Smart Grid and Renewable Energy, 2012, 3, 10-16
http://dx.doi.org/10.4236/sgre.2012.31002 Published Online February 2012 (http://www.SciRP.org/journal/sgre)
A New Method for Optimal Placement of TCSC Based on
Sensitivity Analysis for Congestion Management
Abouzar Samimi1, Peyman Naderi2
1Department of Electrical Engineering, Islamic Azad University Boroujerd Branch, Boroujerd, Iran; 2Department of Electrical Engi-
neering, Shahid Rajaee University, Tehran, Iran.
Received June 5th, 2011; revised December 7th, 2011; accepted December 14th, 2011
ABSTRACT
In this paper a new method has been proposed to determine optimal location and best setting of Thyristor Controlled
Series Compensator (TCSC). Seeking the best place is performed using the sensitivity analysis and optimum setting of
TCSC is managed using the genetic algorithm. The configuration of a typical TCSC from a steady-state perspective is
the fixed capacitor with a thyristor controlled reactor (TCR). The effect of TCSC on the network can be modeled as a
controllable reactance inserted in the related transmission line. This paper employs the DIgSILENT simulator and the
DPL as a programming tool of the DIgSILENT to show the validity of the proposed method. The effectiveness of sug-
gested approach has been tested on IEEE 14-bus system.
Keywords: TCSC; Optimal Placement; Sensitivity Analysis; Genetic Algorithm
1. Introduction
In recent years, with increasing in development of power
networks, the economical operation of power system is
more considered. Because of deregulation and restruc-
turing of the electricity markets use of Flexible AC Trans-
mission Systems (FACTS) devices is inevitable. The
maximum capability of power systems can be exploited
by means of FACTS devices. Nowadays, development of
power electronics switches causes reduction in the cost
of FACTS and therefore application of FACTS devices
especially in distribution networks is more economical.
Because of the economical considerations, installation
of FACTS controller in all of the buses or the lines is
impossible and unnecessary. There are several methods
for finding optimal locations of FACTS devices in power
systems [1-7].
In [1], a sensitivity based method has been suggested
to optimally locate the Thyristor Controlled Series Com-
pensator (TCSC) and Unified Power Flow Controller
(UPFC) for enhancing the system security under different
operating conditions and at optimal settings of FACTS
parameters. The DC power flow equations have been
employed for calculating the sensitivity indices. In [2], a
genetic algorithm (GA) based method is used to deter-
mine the optimal sitting of FACTS controller in power
system. The fitness function is to minimize the genera-
tion cost. In [3], the genetic algorithm is used to seek the
optimal location of multi-type FACTS devices in a power
system. The optimizations are performed on three pa-
rameters: the location of the devices, their types, and
their values. In [4], the Tabu Search (TS) method is used
to solve the combinatorial (i.e. to determine number and
location) problem of FACTS device allocation. Refer-
ence [5] compares three heuristic methods, simulated
annealing (SA), TS and GA, applied to the optimal loca-
tion of FACTS devices in order to enhance the system
security. The objective function is based on indices quan-
tifying the severity of the contingencies in terms of
branch loading and voltage levels. The three methods
lead to similar results, but generally TS and GA converge
faster than SA to an optimal solution. In [6], a real power
flow performance sensitivity index has been proposed to
decide optimal location of FACTS controllers. In [7],
extended voltage phasors approach (EVPA) is proposed
for placement of FACTS controllers in power systems
within the voltage stability viewpoint.
In this paper a new method has been proposed to op-
timally locate TCSC in power systems. The suggested
approach is composed of sensitivity analysis and the ge-
netic algorithm. Finding the best place for TCSC is per-
formed using the sensitivity analysis and sizing of TCSC
is managed using the genetic algorithm. The IEEE 14-
bus system has been applied to test the suggested algo-
rithm. The rest of the paper is organized as follows. Sec-
tion 2 presents the modeling of the TCSC adapted for this
study. The search space in optimal placement of series

