a power system of N buses is,
from [15],
]()([
1 1
kjkjjkkjk
N
j
j
N
k
jkLK QPPQQQPPaP   

(18)
Where Pj and Qj, are the real and reactive power
respectively injected at bus-j while α and β are the loss
coefficients which are defined as
)sin(
)cos(
kj
kj
jk
jk
kj
kj
jk
jk
VV
r
VV
r
a




Where rjk is the real part of the (j-k)th
element of [Zbus]
matrix. This total loss of system if one FACTS device at a time,
is used, can be represented as follows:
)P+(P-P=P jcicLTLT
(19)
The total system real power loss sensitivity factor w.r.t. the
TCSC parameter can be defined as
ck
LKc
k
x
P
b



= line loss sensitivity with respect to TCSC placed in line-
k (k = 1,….Nl)
These factors are computed using equation (19) at a base load
flow solution. Let a line-k between bus-i & bus-j.
C. Real power flow performance index(PI) sensitivity indices
The real power line flow performance index is used to
describe the severity of the system under normal and
contingency cases, as given below [4],










NL
m
n
Lm
Lmm
P
P
n
w
PI
1
2
max
2
(20)
Where PLm is the real power flow and 𝑃𝐿𝑚
𝑚𝑎𝑥
is the rated
capacity of the line-m, n is the exponent in equation, NL is the
number of lines in the power system and wm a real non-
negative weighting coefficient of line which can be used to
reflect the priority of lines. PI will remain a small value if all
the lines are within their power transfer capacity limits and
reach a high value if overload occurs on any line. Thus, it
gives a good measure for safety of the line from overloads for
the given condition of the power system. Almost all the works
on contingency selection algorithms employ the second order
performance indices which suffer from masking effects. Due to
the lack of discrimination, the PI for a case with many small
violations may be comparable with a value to the PI for a case
having one huge violation, is named as masking effect. By
mostly all operational standards, the system having one huge
violation is much more critical than that of a system having
many small violations. Masking effect can be avoided to some
extent using higher order PI, i.e., n > 1. However, in this study,
we have taken the value of exponent n= 2 and wi = 1.
The real power flow PI sensitivity factors w.r.t. the parameters
of TCSC can be represented as,
0



ckxck
k
x
PI
b
(21)
Where Xck is the value of the reactance given by the TCSC
installed in line k.
The sensitivity of PI w.r.t. TCSC parameter which is connected
between bus-i and bus-j can be written as;
ck
lm
lm
lm
N
m
m
ck x
P
P
Pw
x
PI












4
max
3
1
1
(22)
The real power flow in a line - m can be described in terms of
real power injections using DC system power flow equations
where s is the slack bus, as,
















kmforPPS
kmforPS
P N
sn
n
nnmn
N
sn
n
nmn
Lm
...
...........
1
1
(23)
Using equation (23), the following relationship can be
evaluated,
































kmfor
x
P
x
P
S
x
P
S
kmfor
x
P
S
x
P
S
ck
j
ck
j
mi
ck
i
mi
ck
i
mi
ck
i
mi ............
(24)
The term,
00
,





ckck xck
j
xck
i
x
P
x
P
(25)
Can be derived as,

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855
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222
22
22
222
22
00
)(
)(
sin
)(
)cos(2
ijij
ijij
ijji
ijij
ijij
ijji
xck
ic
xck
i
xr
xr
VV
xr
xr
VV
x
P
x
P
ckck













(26)
222
22
22
222
222
00
)(
)(
sin
)(
)cos(2
ijij
ijij
ijji
ijij
ijij
ijjij
xck
jc
xck
j
xr
xr
VV
xr
xr
VVV
x
P
x
P
ckck













