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Engineering, Technology & Applied Science Research Vol. 8, No. 5, 2018, 3380-3386 3380

www.etasr.com Kahouli et al.: Type-2 Fuzzy Logic Controller based PSS for Large Scale Power Systems Stability

Type-2 Fuzzy Logic Controller Based PSS for Large

Scale Power Systems Stability

O. Kahouli

Electrical Engineering

Department, National

Engineering School of

Sfax, University of Sfax,

Sfax, Tunisia

omarkahouli@yahoo.fr

B. Ashammari

Electrical Engineering

Department, College of

Engineering,

University of Hail,

Hail, Saudi Arabia

badr_ms@hotmail.com

K. Sebaa

Electrical and Computer

Sciences Engineering

Department,

University of Medea,

Medea, Algeria

sebaa.karim@univ-medea.dz

M. Jebali

Electrical Engineering

Department, National

Engineering School of

Sfax, University of Sfax,

Sfax, Tunisia

mariam.djebali@yahoo.fr

H. Hadj Abdallah

Electrical Engineering

Department, National

Engineering School of

Sfax, University of Sfax,

Sfax, Tunisia

hsan.haj@enis.rnu.tn

Abstract—In this paper, the application of the fuzzy logic based

power systems stabilizer (FLPSS) to damp power system

oscillation is presented. Various types of fuzzy logic controller are

used to replace the conventional power system stabilizer (CPSS).

The classic fuzzy logic controller based PSS (FLCPSS), the polar

FLC (PFLCPSS) and the interval type-2 fuzzy logic controller

based PSS (IT2FLCPSS) are applied to the New England - New

York interconnected power system and the obtained results are

compared. For coordination purposes, genetic algorithm (GA) is

used to tune the FLCPSS’s gains. The non-linear simulation in

the presence of noise confirms the robustness and the superiority

of the IT2FLCPSS.

Keywords-CPSS; FLCPSS; PFLCPS; IT2FLPSS; GA; prony

analysis

I. INTRODUCTION

Nowadays, power systems are driven to work around their
limits of stability in a fast and flexible way. Hence, modern
power systems may reach disagreeable conditions like poorly
damped electromechanical oscillations. A possible change in
the operating point could lead to weak interconnected lines.
These lines will cause the generation of inter-area oscillations
with poorly damped low frequency modes. Improving the
damping of these modes by the power systems stabilizers
(PSSs) is an open research topic. PSSs are designed around
some operating points, with the change in these operating
points leading to un-damped oscillations, or even to instability.
Recently, fuzzy logic controllers (FLCs) have attracted
considerable attention as candidates for novel control strategies
because of their advantages over conventional computational
systems. Unlike other classical control methods, FLCs are
model-free controllers, i.e. they do not require an exact
mathematical model of the controlled system. Moreover,
rapidity and robustness are their most profound and interesting
properties in comparison to the classical schemes. Designing
PSSs based on FLC has become an active area and satisfactory
results have been obtained [1-3]. These FLCPSSs use the
concept of the T1FLS (type-1 fuzzy logic system). The concept
of the T2FLS (type 2 fuzzy logic system) was initially

proposed as an extension of the classical T1FLS. T2FLS is
very useful in situations where it is difficult to determine an
exact membership function (MF) for a fuzzy set. Hence, it is
very effective for dealing with uncertainties, such as those due
to penetration of the distributed generation in power systems.
However, T2FLSs are more difficult to use and understand
than T1FLS. Despite these difficulties, T2FLS has found
applications in many fields [4–9]. The concept of the
IT2FLCPSS (interval type-2 fuzzy logic controller PSS) has
been introduced in power systems during the last decade.
Authors in [10] presented the use of the T2FS based adaptive
synergetic PSS to improve the stability of the power system.
Others proposed a PSS based on T2FLS to improve power
system stability where differential evolution algorithm is
applied to optimize the IT2FLCPSS parameters and rule base
[11, 12]. On the other hand, for improvement of the voltage
stability, an IT2FLC is proposed and tuned based on the
approximation of the system by the T1 TS fuzzy model [13].
Its drawback is that the application of the IT2FLPSS is only
suitable for small scale power systems in which authors
approximated the dynamics of the power system by the T1TSK
(type 1 Takagi, Sugeno, and Kang) fuzzy model which is then
used to tune the IT2 FLC via the LMI approach. This method is
tested on small systems (two machines) with the third-order
single-axis dynamic model. For realistic large scale power
systems with power electronic devices this method is time
consuming and not easy to be applied as it requires:

1. Two independent highly nonlinear functions by generator

for building of the T1TSF approximation, which is difficult

to obtain for large scale power systems with various power

electronic devices,

2. Four state feedback gains and two controller parameters

tuning for each generator. Also their work is related to the

voltage control.

