Tcsc Fuzzy Stability

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Electric Power Systems Research 78 (2008) 1726–1735

Contents lists available at ScienceDirect

Electric Power Systems Research

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e p s r

A self-tuning fuzzy PI controller for TCSC to improve power system stability

Salman Hameed, Biswarup Das ∗, Vinay Pant

Department of Electrical Engineering, Indian Institute of Technology, Roorkee, Roorkee 247667, Uttarakhand, India

a r t i c l e i n f o

Article history:

Received 7 January 2008

Received in revised form 5 March 2008

Accepted 6 March 2008

Available online 24 April 2008

Keywords:

Thyristor-controlled series capacitor

Self-tuning fuzzy controller

Power system stability

a b s t r a c t

In this paper, a self-tuning fuzzy PI controller (STFPIC) is proposed for thyristor-controlled series capacitor

(TCSC) to improve power system dynamic performance. In a STFPIC controller, the output-scaling factor

is adjusted on-line by an updating factor (˛). The value of ˛ is determined from a fuzzy rule-base definedon error (e) and change of error (e) of the controlled variable. The proposed self-tuning controller is

designed using a very simplecontrol rule-base and themost naturaland unbiased membership functions

(MFs) (symmetric triangles with equal base and 50% overlap with neighboring MFs). The comparative

performances of the proposed STFPIC and the standard fuzzy PI controller (FPIC) have been investigated

on two multi-machine power systems (namely, 4 machine, 2 area systemand 10machine 39 bus system)

through detailed non-linear simulation studies using MATLAB/SIMULINK. From the simulation studies it

has been found out that for damping oscillations, the performance of the proposed STFPIC is better than

thatobtained by the standard FPIC. Moreover, the proposed STFPIC as well as the FPIC have been found to

be quite effective in damping oscillations over a wide range of operatingconditions andare quite effective

in enhancing the power carrying capability of the power system significantly.

© 2008 Elsevier B.V. All rights reserved.

1. Introduction

For economic and ecological reasons, the building of newtrans-

mission lines and expansion of existing transmission systems are

becoming more and more difficult. In this new situation, it is nec-

essary to utilize the existing power transmission system at its

maximum capacityto meet increasing demand of electrical energy.

However, the power transfercapability of an interregional AC trans-

mission system is usually limited by the stability problems. As a

result, power utilitiesare nowplacingmore emphasis on improving

the stability limits of the existingsystems to increase the utilization

of existingtransmission facilities. Inthis context, it is nowadays well

recognized that by applying the flexible AC transmission system

(FACTS) controllers, the stability limits can be enhanced signifi-

cantly [1,2]. Among various FACTS controllers, thyristor-controlled

series capacitor (TCSC) is one of the most promising FACTS deviceshaving a few practical installations around the world [3,4] and has

attracted a lot of attention for designing an effective control law to

enhance the system stability. The various control schemes reported

in the literature for TCSC can be classified into two broad cate-

gories: (a) linearised, eigenvalue analysis based control system and

(b)intelligent technique-based controlscheme.Although the effec-

tiveness of the eigenvalue analysis based control scheme has been

proven in several publications, as pointed out in [5], it is neither

∗ Corresponding author.

E-mail addresses: [email protected], [email protected](B. Das).

simple to develop the linearised system model nor is absolutely

necessary for developing a FACTS damping controller. As a result,

different intelligent technique-based controllers for TCSC have

been suggested in the literature. Fang et al. [5] have proposed an

OTEF descent strategy for designingfuzzy TCSC damping controller.

In this work,the TCSC controller actuallyconsistsof two TCSC fuzzy

controllers and the efficacy of the developed controller has been

tested on a four-generator, two area interconnected power system.

InRef. [6], the authors havepresented a T–Sfuzzymodel schemefor

TCSC which hasbeen tested on a singlemachineinfinitebus (SMIB)

system. Dash et al. have suggested a hybrid fuzzy controller and a

non-linear T–S fuzzy controller for TCSC in [7] and [8], respectively.