(27)
V. CRITERIA F OR OPTIMAL LOCATION
The TCSC device should be placed in the line which is
most sensitive. With the sensitivity indices computed for
TCSC, following opinion has been carried out for its optimal
placement
 In reactive power loss reduction method (Method-2)
TCSC should be placed in that line which have the
most positive loss sensitivity index.
 Where in PI method TCSC should be placed in that
line which have most negative sensitivity index.
VI. FLOWCHART AND ALGORITHM
A. Algorithm
Step 1: - Input line data and bus data
Step 2: - Obtain Y-Bus matrix
Step 3: - Calculate Load Flow for Base Case
Step 4: - Change the Load at each load one by one
Step 5: - Put the TCSC on Each line and vary the line
compensation from 1% to 70 %
Step 6: - Obtain the load flow for each case
Step 7: - Select the results which have removed the
congestion
Step 8: - Select the result having minimum losses from
above selected results.
B. Flow Chart
VII. SIMULATION AND RESULTS
To establish the effectiveness of the proposed methods, it
has been tested on IEEE 9-bus system consisting of 3
generators and 9 lines representing 230kV buses having highly
stressed system with increased load.
Power flow of above 9-bus system & line limit is shown in
table-1. From the load flow, it was found that real power flow
in line-4 is 108.414MW, which is above to its line loading
limit & may create congestion.
START
Define Line data and Bus data
Formation of Bus admittance (Y) matrix
Set iteration counter k=0
Calculate Real and Reactive power
Pi=Vi
2
Gii+ |Vj|(Gijcos(δi – δj) +Bpq sin(δp- δq))
Qp=Vi
2
Bii+ |Vj|(Gijcos(δi – δj) +Bpq cos(δp- δq))
Set XTCSC to Remove Congestion
Calculate power mismatch
Test for
convergence ΔP=s
ΔQ=t
Formation of jacobian Matrix J=
Determine the voltage correction
=
Calculate new bus voltage
Replace and
Calculate Total Power Loss
STOP
Fig.8 IEEE 9-Bus System
G
G
G