In [14] an interval type-2 fuzzy controller-based thyristor
controlled series capacitor (IT2TCSC) has been used along-
side CPSS for improving power system stability on large scale
power systems to damp out the speed and power oscillations

Engineering, Technology & Applied Science Research Vol. 8, No. 5, 2018, 3380-3386 3381

www.etasr.com Kahouli et al.: Type-2 Fuzzy Logic Controller based PSS for Large Scale Power Systems Stability

following different critical faults. They use: i) The active power
line as an input of the IT2TCSC as opposed to the generator
speed, for study of the power system oscillation. ii) The
IT2TCSC use of the sliding surface that leads to the charting
problem. iii) Implementation of two IT2TCSC with the
presence of CPSS.

Based on the research described above, our goal is the
damping of the power system’s oscillation. The proposed
method requires only three gains per generator. Then, attempts
will be made to demonstrate that it can be applied to realistic
power systems, and used for solving the coordination of
IT2FLCPSS for large scale power systems. Hence, various
types of PSS controllers namely FLCPSS [2], PFLCPSS [1],
CPSS and our contribution of IT2FLCPSS are presented in this
paper. This is achieved by applying the previously mentioned
FLCPSSs to a 68-bus, 16-machine power system, which is
large and close to realistic power systems. Several scenarios are
considered to verify the robustness of the proposed method.
The nonlinear simulation and eigenvalue analysis demonstrate
the significant improvement of dynamic oscillations by the
IT2FLCPSS under each scenario.

II. TYPE-2 FUZZY LOGIC SYSTEM DESIGN

The structure of the T2FLS is shown in Figure 1. T2FLS is
similar to T1FLS. The main difference between them is that
T2FLS requires a type-reduced process to convert the output of
the fuzzy inference engine into a type-reduced set and at least
one of the fuzzy sets is T2. The crisp output is obtained by the
defuzzyfication of the type-reduced set. The T2FLS can
efficiently simplify the computational process of type-reduction
and is very simple to use [5].

Fig. 1. Structure of a T2FLS

Consider a type-2 TSK fuzzy logic system having n inputs,

1 1,..., ...n nx x x X X
 = ∈ × ×  and one output y Y∈ . In

order to construct the fuzzy rules we assume that there are M
rules in the type-2 fuzzy system, where the i

th
rule has the

following form:

1 1
: is and...and is Theni i i i i

n n
R if x F x F y C=� � (1)

where
1 2, ,...,
i i i

n
F F F� � � are antecedent linguistic terms

modelled by the interval type-2 triangular fuzzy sets (Figure 2),
iy is the output of thi rule

iR and the consequent parameter

iC is an interval type-1 set. In Figure 2, the footprint of

uncertainty (FOU) of each membership function (MF) can be
represented as a bounded interval in terms of the upper MF

( )i
j

jF
xµ

� and the lower MF ( )i
j

jF
xµ

� , where:

( ) max(min( , ),0)

( ,a ,b ,c )

and ( ) 0.8 ( )

i
j

i i
j j

j j j j

jF
j j j j

j j j j

j jF F

x a c x
x

b a c b

tri x

x x

µ µ

− −
=

− −
≡

= ⋅

�

� �

(2)

,
j

a
j

b and
j

c are the parameters of triangular primary MF of

the type-2 fuzzy set
i
j

F� .

Fig. 2. Interval type-2 triangular MFs for antecedents sets.