Both these schemes have been tested on a three machine, six bus

system with two TCSCs installed in the study system. In Ref. [9], the

authors have proposed a new design technique, namely F-HGAPSO,

to design the fuzzy controller. The effectiveness of their proposed

controller has been tested on a SMIB system. Laiq Khan and Lo [10]

have presented a hybrid micro-GA based fuzzy controller for TCSC.

The performance of the proposed TCSC controller has been tested

on the three machine, nine bus system. However,in this work, both

TCSC and UPFC were considered in the study system. In Ref. [11],

the authors have proposed a combination of a fuzzy controller and

a conventional PI controller for TCSC andthe validity of thisstrategy

has been tested on a two area four-machine power system.

From the above discussion it is observed that thedifferentfuzzy

controlstrategies proposedin theliteraturehave beentested on rel-

atively small test systems. This paper aims to extend the work on

0378-7796/$ – see front matter © 2008 Elsevier B.V. All rights reserved.

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S. Hameed et al. / Electric Power Systems Research 78 (2008) 1726–1735 1727

Fig. 1. Block diagram of the PI-type FLC (FPIC).

Fig. 2. MFs for e, e and u. N: negative; P: positive; ZE: zero; B: big; M: medium; S: small.

application of intelligent control technique for TCSC control design

further. Specifically, in this paper, a new self-tuning fuzzy PI con-

trol for TCSC is proposed to enhance the power system stability.

Further, the effectivenessof the developedTCSC controller has been

tested on a relativelylarge 10machine 39 bus system (whichhas not

been used in earlier publications [5–11]). This paper is organized

as follows. Section 2 describes the proposed fuzzy logic controller

for TCSC. Section 3 presents the main results of this work. Finally,

Section 4 discusses the conclusions of this work.

2. Fuzzy PI controller

The block diagram of the fuzzy PI controller (FPIC) is shown in

Fig. 1 [12,13]. In this figure, e(k) is the error at the kth sample and

it can be written as e(k) = ysp – y(k) where, y(k) is the actual system

output and ysp theset-point or desired system output at kth sample,

respectively. The change in error is defined as

e(k) = e(k)− e(k− 1) (1)

The quantities e and e are converted to normalized quantities

eN and eN, respectively by using the scaling factors (SFs) Ge andGe. These normalized quantities eN and eN are crisp in nature

and therefore need to be first converted to their corresponding

fuzzy variables. After fuzzification, the fuzzified inputs are given

to the fuzzy inference mechanism which, depending on the given

fuzzy rule base,gives the normalized incremental change in control

output (uN). The output uN is converted into actual incremen-

tal change in control output (u) by using the scaling factor Gu.

For implementing the fuzzy inference engine, the “min” operator

for connecting multiple antecedents in a rule, the “min” implica-

tion operator, and the “max” aggregation operator have been used.

Actually, the output uN from the inference mechanism is fuzzy

in nature, hence, to determine the crisp output, these fuzzy out-

puts need to be defuzzified. The centroid defuzzification scheme

has been used here for obtaining the output u as shown in Fig. 1.

Finally, the actual value of the controller output (u) is computed by

u(k) = u(k− 1)+u(k) (2)

The relationships between the SFs (Ge, Ge and Gu) and the input

and output variables of the FPIC are as follows:

eN = Gee

eN = Gee

u = GuuN

Here Ge, Ge and Gu are the SFs for e, e and u, respectively and

eN, eN and uN are normalized quantities. The SFs are the main

parameters used for tuning any fuzzy logic controller (FLC)because

variation of the SFs changes the normalized universe of discourse

of input and output variables and their correspondingmembership

functions. Generally, selection of suitable values for Ge, Ge and Gu

are made based on the knowledge about the process to be con-

trolled and sometimes through trial and error to achieve the best

possible control performance. This is so because, unlike conven-

tional non-fuzzy controllers, there is no well-defined method for

selecting appropriate values of SFs for FLC. However, if required,it is possible to tune these parameters to achieve a given con-

