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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: biswafee@yahoo.com, biswafee@iitr.ernet.in(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.
doi:10.1016/j.epsr.2008.03.005
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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
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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.
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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.
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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.
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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.
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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.
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Fig. 16. Active power flow in line 39–36 and TCSC capacitive reactance with FPIC
for 75% increased loading.
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
for 75% increased loading.
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
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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
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S. Hameed et al. / Electric Power Systems Research 78 (2008) 1726–1735 1735
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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