The inference engine combines the fuzzy rules in order to
map the crisp inputs to interval type-2 fuzzy output sets. Based
on the input and the antecedents of the rules, it calculates a
firing interval for each rule and then applies these firing levels

to the consequent fuzzy sets. The firing interval [ , ]i if f of the

thi rule is an interval type-1 set, which is determined by its

left-most and right-most points
i
f and

i
f such that :

1 2
1 2( ) ( ) ... ( )i i i

i
nF F F

f x x xµ µ µ= ∗ ∗ ∗
� � � (3)

1 2
1 2( ) ( ) ... ( )i i i

i
nF F F

f x x xµ µ µ= ∗ ∗ ∗
� � � (4)

where ( )i
j

jF
xµ

� and ( )i
j

jF
xµ

� represent the membership values

of the lower and the upper membership functions of the crisp

input
j

x to the type-2 fuzzy set
i
j

F� in the thi rule. When

interval type-2 fuzzy sets are used for the antecedents, and
interval type-1 fuzzy sets are used for the consequent sets of
Type-2 TSK rules, the final output can be expressed as [4, 5]:

,
l r

Y y y =   (5)

The output Y

is an interval type-1 set, therefore, only its two

endpoints
l

y and
r

y need to be computed which can be

Engineering, Technology & Applied Science Research Vol. 8, No. 5, 2018, 3380-3386 3382

www.etasr.com Kahouli et al.: Type-2 Fuzzy Logic Controller based PSS for Large Scale Power Systems Stability

represented as an expansion of fuzzy basis functions (FBFs),
as:

1 1

M Mi i i
l l l li i

yu f u f
= =

= ⋅∑ ∑ (6)

1 1

M Mi i i
r r r ri i

y f u f
= =

= ⋅∑ ∑ (7)

where i
l
f and i

r
f denote the firing strength membership grades

contributing to the left-most-point
l

y and the right-most-point

r
y respectively, i

l
u and i

r
u are the singleton lower and upper

control actions of the consequences part. From the type-
reduction stage a type-reduced set exists for each output. The
crisp output of the controller is equal to the mind point of the
type-reduce set:

+
= l r

y y
y (8)

using the iterative procedure given in [15]. The computation
procedure is briefly provided below.

Initially, the right-most point
r

y is computed. Without loss

of generality, it is assumed that the parameters
i

u are arranged

in ascending order, i.e.,
1 2 3

......
M

u u u u≤ ≤ ≤

• Step_1: Compute
r

y in (7) by initially setting

( ) / 2i i i
r
f f f= + , for i=1, 2, ……., M and let '

r r
y y=

• Step_2: Find k ( 1 1k M≤ ≤ − ) such that
1k k

r
u y u +′≤ ≤ .

• Step 3: Compute
r

y in (7) with i i
r
f f= for i k≤ and

i i
r
f f= for i k> , then set

r r
y y′′ = .

• Step 4: If
r r

y y′′ ′≠ , then go to step 5. If
r r

y y′′ ′= then

set
r r

y y ′′= and go to step 6.

• Step 5: Set
r r

y y ′′′ = and return to step 2.

• Step 6: End.

The procedure to compute
l

y is very similar, only two

changes need to be made. In step 2, we need to find

'1 1k M≤ ≤ − such that 1k k
l

u y u +′≤ ≤ , and in step 3, let

i i
l
f f= for 'i k≤ and i i

l
f f= for 'i k> .

III. FUZZY LOGIC BASED PSS

Selection of the input variables of the FLC based PSS

depends on the nature of the controlled plant and the desired
outputs. Generally, it is common to use the output error and
their derivative (or their integral). Since the goal of this work is
the improvement of the system damping, the speed deviations
and their derivative are used as shown in Figure 3.

Fig. 3. Fuzzy logic based PSS.

A. FLCPSS and IT2FLC

The structure of these two controllers is similar, with small

differences. The speed deviation
i
ω∆ and acceleration

deviation
i
ω∆ � of ith generator are used as the inputs of the

FLCPSS and the IT2FLCPSS in this paper. The output control

signal from the FLCPSS (
i

FLCPSS
U ) is injected to the

summing point of the automatic voltage regulator (AVR)

where an eventual CPSS should be connected. To convert the

measured input variables of the FLCPSS into suitable

linguistic variables, seven fuzzy subsets NB, NM, NS, ZO, PS,

PM, PB are chosen. The MFs for the input variables, as used

in the present study, are shown in Figure 4. In this study, both

inputs of FLCPSS and IT2FLCPSS have seven subsets. Thus,

a fuzzy table consisting of forty nine rules should be

constructed. Table I shows a rule table obtained by the trial

error based on the result obtained from the CPSS.