Volume: 5 Issue: 7 851 – 857
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856
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TABLE I. 9-BUS POWER FLOW
Line From – To Real Power Flow Real Power Flow Limit
1 1 – 4 148.756 300
2 2 – 7 163.000 250
3 3 – 9 085.000 200
4 4 – 5 108.414 110
5 5 – 7 093.095 110
6 6 – 4 039.969 50
7 7 – 8 066.723 70
8 8 – 9 033.687 50
9 9 – 6 051.117 70
TABLE II. CALCULATED SENSITIVITY INDICES
Line aij bij cij
1 0.2082 0.0326 2.0957
2 0.5856 0.1048 0.3189
3 0.3027 0.0036 0.0010
4 0.5192 0.0041 0.0141
5 0.4903 0.0009 1.4953
6 0.0374 0.0006 5.7528
7 0.3015 0.0011 -0.0195
8 0.2834 0.0034 3.1265
9 0.2917 0.0143 1.4406
The sensitivity factors of reactive power loss reduction and
real power flow performance index with respect to TCSC
control parameter has been computed and are shown in table-
2. The sensitive lines are highlighted in table-2. It can be
noticed from table-2 that line-4 is more sensitive according to
total system reactive power loss reduction method. Line-7 is
more sensitive according to real power flow performance
index method but line-4 & 5 can also be considered because
these line also seems to be sensitive. System power flow result
after placing TCSC in 4, 5, 6 7, 8 & 9 is shown in table-4. The
value of control parameters of TCSC for computing power
flow are taken as per table-3.
TABLE III. CONTROL PARAMETER OF XTCSC
Line Compensation TCSC
4 50% 0.04250
5 60% 0.09660
6 30% 0.02760
7 50% 0.03600
8 40% 0.04032
9 70% 0.11900
TABLE IV. POWER FLOW AFTER PLACING TCSC
Line
Power
flow
without
TCSC
Power
Flow with
TCSC in
line 4
Power
Flow with
TCSC in
line 5
Power
Flow with
TCSC in
line 6
Power
Flow with
TCSC in
line 7
Power
Flow with
TCSC in
line 8
Power
Flow with
TCSC in
line 9
1 148.756 148.595 149.232 148.827 148.706 148.830 148.716
2 163.000 163.000 163.000 163.000 163.000 163.000 163.000
3 085.000 085.000 085.000 085.000 085.000 085.000 085.000
4 108.414 118.705 089.652 104.103 113.592 104.304 118.964
5 093.095 083.042 115.818 100.798 090.882 100.554 085.294
6 039.969 029.629 059.579 044.724 035.114 044.526 029.752
7 066.723 077.584 047.182 062.202 072.118 062.446 077.706
8 033.687 022.962 053.429 038.393 028.497 038.166 022.964
9 051.117 061.926 031.571 046.607 056.503 046.834 062.036
TABLE V. REACTIVE POWER LOSS
Line
Reactive
Power
Loss
without
TCSC
Reactive
Power
Loss with
TCSC in
line 4
Reactive
Power
Loss with
TCSC in
line 5
Reactive
Power
Loss with
TCSC in
line 6
Reactive
Power
Loss with
TCSC in
line 7
Reactive
Power
Loss with
TCSC in
line 8
Reactive
Power
Loss with
TCSC in
line 9
1 94.941 96.490 83.875 97.650 94.859 94.340 90.011
2 59.110 48.571 56.085 58.915 60.035 52.554 58.180
3 41.110 38.900 39.587 37.137 37.308 46.623 42.091
4 55.262 55.083 46.771 55.220 54.868 54.219 54.847
5 23.569 11.317 18.677 24.360 23.268 25.103 22.603
6 23.094 24.690 21.498 25.556 23.422 23.585 19.071
7 17.656 20.045 19.731 16.685 18.818 10.003 17.757
8 22.473 20.529 20.444 23.353 18.552 28.577 22.925
9 13.665 13.497 14.240 08.985 13.950 12.803 14.149
It can be seen in table-4 that congestion has been removed
in line 4 after placing TCSC in line 6 & 8 and also get reduced
system reactive power loss. Also there is not much
improvement in congestion and PI after placing TCSC in line
4 & 5 but as seen in table-2 that line 7 is more sensitive and
hence the placement of TCSC in line 7 is the most optimal for
reducing PI and congestion relief.
VIII.CONCLUSION
Congestion management is a critical issue in interconnected
power systems. FACTS devices such as TCSC can help to
reduce the flows in heavily loaded lines by controlling the
power flows in the network by changing the impedance of any
particular line. Because of the high costs of FACTS devices, it
is important to get the optimal location for placement of these
devices.
Here three sensitivity factor based methods have been
discussed for determining the optimal location and optimal
percentage of compensation of TCSC in an electricity market
and the optimum percentage of compensation is calculated to
reduce the losses to its minimum level. In a system, the
optimal locations of TCSC can be achieved based on the
sensitivity factors aij, bij and cij and then optimal location is
selected based on minimizing Total system power loss. Test

Volume: 5 Issue: 7 851 – 857
_______________________________________________________________________________________________
857
_______________________________________________________________________________________
results obtained for 9-bus power systems shows that these
sensitivity factors can be adequately used for determining the
optimal location of TCSC in power system. Transmission
losses for three sensitivity methods were compared with a 9
Bus model’s MATLAB programming results. Test results
divulge that the proposed methods are useful in managing
congestion & to find the optimal location of TCSC.
REFERENCES
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parameters using MATLAB/Simulink for performance
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[5] Mrinal Ranjan, B. Vedik, ―Op timal Location of FACTS
Devices in a Power Sy stem by M eans of Sensitivity Analy
sis‖ Science Road Publishing Corporation, Trends in
Electrical and Computer Engineering TECE 1(1) 1-9, 2011
[6] Nazanin Hosseinipoor, Sy ed M.H Nabavi, ―Optimal Locating
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Management in Deregu alted Power M arkets‖
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