A New Method for Optimal Placement of TCSC Based on Sensitivity Analysis for Congestion Management 11
capacitive compensators in real power systems is usually
sizable. Use of the approaches like sensitivity analysis
can reduce the search space. In Section 3 some sensitiv-
ity indices have been presented. The best setting of TCSC
is performed by genetic algorithm in Section 4. Finally
numerical results along with some observations and dis-
cussions are presented in Section 4. DIgSILENT soft-
ware which contains a powerful programming language
called DPL1 has been prepared required facilities to exe-
cute the proposed algorithms and corresponding simula-
tions.
2. TCSC Modeling
The IEEE defines the TCSC as a capacitive reactance
compensator which consists of three main components:
capacitor bank C, bypass inductor L and bidirectional
thyristors SCR1 and SCR2. Series capacitive compensa-
tion has been used to increase line power transfer as well
as to enhance system stability. Figure 1 shows the main
circuit of a TCSC.
The firing angles of the thyristors are controlled to ad-
just the TCSC reactance according to the system control
algorithm, normally in response to some system parame-
ter variations. According to the variation of the thyristor
firing angle or conduction angle, this process can be
modeled as a fast switch between corresponding reac-
tance offered to the power system. Assuming that the
total current passing through the TCSC is sinusoidal, the
equivalent reactance at the fundamental frequency can be
represented as a variable reactance XTCSC. The TCSC can
be controlled to work either in the capacitive or the in-
ductive zones avoiding steady state resonance. There
exists a steady-state relationship between the firing angle
αand the reactance XTCSC. This relationship can be de-
scribed by the following equation [8]:
 

Cl
TCSC
lC
XX
X
X
X

  (1)
where,

π
π2sin
lL
XX 


 (2)
α is the firing angle, XL is the reactance of the inductor
and Xl is the effective reactance of the inductor at firing
Figure 1. Configuration of a TCSC.
angle. In this paper the TCSC is taken as continuous va-
rying capacitor. The effective series transmission im-
pedance is given by:


1
eff
X
kX

 (3)
where k is the degree of series compensation
TCSC
X
k
X
 (4) 01k0

In the simulations of this paper, only the capacitive re-
gion has been used. Hence the compensation level varies
from zero to the maximum level of 0.7. Figure 2 shows a
transmission line with a TCSC.
In some references a static Power Injection Model
(PIM) of the TCSC has been presented. The injection
model represents the TCSC as a device that injects cer-
tain amount of active and reactive power in a node [1].
 
2cos sin
iciiji jijijijij
PVGVVGB 


   

 (5)




2sin cos
iciijshi jijijijij
QVBBVVG B 

  

(6)
 
2cos sin
jcjiji jijijijij
PVGVVG B 


 
 

 (7)




2sin cos
jcjijshi jijijijij
QVBBVVG B 

  

(8)
where,

2
2
ij
ij
ijij c
r
G
rxx
 (9)



2
2
ij c
ij
ijij c
xx
B
rxx

 (10)
3. Sensitivity Analysis for Optimal
Placement o f TCSC
Many sensitivity performance indices have been pro-
posed for the analysis of power systems. There are some
sensitivity indices which have the most attraction for
optimal placement of series compensators.
Figure 2. Static model of line with TCSC.
1DIgSILENT Programming Language.

A New Method for Optimal Placement of TCSC Based on Sensitivity Analysis for Congestion Management
12
3.1. Sensitivity Analysis for Optimal Placement
of TCSC
Here we look at a method based on the sensitivity of the
total system reactive power loss with respect to the con-
trol variable of the TCSC. For TCSC placed between
buses i and j, we consider net line series reactance as a
control parameter. Loss sensitivity with respect to control
parameter of TCSC placed between buses i and j can be
written as [9]:

22
22
2
22
2cos ij ij
L
ijijij ij
ij ij ij
rx
Q
aVVVV
xrx



 

 (11)
3.2. Sensitivity Analysis for Optimal Placement
of TCSC
The sensitivity
j
c
a of transmission loss (PLj) on a series
compensated line-j with respect to series capacitive reac-
tance (Xcj) is defined as follows [10]:
22
0
22cos
cj
jLk
cijij
cj X
P
aVVVV
X





ijijij
GB

PQ
(12)
3.3. Total System Loss Sensitivity Index
The real power loss of a system having N bus is:

11
NN
LTjkj kjkjkj kjk
jk
PPPQQQP 





(13)
where Pj and Qj respectively, are the real and reactive
power injected at bus-j and α, β are the loss coefficients
defined by:

cos
jk

j
kj
jk
r
VV k

  (14)

sin
jk

j
kj
jk
r
VV k

  (15)
where rjk is the real part of the j-kth element of Zbus matrix.
Using power injection model of FACTS this total loss if
FACTS device, one at a time is used, can be written as
[10]:


L
TLT icjc
PP PP

 (16)
The total system real power loss sensitivity factors
with respect to the parameters of TCSC placed at line-k
can be defined as [10]:
0
ck
kLT
C
ck X
P
bX

 (17)
Consider a line-k connected between bus-i and bus-j.
The total system loss sensitivity with respect to TCSC
can be derived as given below [10]:
00
00
0
ck ck
ck ck
ck
j
ki LT LT
c
ick jck
XX
j
i LT LT
ickjck
XX
jc
ic
ckckX
P
P PP
bPX PX
Q
Q PP
QX QX
P
P
XX





 

 

 

 







(18)
where,

1
2
N
LT
im mimm
m
i
PPQ
P





(19)