TABLE I. RULES FOR FLCPSS AND IT2FLCPSS

∆ω

NB NM NS ZO PS PM PB

�∆ω

NB NL NL NL NM MN NS ZO

NM NL NL NM NM NS ZO PS

NS NL NM NS NS ZO PS PM

ZO NM NM NS ZO PS PM PM

PS NM NS ZO PS PS PM PL

PM NS ZO PS PM PM PL PL

PB ZO PS PM PM PL PL PL

The triangular shape function is chosen to follow the work
in [1, 2]. The Gaussian shape function can also be used.
However in our study, for better performance, triangular shape
and 7 MFs are used. Quicker response is observed with 3 MFs,
but with poorer performance. The best compromise between
performance and simulation time is realized by 7 MFs as is also
suggested in [2]. In order to take a crisp control action, the
fuzzy control action inferred from the fuzzy control algorithm
must be defuzzyfied. To ensure that all the fired rules have
some contribution in the control action, the method of the
center of gravity is employed in this study. IT2FLCPSS
requires a reduction strategy. The reduction used in this paper

is centroid method. The input gains
i

Kω ,
i

Kω� and the output

gain
i

FLCPSS
Ku , are used to properly scale the fuzzy input and

output variables.

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www.etasr.com Kahouli et al.: Type-2 Fuzzy Logic Controller based PSS for Large Scale Power Systems Stability

(a) Membership functions for FLCPSS

(b) Membership functions for IT2FLCPSS

Fig. 4. Membership functions.

B. PFLCPSS

PFLCPSS has been originally developed in [1]. The

concept of this controller is based on the sign of ω∆ and ω∆ � .
Two membership functions are created (N(θ),Ρ(θ)) to represent
four situations. The stabilizing signal is calculated using the
following steps:

1. Determine the piecewise linear fuzzy MFs Ν(θ) and Ρ(θ)

as described in [1] and reproduced in Figure 5. These MFs

use the angle θ obtained from the phase plane

1( tan ( / ))θ ω ω−= ∆ ∆� .

2. Compute the stabilizing signal ( )U k using

max

( ) ( )
( ) ( )

( ) ( )

N P
U k Gc k U

N P

θ θ

−
= ⋅ ⋅

+
(9)

where ( )Gc k is the gain whose value is given by (10):

( )
2 2 if

1 otherwise
G

rR
k

R D
c

ω ω
 = ∆ +∆ <= 


�
(10)

Parameter Dr should be adjusted to it optimal value. For
optimal parameter setting, various performance indices can be
used and minimized by traditional or meta-heuristic methods.
In this paper, Dr is equal to 0.98. The value of Umax depends

on the synchronous machine to be studied (it is equal to 0.02pu
in this study). We call this stabilizer Polar FLPCSS.

Fig. 5. Membership functions for PFLCPSS

C. CPSS

The PSS or CPSS is employed to add supplementary
damping to the rotor oscillations of the synchronous machine
by controlling its excitation. The electromechanical oscillations
of the electrical generators must be effectively damped to
maintain the system stability. The output signal of the PSS is
introduced as an additional signal to the AVR (UPSS) to the
excitation system block. The PSS input signal can be the
machine speed deviation. The PSS can be modeled by the
following non-linear system (Figure 6):

Fig. 6. Conventional power system stabilizer model block diagram.

To obtain an adequate damping, PSS should provide a
moderate phase advance at frequencies of interest in order to
compensate for the inherent lag between the field excitation
and the electrical torque induced by the PSS action. The model
consists of a low-pass filter, a general gain, a washout high-
pass filter, a phase-compensation system, and an output limiter.
The gain KPSS determines the amount of damping produced
by the stabilizer. The washout filter eliminates low frequencies

that are present in the ω∆ signal and allows the PSS to respond
only to speed changes. The phase-compensation system is
represented by a cascade of two first-order lead-lag transfer
functions used to compensate the phase lag between the
excitation voltage and the electrical torque of the synchronous

machine. For comparison, a ω∆ conventional type PSS
(CPSS) is designed under the same scenarios used in [16].
CPSSs parameters can be obtained by the classical method of
searching for the close fit to the ideal case from a number of
phase compensator characteristics. PSS parameters are
computed by the root locus method [17]. However, in this
paper PSS parameters are taken from [16], in which GA was
used to find the parameters that give the best damping ratio �.

