A New Method for Optimal Placement of <i>TCSC</i> Based on Sensitivity Analysis for Congestion Management

doi:10.4236/sgre.2012.31002

Paper Menu >>

Journal Menu >>

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.

Email: [email protected], [email protected]

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]:

 



TCSC





 (1)

where,



π2sin



 (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:





eff



 (3)

where k is the degree of series compensation

TCSC

 (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,



ijij c

rxx

 (9)







ij c

ijij c

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

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]:



2cos ij ij

ijijij ij

ij ij ij

aVVVV

xrx







 



 (11)

3.2. Sensitivity Analysis for Optimal Placement

of TCSC

The sensitivity

a of transmission loss (PLj) on a series

compensated line-j with respect to series capacitive reac-

tance (Xcj) is defined as follows [10]:

22cos

jLk

cijij

cj X

aVVVV











ijijij



(12)

3.3. Total System Loss Sensitivity Index

The real power loss of a system having N bus is:



LTjkj kjkjkj kjk

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



VV k





 (14)



sin



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]:





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]:

kLT

ck X

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]:

ck ck

LT LT

ick jck

LT LT

ickjck

ckckX

bPX PX

QX QX











 







 















(18)

where,



im mimm

PPQ











(19)



immim m

PQP











(20)

 

22 22

2cos

sin

ck ck

iic

iij ij

ck ck

ij ijijij

ij ij

ij ijij ij

PP VVV

rxr x

rx rx





 













(21)

 

22 22

2cos

sin

ck ck

iic

iij ij

ck ck

ij ijijij

ij ij

ij ijij ij

PP VVV

rxr x

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:









 (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

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

SI can be rewritten as:

A New Method for Optimal Placement of TCSC Based on Sensitivity Analysis for Congestion Management 13

mjX

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

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:

max

mLm









 (26)

where,

max

: Apparent power flow in line m

P: The rated capacity of line-m

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:









(27)

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

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

max

mLm









 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

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.

REFERENCES

[1] J. G. Singh, S. N. Singh and S. C. Srivastava, “Enhance-

ment of Power System Security through Optimal Place-

ment of TCSC and UPFC,” Power Engineering Society

General Meeting, Tampa, 24-28 June 2007, pp. 1-6.

[2] H. C. Leung and T. S. Chung, “Optimal Placement of

FACTS Controller in Power System by a Genetic-Based

Algorithm,” Proceedings of the IEEE International Con-

ference on Power Electronics and Drive Systems, 27-29

July 1999, pp. 833-836.

[3] S. Gerbex, R. Cherkaoui and A. J. Germond, “Optimal

Location of Multi-Type FACTS Devices in a Power Sys-

tem by Means of Genetic Algorithms,” IEEE Transactions

on Power Systems, Vol. 16, No. 3, 2001, pp. 537-544.

doi:10.1109/59.932292

[4] H. Mori and Y. Goto, “A Parallel Tabu Search Based

Method for Determining Optimal Allocation of FACTS in

Power Systems,” Proceedings of the International Con-

ference on Power System Technology, Perth, 4-7 December

2000, pp. 1077-1082. doi:10.1109/ICPST.2000.897170

[5] S. Gerbex, R. Cherkaoui and A. J. Germond, “Optimal

Location of FACTS Devices to Enhance Power System

Security,” Proceedings of the Conference on Power Tech-

nology, Bologna, 23-26 June 2003, p. 7.

doi:10.1109/PTC.2003.1304363

[6] J. G. Singh, S. N. Singh and S. C. Srivastava, “Enhancement

of Power System Security through Optimal Placement of

TCSC and UPFC,” Power Engineering Society General

Meeting, Tampa, 24-28 June 2007, pp. 1-6.

[7] N. K. Sharma, A. Ghosh and R. K. Varma, “A Novel

Placement Strategy for Facts Controllers,” IEEE Trans-

actions on Power Delivery, Vol. 18, No. 3, 2003, pp. 982-

987. doi:10.1109/TPWRD.2003.813874

[8] C. Schaffner and G. Andersson, “Performance of a TCSC

for Congestion Relief,” Proceedings of the Conference on

Power Technology, St. Petersburg, 23-27 June, 2005, pp.

1-3.

[9] H. Besharat and S. A. Taher, “Congestion Management

by Determining Optimal Location of TCSC in Deregu-

lated Power Systems,” International Journal of Electrical

Power & Energy Systems, Vol. 30, No. 10, 2008, pp.

563-568. doi:10.1016/j.ijepes.2008.08.007

[10] S. N. Singh and A. K. David, “Congestion Management

by Optimizing FACTS Device Location,” Proceedings of

the International Conference on Electric Utility Deregu-

lation and Restructuring and Power Technologies, Lon-

don, 4-7 April 2000, pp. 23-28.

[11] S. A. Taher and H. Besharat, “Transmission Congestion

Management by Determining Optimal Location of FACTS

Devices in Deregulated Power Systems,” American Jour-

nal of Applied Sciences, Vol. 5, No. 3, 2008, pp. 242-247.

[12] Y. Shi, K. Mwanza and L. A. Tuan, “Valuation of FACTS

for Managing Congestion in Combined Pool and Bilateral

Markets,” Proceedings of Power Engineering Society Con-

ference and Exposition in Africa, Johannesburg, 16-20 July

2007, pp. 1-7. doi:10.1109/PESAFR.2007.4498031

[13] N. Acharya and N. Mithulananthan, “Locating Series

FACTS Devices for Congestion Managementin Deregu-

lated Electricity Markets,” Electric Power Systems Re-

search, Vol. 77, No. 3-4, 2006, pp. 352-360.

doi:10.1016/j.epsr.2006.03.016