1
2
N
LT
immim m
m
i
PQP
Q





(20)
 
2
00
22
22
22 22
2cos
sin
ck ck
iic
iij ij
ck ck
XX
ij ijijij
ij ij
ij ijij ij
PP VVV
XX
rxr x
VV
rx rx



 






(21)
 
2
00
22
22
22 22
2cos
sin
ck ck
iic
iij ij
ck ck
XX
ij ijijij
ij ij
ij ijij ij
PP VVV
XX
rxr x
VV
rx rx



 






(22)
3.4. Real Power Flow Sensitivity Index
In this section, a new real power flow sensitivity index
with respect to the parameter of TCSC placed in line j is
introduced as:
1
l
N
m
jm
m
j
P
SI
X




 (23)
In this index, TCSC has been modeled as a variable se-
ries capacitive reactance XTCSC. Therefore, the total line
reactance decreases. This index demonstrates the sum of
variation of real power flow in all lines with respect to
the change of reactance of line j. m

is a weighted fac-
tor which can be selected higher for congested lines. In
this study m

is selected five for congested lines.
Calculating of the
j
SI index can be performed using
DC power flow equations [11]. But for accurate calcula-
tion, this index is computed using AC power flow. For
this purpose, the line reactance would be very little
changed around the operating point subject to the other
conditions are fixed. Hence
j
SI can be rewritten as:

A New Method for Optimal Placement of TCSC Based on Sensitivity Analysis for Congestion Management 13
10
l
j
N
m
jm
mjX
P
SI X 



 (24)
This index is calculated for all the lines. After that SI-
min and SImax are specified by sorting the SI values, nor-
malized real power flow index is defined as:
min
max min
j
j
SI SI
SIn SI SI

 (25)
TCSC must be placed in a line having the most posi-
tive sensitivity index.
4. Optimal Setting of TCSC Using the
Genetic Algorithm
The genetic algorithm has been used to find the optimum
sizing of TCSCs. Genetic algorithms are based on the
mechanisms of natural selection. The principles and de-
tails of the genetic algorithm have been presented in
many references.
4.1. Objective Function
The objective function has been made of the severity of
the system loading by the following relationship:
Minimize:
2
max
1
l
n
N
Lm
mLm
S
FS




 (26)
where,
L
m
P
max
: Apparent power flow in line m
L
m
N
P: The rated capacity of line-m
l
The objective function F will be small when all the
lines are within their limits and reach a high value when
there are overloads. Thus, it provides a good measure of
severity of the line overloads for given state of the power
system. Most of the works on contingency selection algo-
rithms utilize the second order performance indices which,
in general, suffer from masking effects. The lack of dis-
crimination, in which the performance index for a case
with many small violations may be comparable in value
to the index for a case with one huge violation, is known
as masking effect. By most of the operational standards,
the system with one huge violation is much more severe
than that with many small violations. Masking effect to
some extent can be avoided using higher order perform-
ance indices. However, in this study, the value of expo-
nent has been taken as 2.
: The number of power system lines
4.2. Initial Population
Some responses as chromosomes of initial population
must be created for starting algorithm. The length of each
chromosome (the number of genes formed a chromo-
some) is the number of decimal places. In fact every gene
is a number between 0 - 9 and each chromosome shows
exact the degree of series compensation (k) for TCSC.
4.3. Selection Operator
The best solutions in the current population are selected
by roulette wheel technique.
4.4. Crossover Operator
Two random chromosomes in the middle generation are
selected. Then a random number (n) between 1 to the
length of chromosome are selected and pairs of selected
chromosomes from n-th gene to later are swapped to
each other to produce new chromosomes.
4.5. Mutation Operator
To test each element for fitness and to avoid algorithm
stopping at a local optimum some solutions are also ran-
domly modified. Therefore a chromosome is selected
randomly, then some of it genes are replaced with an-
other random numbers.
5. Numerical Results
The case study for examination of the proposed algo-
rithm is the IEEE 14-bus system.
All the loads of IEEE 14-bus system have been mod-
eled by the following polynomial equations:
0
0
V
PP
V




(27)
0
0
V
QQV




(28)
where P0 and Q0 stand for the real and reactive powers
consumed at a reference voltage V0. In this study the
value of exponents have been taken as 1.6


and
1.8


. In addition a 30% increasing coefficient for
active and reactive power loads rather than the base val-
ues is considered.
Having been calculated the real power flow sensitivity
indices, the results are shown in Table 1 Regarding to
the results shown in Table 1, line 1 - 5 has the most posi-
tive sensitivity index. Therefore this line is selected for
installing of TCSC. Analyzing the results of loading, it
was clear this place is close to the most congested line 1 -
2. Figure 3 shows situation of this place on the network.
The degree of compensation (k) is calculated as 0.59 by
implementing the genetic algorithm.
Table 2 shows the loading of lines in the base state
and after placing TCSC in line 1 - 5. The most congested