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IV. MULTIMACHINE POWER SYSTEM MODEL

A 16-machine power system, as shown in Figure 7, is used
to test the proposed IT2FLCPSS. This power system comprises
of five coherent areas representing a reduced model of the New
England and New York interconnected system. The solid lines
indicate the major weak tie lines that cause the low frequency
inter-area oscillations. Each of the areas 1, 2 and 3 contains a
single large generator, which is represented by its aggregated
equivalent model. Area 4 is modeled with an equivalent
generator in addition to more normally sized generators. Area 5
has the most detailed modeling that includes static exciters,
thermal turbines and governors on all generators. The power
system is modeled by a set of non-linear differential equations
[18]:

( , )x f x u=� (11)

where x is a vector state , , , , ,
q d d s

x E Eδ ω ψ ψ ′ ′′ ′ ′′=   and u is

the vector of the PSS, IT2FLCPSS, PFLCPSS or FLCPSS
output signals. Details of network parameters are given in [17].
To assess the FLCPSSs four scenarios are tested (Table II).

Fig. 7. New England - New York interconnected power system model

TABLE II. SCENARIOS CONSIDERED

Scenario no Description

1 Line 28-29 out of service

2 Line 1-2 out of service

3 Lines 25-26 and 3-18 out of service

4 Line 41-42 out of service

A. Tuning of the Gains

Each fuzzy logic controller requires an adequate tuning of

the input gains
i

K
ω

,
i

K
ω�

and the output gains
FLCPSS i

(Figure 3). These gains are used to properly scale the fuzzy
input and output variables of the FLC based PSS. Generally,
these gains can be obtained by a tedious trial-and-error process
for small size systems. But for large scale systems the use of
such a technique is impossible. As the aim of this work
concerns large scale power systems, an optimization based GA
method is proposed to compute these parameters. The objective

of the off-line tuning algorithm is to change the controller gains
to obtain the desired system response. The tuning algorithm
tries to minimize the system overshoot index J:

/ 16

1 1
min ( , , ) ( )

T Ts

i i FLCPSS ik i
J K K Ku kω ω ω

= =
= ∆∑ ∑� (12)

where T is the simulation time (11 seconds). It is very time
consuming to use the non-linear simulation. For this reason the
linearized power system is used to speed-up this process. The
main elements of the GA used to resolve this optimization
problem are defined in [16]. GA is stopped when a maximum
number of generations (100) is reached. Obtained parameters
by the GA are summarized in Table III. From Figure 8 it is
clear that this solution is stable as it is reached at 60
generations. Table III shows the input and the output gains.
Without control, the eigenvalue analysis confirms that the
power system is unstable [16, 19]. Four contingencies are
applied to assess the performance of the four controllers
(CPSS, FLCPSS, PFLCPSS and IT2FLCPSS). The parameters
of CPSS for generators 1 to 16 are obtained using the GA
procedure [16].

Fig. 8. Convergence of the GA optimization

TABLE III. GAINS CONSTANTS

mach.
ι
ω
Κ

K
ω�

FLCi
Ku mach.

K
ω

K
ω�

FLCi
Ku

#01 4.26 2.51 0.95 #09 2.86 8.36 0.98

#02 3.42 6.62 0.95 #10 1.38 4.82 0.81

#03 4.05 4.17 0.93 #11 1.46 3.02 0.87

#04 3.28 4.26 0.78 #12 3.12 3.04 0.89

#05 2.04 6.97 0.85 #13 4.45 1.35 0.83

#06 1.24 4.57 0.99 #14 2.79 0.39 0.66

#07 3.72 6.12 0.96 #15 2.15 1.81 0.41

#08 0.39 6.28 0.79 #16 3.34 2.82 0.31

The 1st (resp. 2nd, 3rd) contingency consists on the

application of the three-phase to ground fault in line 1-2 (resp.
line 28-29, line 41-42) at 0.1s, and cleared after 6 cycles. In the
fourth contingency, the application of the three-phase to ground
fault in line 3-18 at 0.1s is considered, which is then cleared
after 6 cycles. For the system with CPSS, linear analysis is
carried out by the perturbation method for building the state
space system, after which the modes correspond to the
eigenvalues of the linearized system. However, in the presence
of IT2FLCPSS the modes are obtained by Prony analysis as it
is not possible to use the perturbation method, as in the case of