trol objective using some optimization techniques. In this work,

the appropriate values for Ge, Ge and Gu have been determined

Table 1

Rule base for u

e/e NB NM NS ZE PS PM PB

NB NB NB NB NM NS NS ZE

NM NB NM NM NM NS ZE PS

NS NB NM NS NS ZE PS PM

ZE NB NM NS ZE PS PM PB

PS NM NS ZE PS PS PM PB

PM NS ZE PS PM PM PM PB

PB ZE PS PS PM PB PB PB



1728 S. Hameed et al. / Electric Power Systems Research 78 (2008) 1726–1735

Fig. 3. Flowchart of the GA optimization algorithm.

by using genetic algorithm (GA) [14,15] as described in the next

subsection.

Each fuzzy control rule in the controller rule base is of the form

“If e is E and e is E, then u is U ”

where E, E and U are the fuzzy sets corresponding to error,

change in error and the incremental change in the control output,

respectively. In this work, for both the inputs (e and e) and the

output (u), seven fuzzy subsets have been used. These are: PB

(positive big), PM (positive medium), PS (positive small), ZE (zero),

NS (negative small), NM (negative medium) and NB (negative big).

Table 2

Ranges for the different scaling factors

Parameters Ge Ge Gu

Minimum range 0 0 0

Maximum range 0.5 1 1

Table 3

Parameters used in genetic algorithm

Parameter Value/Type

Maximum generations 50

Population size 25

Mutation rate 0.1

Crossover operator Scattered

For each of these fuzzy sets, triangular membership function (MF)

has been used. These membership functions have been defined on

the common normalized domain [−1, 1] and are shown in Fig. 2.

From this figureit is observed that the triangles are symmetricwith

equal base having 50%overlap with neighboringMFs. As each of the

twoinputs hassevenfuzzy sets,thereare altogether49 controlrules

in the FPIC. The rule base for computing the output u is shownin Table 1 which is a widely used rule base designed with a two-

dimensional phase plane [16,17]. The control rules in Table 1 are

built based on thecharacteristics of the step response.For example,

if the output is falling far away from the set point, a large con-

trol signal that pulls the output toward the set point is expected,

whereas a small control signal is required when the output is near

and approaching the set point.

2.1. Tuning of scaling factors using GA

In this work, the scaling factors have been tuned such that

the power system oscillations are minimized after a disturbance

Fig. 4. Block diagram of the STFPIC.




Fig. 5. MFs for gain updating factor (˛). ZE: zero; V: very; B: big; M: medium; S: small.

takes place. Specifically, the aim is to minimize the error between

the actual steady state power flowing through the line (P ref )

(in which the TCSC is installed) and the actual power flowing

through that particular line (P actual ) following a disturbance. Vari-

ous performance indices can be used to represent the above goal

mathematically. In this paper, the integral of the squared error (ISE)

[18] as shown in Eq. (3) has been selected as it tends to place a

greater penalty on large errors. This goal can be formulated as the

minimization of the objective function F , where

F =

t sim

0

e2 p(t ) dt (3)

InEq. (3), e p(t ) = P ref −P actual isthe error inpower flow inthe line

following a disturbance and t sim is the total time period of simula-

tion. As theobjective function of Eq. (3) is non-convex in nature, GA

has been usedto minimize F.The overall flowchart foroptimization

using GA is shown in Fig. 3.

Initially, a number of populations (N ) have been generated for

the scaling factors. Each of the populations consists of the binary

strings corresponding to the scaling factors Ge, Ge and Gu. These

strings are created in a random fashion with the constraint that the

values of Ge, Ge and Gu should lie within their specified ranges.The

ranges chosen for each of these scaling factors are shown in Table 2while the parameters used in GA are shown in Table 3. For each of