A New Method for Optimal Placement of TCSC Based on Sensitivity Analysis for Congestion Management
14
Table 2. Loading of lines before and after placing TCSC. Table 1. The real power flow sensitivity indices.
Line Rated Voltage
(kV)
Rating
(MVA)
% Loading
without TCSC
% Loading
with TCSC
1 - 2132 150 138.5 106.2
1 - 5132 150 65.5 97.4
10 - 11400 50 15.7 19.1
12 - 13400 50 4.0 4.4
12 - 6400 50 22.2 22.4
14 - 13400 50 15.7 18.0
2 - 5132 150 35.3 21.8
3 - 2132 150 63.5 58.1
3 - 4132 150 22.8 28.4
4 - 2132 150 48.2 37.7
4 - 5132 150 56.6 70.6
6 - 11400 50 20.8 24.3
6 - 13400 50 51.1 52.3
7 - 8400 60 40.2 40.0
9 - 10400 50 33.2 33.3
9 - 14400 50 35.8 34.8
9 - 7400 75 17.2 17.3
Line SI(j) SIn(j)
1 - 2 –24.2878 0
1 - 5 12.4146 1
10 - 11 –0.0126 0.6614
12 - 13 –0.0218 0.6612
12 - 6 –0.1296 0.6582
14 - 13 –0.0110 0.6614
2 - 5 –5.0649 0.5238
3 - 2 1.3038 0.6973
3 - 4 –0.3280 0.6528
4 - 2 –2.6979 0.5882
4 - 5 2.3310 0.7253
6 - 11 0.0074 0.6620
6 - 13 0.3161 0.6704
7 - 8 0.0132 0.6621
9 - 10 –0.0588 0.6601
9 - 14 0.0117 0.6621
9 - 7 –0.3549 0.6521
TCSC
Figure 3. the IEEE 14-bus system in DIgSILENT.

A New Method for Optimal Placement of TCSC Based on Sensitivity Analysis for Congestion Management 15
line has a 138.5% loading in the base state. After install-
ing TCSC in line 1 - 5 the loading of line 1 - 2 decreases
to 106.2% in exchange for a loading increment of line 1 -
5 and line 4 - 5. As previously mentioned, by most of the
operational standards, the system with one huge violation
is much more severe than that with many small violations.
As it is seen in Table 2, the loading changes of other
lines are negligible. The result of optimal placement of
TCSC via suggested approach corresponds to the results
Table 3. Voltag e magnitude of buses before and after placing
TCSC.
Bus Voltage in p.u. without TCSC Voltage in p.u. with TCSC
1 1.060 1.060
2 1.021 1.027
3 0.971 0.976
4 0.971 0.976
5 0.986 0.990
6 0.918 0.922
7 0.952 0.957
8 0.995 0.999
9 0.939 0.943
10 0.924 0.928
11 0.916 0.920
12 0.898 0.902
13 0.894 0.898
14 0.892 0.896
of other approaches in other references [12,13]. There-
fore the validity of the proposed method is confirmed.
Bus voltage level before and after compensation proc-
ess is shown in Table 3. In spite of effective relief of
congestion, it is clear the improvement of voltage stabil-
ity is negligible and there is impermissible voltage drop
at some of the buses.
Other results of load flow calculation before and after
installing of TCSC are shown in Table 4.
6. Conclusion
In this paper a new method has been proposed to opti-
mally locate TCSC in power sytems. The suggested ap-
proach is composed of sensitivity analysis and genetic
Table 4. Results of load flow calculation before and after
compensation with TCSC.
Parameter Without TCSC With TCSC
Active Power Generation (MW) 362.25 363.36
Reactive Power Generation (MVAr) 162.77 142.82
Active Losses (MW) 25.55 26.66
Reactive Losses (MVAr) 62.15 42.2
% Ploss % 7.05 % 7.34
2
max
1
l
n
N
Lm
mLm
S
FS




 4.335 2.697
Figure 4. Loading profile before and after compensation.

A New Method for Optimal Placement of TCSC Based on Sensitivity Analysis for Congestion Management
16
algorithm. First, the appropriate modeling of the TCSC
has been presented. After introducing some sensitivity
indices, sensitivity analysis approach has been utilized to
find optimal placement of series compensators. In this
process, a real power flow sensitivity index has been
presented. Then the setting of TCSC has been defined by
GA. The objective function has been made of the sever-
ity of the system loading. The result of load flow calcula-
tion before and after compensation process shows reduc-
tion of loading in congested lines.
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