G14

40 48 47

31 30

63
G10

G11

32
38

G15

G16

51
45

G13

33
9

25
26

18
17

54
10

4 14

20
5

area 4

area 5

area 2

area 3

a
re
a
1

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the presence of CPSS. Prony analysis is a method for extracting
sinusoidal exponential signals from time series data, by solving
a set of linear equations. Assuming N complex data samples
X[1],…, X[N] the investigated function can be fitted by M
exponential functions:

1
(̂ )

2
i i

N
tj

i
i

f t Ae
φλ

=∑ (13)

In order to perform the damping of the power system
oscillations by PSSs, several sensors are necessary. However,
sensor readings are often noisy. In order to simulate the impact
of the measurement uncertainty on the performance of T1 FLC
based PSS and T2 FLC based PSS, random noise with normal
distribution is added to the measurement values of rotating
speed and acceleration. To carry out a quantitative comparison
between the controllers, three well known performance criteria
are used [5]: the integral of square error,

16 2
1

ISE ( )
nn

t dtω
=

= ∆∑ ∫ , the integral of the absolute value
of the error,

1
IAE ( )

nn
t dtω

=
= ∆∑ ∫ , and the integral of

the time multiplied by the absolute value of the error,
16

1
ITAE ( )

nn
t t dtω

=
= ⋅ ∆∑ ∫ . Generally, these indexes of

performance are used in the optimal tuning of the controller. In
this work, these will be employed to assess the stability of the
closed loop system. Minimum value of ISE means that the
controller will eliminate large errors quickly, but will tolerate
small errors persisting for a long period. A system with
minimum IAE tends to produce slower response than ISE
optimal systems, but usually with less oscillation. A system
with small ITAE settles much more quickly than the other two
errors. In Table IV, the values for ISE, IAE and ITAE are
summarized considering noise of 0.02pu and 0.05pu applied to
the speeds and accelerations of all 16 machines and only in the
case of the first contingency.

TABLE IV. PERFORMANCE CRITERIA VALUES UNDER 1ST
CONTINGENCY IN PRESENCE OF 0.02PU AND 0.05PU NOISE

Noise of 0.02pu Noise of 0.05pu

Avg. Value Std. Dev. Avg. Value Std. Dev.

CPSS

ISE 2.46e-02 5.60e-03 3.49e-02 3.55e-02

IAE 8.23e-01 7.99e-02 9.65e-01 3.09e-01

ITAE 5.26e+00 5.02e-01 5.91e+00 2.56e+00

PFLCPSS

ISE 1.75e-05 2.03e-07 2.05e-05 7.15e-07

IAE 1.92e-02 1.63e-04 2.85e-02 5.77e-05

ITAE 5.27e-02 8.13e-04 1.12e-01 2.77e-03

FLCPSS

ISE 1.75e-05 2.95e-07 2.05e-05 6.17e-07

IAE 1.99e-02 3.69e-04 2.86e-02 3.51e-04

ITAE 5.73e-02 9.39e-04 1.12e-01 2.98e-03

IT2FLCPSS

ISE 1.74e-05 9.42e-08 1.98e-05 6.55e-08

IAE 1.92e-02 1.63e-04 2.85e-02 3.51e-04

ITAE 4.92e-02 8.35e-04 1.11e-01 3.13e-03

In Table V, the behavior of controllers with the influence of

model uncertainty is presented. Furthermore each value
represents the average and the standard deviation of the three
performance criteria which are calculated for 10 samples. A
closer inspection of Table V reveals that the criteria values for
T1 FLCPSS and IT2FLCPSS type-2 FLC are similar. This is

due to the mitigation effect of these uncertainties by the FLS.
In such a case, it is advisable to select a T1 FLCPSS since it is
easier to implement. However, with the performance criteria
values shown in Table IV one can suggest that at the lower
values of ISE, IAE, and ITAE, the best system response is
obtained when using an IT2FLCPSS. These results
demonstrate the ability of the proposed controller to cope with
an uncertain process and its potentiality to outperform its T1
counterpart.