these N sets of values of Ge, Ge and Gu, time domain non-linear

simulation studies have been carried out for evaluating the objec-

tive function F of Eq. (3). For this purpose, a value of 80s has been

chosen for t sim. Based on the values of the objective function, out

of these N possible solutions, the good solutions are retained and

the others are eliminated (following the principle of survival of the

fittest). The selected solutions undergo the processes of reproduc-

tion, crossover, and mutationto create a newgeneration of possible

solutions (which are expected to perform better than the previous

generation). This process of production of a newgeneration and its

Table 4

Rule base for ˛

e/e NB NM NS ZE PS PM PB

NB VB VB VB B SB S ZE

NM VB VB B B MB S VS

NS VB MB B VB VS S VS

ZE S SB MB ZE MB SB S

PS VS S VS VB B MB VB

PM VS S MB B B VB VB

PB ZE S SB B VB VB VB

evaluation is repeated againand again. The algorithmstops when a

pre-defined maximum number of generations is achieved. The con-

cepts of reproduction, crossover and mutation are nowadays well

known in the literature [14,15] and hence are not described further

in this paper.

2.2. Self-tuning fuzzy PI controller (STFPIC)

After the scaling factors are found by GA, for enhancing the per-

formance of the FPIC, the output SF is further modulated on-line

by a factor ‘˛’, thereby making it a ‘self-tuning FPIC’. Essentially,

a STFPIC is an adaptive FLC. A FLC is called adaptive if any one of its tunable parameters (scaling factors, membership functions and

rules) changes on-line whenthe controller is beingused, otherwise

it is a non-adaptive or conventional FLC [16]. An adaptive FLC that

fine tunes an already working controller by modifying either its

membership functions or scaling factors or both of them is called a

self-tuningFLC. Theblock diagram of the proposed STFPICis shown

in Fig. 4 [13]. Fig. 4 shows that the output SF (gain) of the controller

is modified by a self-tuning mechanism (indicated by the dotted

boundary). Thus, the output-scaling factor of the self-tuning FLC

does not remain fixed while the controller is in operation, rather

it is modified in each sampling time by the gain updating factor ˛,

Fig. 6. TCSC in a two-area four-generator system.




Fig. 7. Generators rotor angles with FPIC for base case.

depending on the trend of the controlled process output. The gain

updating factor (˛) is determined using fuzzy rules of the form

“If e is E and e is E then ˛ is ˛”

From Fig.4 it is observedthatthe valueof iscomputedfromthe

normalized values of e ande bya fuzzyrulebase.The membership

functions used for e and e are exactly same as those used in FPIC.

Moreover, the same fuzzy operators as in Fig. 1 have also been used

in this case. The membership functions for the factor ˛ are defined

in the domain [0,1] and are shown in Fig. 5. As each of the two

inputs (e and e) to the fuzzy rule base (corresponding to ˛) has

seven fuzzified variables, the rule base has 49 rules for computing

the value of ˛. Table 4 shows the rule base for computing ˛. This

rule base has been designed to improve the control performance

under large disturbances such as three-phase short circuit on the

transmission lines, a sudden loss of generating unit or a large loss

of load, etc. For example, immediately after a large disturbance, e

may be small but e will be sufficiently large (they will be of same

sign) and, for this case, ˛ is supposed to be large to increase the

gain. Therefore, under these circumstances, the appropriate rules

are “IF e isPS and e isPM THEN˛ isB” or“IF e is NSande is NM

THEN ˛ is B”. On the other hand, for steady state conditions (i.e.,e≈0 and e≈0), controller gain should be very small (e.g., IF e is

ZE and e is ZE THEN ˛ is ZE) to avoid chattering problem around

the set point. Further justification for using the rule base in Table 4

can be found in [12].

The principal steps for STFPIC can be summarized as follows:

• Step 1: Tune the SFs of the STFPIC without the gain tuning mech-

anism and assuming ˛= 1 (i.e., conventional FLC) for a given

process to achieve a reasonably good control performance. Here,

genetic algorithm [19] has been used for tuningthe conventional

FLC. Atthe end of this step, weget a good controller without self-

tuning and this controller becomes the starting point (input) for

the self-tuning controller in Step 2.

• Step 2: Following [12], set the output SF (Gu) of the self-tuning

FLC K times greater than that obtained in Step 1 keeping the val-

ues of Ge and Ge same as those of the conventional FLC. In this

step ˛=1, which is obtained from the rule base in Table 4. This

enhancement of Gu for the STFPI is found empirically [12] with

an objective to improve the control performance.

3. Case studies

In this work, the effectiveness of the proposed self-tuning FPIC

has been validated on two differentmulti-machine power systems:

(a) 2 area 4 machine system and (b) 10 machine 39 bus system. In

thenext subsection, thedetails of these two systems are presented.

Fig. 8. Active power flow in line 11–10 and TCSC capacitive reactance with FPIC for

base case.




Fig. 9. Rotor angle of generator 2 with STFPIC for base case.

3.1. Study systems

The schematic diagram of thefirst study system of this work, i.e.

the two area four machine system is shown in Fig. 6. The detailed

data of this system can be found in [20]. In this system, machines

1 and 2 form a coherent group, and machines 3 and 4 form the

other coherent group. There are three tie lines connecting the two

coherent areas. As shown in Fig. 6, a TCSC has been assumed to be

installed in one of these tie lines. TCSC is inserted in the middle of

one tie line. Due to lack of space, the one line diagram of the 10

machine system is not shown in this paper. However, the data of

this system has been taken from [21] and is given in the Appendix

A for ready reference. In this system, a TCSC has been assumed

Fig. 10. Active power flow in line 11–10 and TCSC capacitive reactance with STFPIC

for base case.

to be installed in the middle of the line connecting buses #39

and #36.

3.2. System modelling

In thiswork,the synchronous generator hasbeen represented by

a field circuit on the d-axis and one equivalent damper winding on

the q-axis. The machine differential equations and the differential

equationfor the static exciter for the ith machine(suffix i is not used

in these equations just for simplicity) are given below. The system

loads are represented by constant impedances.

dı

dt = ω−ωs (4)

Fig. 11. Generators rotor angles with FPIC for 10% increased loading.




Fig.12. Activepower flowin line 11–10 andTCSC capacitive reactance with FPIC for

10% increased loading.

dω

dt =

1

2H[−D(ω−ωs) + T m − T e] (5)

dEq

dt =

1

T d0

[−Eq + ( xd − xd)id + E fd] (6)

dEd

dt =

1

T q0

[−Ed − ( xq − xq)iq] (7)

dE fddt

=1

T A[−Efd + K A(V ref − V t )] (8)

However, IEEE Type I exciter has been used for 10-machine 39-

bus system. The differential equations for this exciter are

dE fddt

= −K E + SE(E fd)T E

E fd + V RT E

(9)

where SE(E fd) = AexeBexE fd

dV Rdt

=−V RT A

+K ARF T A

−K AK F T AT F

E fd +K A(V ref − V t )

T A(10)

Fig. 13. Rotor angle of generator 2 with STFPIC for 10% increased loading.

Fig. 14. Active power flow in line 11–10 and TCSC capacitive reactance with STFPIC

for 10% increased loading.

dRF dt = −RF T F

+K F E fd

(T F )2 (11)

The electrical torque, T e is expressed as follows

T e = Edid + Eqiq + ( xd − xq)idiq (12)

The notations used in the above Eqs. (4–12) are quite standard

and hence they are not defined in this paper. For more details, the

readers are suggested to refer [21].

3.3. Simulation results

In this paper, the effectiveness of the proposed FPIC and STF-

PIC controllers has been studied through detailed non-linear time

domain simulation studies underthree phase, five cycle, solidshort

circuit faults. The short circuit faults have been assumed to occurat

t = 5 s. The simulation studies have been carried out in the MAT-

LAB/SIMULINK environment [22]. For illustrating the efficacy of

the fuzzy controllers developed in this work, results pertaining

to three different situations are presented. These situations are:

(a) study system without any TCSC, (b) study system with a TCSC

controlled by FPIC and (c) study system with a TCSC controlled by

STFPIC. The simulation results pertaining to these three cases are

Fig. 15.Rotor angle of generator 3 for 75% increased loading.




Fig. 16. Active power flow in line 39–36 and TCSC capacitive reactance with FPIC


Fig. 17. Rotor angle of generator 3 for 75% increased loading with STFPIC.

presented below for both the study systems. In the following fig-

ures, themachinerotor angles have been measured with respect to

the centre of inertia (COI) [21].

3.3.1. Two area four machine system

In this system, the short circuit fault has been assumed to take

place at bus9. Thevariationsof the machine rotor angles andactivepower flow in line 11−10 (P 11−10) for the base case loading condi-

Fig.18. Active power flow in line 39–36 and TCSC capacitive reactance with STFPIC


tion (the loading condition as described in [20]) are displayed in

Figs. 7 and 8(a) corresponding to scenario (a) and (b), respectively.

In Fig. 7, the dotted lines show the variations of rotor angles with-

out (w/o) TCSC whereas the variations of angles with TCSC FPIC

are depicted with solid lines. From Figs. 7 and 8(a), it is observed

that there are substantial oscillations in the system (without any

TCSC),which is dampedto a largeextentby theproposed TCSC FPIC.

The variation of the TCSC reactance ( X TCSC) is shown in Fig. 8(b) for

situation (b). The performance of the proposed TCSC STFPIC vis-a-

vis that obtained with TCSC FPIC is depicted in Figs. 9 and 10. For

implementing STFPIC, a value of 3 has been chosen for K . In Fig. 9,

the variation of the rotor angle of machine 2 are shown whereas

in Fig. 10(a) and (b), the variations of P 11−10 and X TCSC are shown

respectively. From these figures it is observed that application of TCSC STFPIC improves the system damping further as compared to

TCSC FPIC.

To investigate the performance of the proposed TCSC controller

at enhanced loading condition, simulationstudies were carried out

by increasing the system loads by 10% from the base case loading

condition. The results are shown in Figs. 11 and 12 corresponding

to scenario (a) and (b), respectively. From Figs. 11 and 12(a) it is

observed that at 10% higherloading, the systemis unstablewithout

TCSC, which is made stable with acceptable level of damping by

the proposed TCSC FPIC. Fig. 12(b) shows the variation of the TCSC

reactance for this case with TCSC FPIC only. The performance of the

TCSC STFPIC for this loading condition is shown in Figs. 13 and 14.

Again, from these figures it is observed that the system damping

improves further (as compared to that obtained by TCSC FPIC), by

using TCSC STFPIC.

Table A1

Machine data for 39 bus system

Parameter xd (p.u.) xd

(p.u.) T do

(s) xq (p.u.) xq (p.u.) T qo (s) H (s) D (p.u.) x1 (p.u.)

M/C 1 0.295 0.0647 6.56 0.282 0.0647 1.5 30.3 0 0.0518

M/C 2 0.02 0.006 6 0.019 0.006 0.7 500 0 0.0048

M/C 3 0.2495 0.0531 5.7 0.237 0.0531 1.5 35.8 0 0.0425

M/C 4 0.33 0.066 5.4 0.31 0.066 0.44 26 0 0.0528

M/C 5 0.262 0.0436 5.69 0.258 0.0436 1.5 28.6 0 0.0349

M/C 6 0.254 0.05 7.3 0.241 0.05 0.4 34.8 0 0.04

M/C 7 0.295 0.049 5.66 0.292 0.049 1.5 26.4 0 0.0392

M/C 8 0.29 0.057 6.7 0.28 0.057 0.41 24.4 0 0.0456

M/C 9 0.2106 0.057 4.79 0.205 0.057 1.96 34.5 0 0.0456

M/C 10 0.2 0.004 5.7 0.196 0.004 0.5 42 0 0.0032




Table A2

Exciter data for 39 bus system

K A (p.u.) T A (s) K E (p.u.) T E (s) E fd min (p.u.) E fd max (p.u.) K F (p.u.) T F (s) Aex (p.u.) Bex (p.u.)

Ex1 6 0.05 −0.63 0.41 −6 6 0.25 0.5 0.705 0.288

Ex2 20 0.2 1.0 0.314 −6 6 0.063 0.35 0 0

Ex3 5 0.06 −0.02 0.5 −6 6 0.08 1.0 0.0184 0.625

Ex4 40 0.02 1.0 0.73 −6 6 0.03 1.0 0 0

Ex5 5 0.06 −0.05 0.5 −6 6 0.08 1.0 0.0035 0.82

Ex6 5 0.02 −0.04 0.47 −6 6 0.075 1.25 0.0021 0.857Ex7 40 0.02 1.0 0.73 −6 6 0.03 1.0 0.493 0.311

Ex8 5 0.02 −0.05 0.53 −6 6 0.085 1.26 0.0028 0.837

Ex9 40 0.02 1.0 1.4 −6 6 0.03 1.0 0.61 0.3

Ex10 25 0.06 −0.02 0.50 −6 6 0.08 1.0 0 0

3.3.2. Ten machine 39 bus system

In this system, the short circuit fault has been assumed to take

place at bus 24. A large number of simulation studies have been

carried out at various increased system loading conditions to inves-

tigate the suitability of the proposed TCSC controller for enhancing

the power carrying capacity of the system. From these studies it

has been found that the proposed TCSC controller helps to increase

Table A3

Line data for 39 bus system

Line no. Bus Impedance B/2 (p.u.)

From To R (p.u.) X (p.u.)

1 22 6 0 0.0143 0

2 16 1 0 0.0250 0

3 20 3 0 0.0200 0

4 39 30 0.0007 0.0138 0

5 39 5 0.0007 0.0142 0

6 32 33 0.0016 0.0435 0

7 32 31 0.0016 0.0435 0

8 30 4 0.0009 0.0180 0

9 29 9 0.0008 0.0156 0

10 25 8 0.0006 0.0232 0

11 23 7 0.0005 0.0272 0

12 12 10 0 0.0181 013 37 27 0.0013 0.0173 0.1608

14 37 38 0.0007 0.0082 0.06595

15 36 24 0.0003 0.0059 0.0340

16 36 21 0.0008 0.0135 0.1274

17 36 39 0.0016 0.0195 0.1520

18 36 37 0.0007 0.0089 0.0671

19 35 36 0.0009 0.0094 0.0855

20 34 35 0.0018 0.0217 0.1830

21 33 34 0.0009 0.0101 0.08615

22 28 29 0.0014 0.0151 0.1245

23 26 29 0.0057 0.0625 0.5145

24 26 28 0.0043 0.0474 0.3901

25 26 27 0.0014 0.0147 0.1198

26 25 26 0.0032 0.0323 0.2565

27 23 24 0.0022 0.0350 0.1805

28 22 23 0.0006 0.0096 0.0923

29 21 22 0.0008 0.0135 0.127430 20 33 0.0004 0.0043 0.03645

31 20 31 0.0004 0.0043 0.03645

32 19 2 0.0010 0.0250 0.6000

33 18 19 0.0023 0.0363 0.1902

34 17 18 0.0004 0.0046 0.0390

35 16 31 0.0007 0.0082 0.06945

36 16 17 0.0006 0.0092 0.0565

37 15 18 0.0008 0.0112 0.0738

38 15 16 0.0002 0.0026 0.0217

39 14 34 0.0008 0.0129 0.0691

40 14 15 0.0008 0.0128 0.0671

41 13 38 0.0011 0.0133 0.1069

42 13 14 0.0013 0.0213 0.1107

43 12 25 0.0070 0.0086 0.0730

44 12 13 0.0013 0.0151 0.1286

45 11 12 0.0035 0.0411 0.34935

46 11 2 0.0010 0.0250 0.3750

the system power carrying capacity quite significantly. As it is not

possible to include all the simulation results in the paper due to

lack of space, a few representative results are presented below to

illustrate theeffectivenessof the proposedTCSC fuzzy controller for

enhancing the power carrying capacity of the system under study.

The performance of the proposed TCSC FPIC at 75% enhanced

loading condition (from the base case loading condition as

described in [21]) is shown in Figs. 15 and 16. From these figures

it is observed that at 75% increased loading condition, the systembecomes unstable upon occurrence of the fault (without any TCSC)

while the proposed TCSC FPIC is able to stabilize the system. The

operation of the TCSC STFPIC at 75% enhanced loading condition

is shown in Figs. 17 and 18. For implementing STFPIC, a value of

10 has been chosen for K . From these figures (Figs. 17 and 18) it

Table A4

Bus data for 39 bus system

Bus Type P L (p.u.) Q L (p.u.) P G (p.u.) Q G (p.u.)

1 Swing 0.0920 0.0460 5.4282 1.5724

2 PV 11.0400 2.5000 10.000 2.2624

3 PV 0 0 6.5000 1.6606

4 PV 0 0 5.0800 1.5510

5 PV 0 0 6.3200 0.83816 PV 0 0 6.5000 2.8105

7 PV 0 0 5.6000 2.2967

8 PV 0 0 5.4000 0.2757

9 PV 0 0 8.3000 0.5970

10 PV 0 0 2.5000 1.8388

11 PQ 0 0 0 0

12 PQ 0 0 0 0

13 PQ 3.2200 0.0240 0 0

14 PQ 5.0000 1.8400 0 0

15 PQ 0 0 0 0

16 PQ 0 0 0 0

17 PQ 2.3380 0.8400 0 0

18 PQ 5.2200 1.7600 0 0

19 PQ 0 0 0 0

20 PQ 0 0 0 0

21 PQ 2.7400 1.1500 0 0

22 PQ 0 0 0 023 PQ 2.7450 0.8466 0 0

24 PQ 3.0860 0.9220 0 0

25 PQ 2.2400 0.4720 0 0

26 PQ 1.3900 0.1700 0 0

27 PQ 2.8100 0.7550 0 0

28 PQ 2.0600 0.2760 0 0

29 PQ 2.8350 0.2690 0 0

30 PQ 6.2800 1.0300 0 0

31 PQ 0 0 0 0

32 PQ 0.0750 0.8800 0 0

33 PQ 0 0 0 0

34 PQ 0 0 0 0

35 PQ 3.2000 1.5300 0 0

36 PQ 3.2940 0.3230 0 0

37 PQ 0 0 0 0

38 PQ 1.5800 0.3000 0 0

39 PQ 0 0 0 0




is clearly observed that the proposed TCSC STFPIC improves the

system stability further as compared to TCSC FPIC.

4. Conclusion

In this paper, a self-tuning fuzzy logic controller has been

proposed for TCSC to improve the power system damping. The

effectiveness of the proposed STFPIC has been validated on twomulti-machine power systems through detailed non-linear simu-

lation studies under wide variation of operating conditions. Also

theperformanceof STFPIC hasbeen comparedto thatobtained with

the standardFPIC. From the simulation studies it hasbeen observed

that both FPIC and STFPIC help to enhance the system power car-

rying capability quite significantly. However, the performance of

the proposed STFPIC for damping oscillations is better than that

obtained by the standard FPIC and the superiority of the proposed

STFPICover thestandard FPIC becomes more pronounced at higher

loading conditions of the power system.

Appendix A

The data for 39 bus system are given in Tables A1–A4 below.

List of symbols

e(k) error at kth sample

e(k) change in error

eN normalized error

eN normalized change in error

ep(t ) error in power flow in the line following a disturbance

Ge scaling factor corresponding to error

Ge scaling factor corresponding to change in error

Gu scaling factor corresponding to control output

P actual actual power flowing through the line following a distur-

bance

P ref reference or steady state power flowing through the line

t sim total time period of simulation

uN normalized incremental change in control output

u(k) control output at kth sample

u(k) actual incremental change incontrol outputat kth sample

ysp set-point or desired system output

y(k) actual system output at kth sample

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