TABLE V. PERFORMANCE CRITERIA VALUES FOR PSS-VARIOUS
MODELS (SCENARIOS)

Scenarios #

(Modeling uncertainty)

1 2 3 4

ISE

CPSS 0.0197 0.0298 0.0735 0.0040

PFLCPSS 0.0117 0.0196 0.0462 0.0007

FLCPSS 0.0116 0.0200 0.0461 0.0005

IT2FLCPSS 0.0118 0.0198 0.0471 0.0011

IAE

CPSS 4.6459 4.2780 6.2612 2.0789

PFLCPSS 1.9978 2.6958 3.7928 1.1379

FLCPSS 1.9626 2.6276 3.6820 0.9862

IT2FLCPSS 2.1615 2.9320 4.2134 1.5209

ITAE

CPSS 6.7013 5.2684 8.0880 3.3461

PFLCPSS 2.0698 3.0261 4.2960 1.6868

FLCPSS 2.0020 2.8350 4.0587 1.3968

IT2FLCPSS 2.5119 3.7904 5.3436 2.7344

V. CONCLUSION

The application of three fuzzy logic-based control
algorithms as power system stabilizers is described in this
paper. Time domain simulation and modal analysis performed
with various stabilizers, over a wide range of operating
conditions with different disturbances, have demonstrated the
effectiveness and robustness of this control algorithm. A
comparison of the performance of the four algorithms (the
three fuzzy logic-based and the conventional) shows that the
three controllers generally provide better performance than a
fixed parameter conventional stabilizer. Although all four
algorithms provide acceptable performance, IT2FLCPSS is the
most suitable when the presence of measurement uncertainties
(noise) is more pronounced. Also, due to its simplicity it can be
easily implemented for the control of large scale power
systems.

REFERENCES

[1] T. Hiyama, “Development of fuzzy logic power system stabilizer and
further studies”, 1999 IEEE International Conference on Systems, Man,
and Cybernetics, Tokyo, Japan, October 12-15, 1999

[2] M. Sanaye-Pasand, O. P. Malik, “Implementation and laboratory test
results for a new fuzzy logic based PSS”, 1996 Canadian Conference on
Electrical and Computer Engineering, Calgary, Canada, May, 26-29,
1996

[3] M. A. M. Hassan, O. P. Malik, “Implementation and laboratory test
results for a fuzzy logic based self-tuned power system stabilizer”, IEEE
Transactions on Energy Conversion, Vol. 8, No. 2, pp. 221-228, 1993

[4] Q. Liang, J. M. Mendel, “An introduction to type-2 TSK fuzzy logic
systems”, 1999 IEEE International Fuzzy Systems, Seoul, South Korea,
August, 22-25, 1999

[5] S. Barkat, A. Tlemcani, H. Nouri, “Noninteracting adaptive control of
pmsm using interval type-2 fuzzy logic systems”, IEEE Transactions on
Fuzzy Systems, Vol. 19, No. 5, pp. 925-936, 2011

Engineering, Technology & Applied Science Research Vol. 8, No. 5, 2018, 3380-3386 3386

www.etasr.com Kahouli et al.: Type-2 Fuzzy Logic Controller based PSS for Large Scale Power Systems Stability

[6] X. Lu, M. Liu, J. Liu, “Design and optimization of interval type-2 fuzzy
logic controller for delta parallel robot trajectory control”, International
Journal of Fuzzy Systems, Vol. 17, No. 1, pp. 595-608, 2015

[7] T. Kumbasar, H. Hagras, “A self-tuning zslices-based general type-2
fuzzy picontroller”, IEEE Transactions on Fuzzy Systems, Vol. 23, No.
1, pp. 991-1013, 2015

[8] A. Padhi, Hardware Realization of Interval Type 2 Fuzzy Logic
Controller, PhD Thesis, National Institute of Technology, Rourkela,
India, 2015

[9] K. Su, S. Huang, C. Yang, “Development of robotic grasping gripper
based on smart fuzzy controller”, International Journal of Fuzzy
Systems, Vol. 19, No. 1, pp. 190-206, 2017

[10] E. Nechadi, M. Harmas, A. Hamzaoui, N. Essounbouli, “Type-2 fuzzy
based adaptive synergetic power system control”, Electric Power
Systems Research, Vol. 88, pp. 9-15, 2012

[11] Z. Sun, N. Wang, D. Srinivasan, Y. Bi, “Optimal tunning of type-2 fuzzy
logic power system stabilizer based on differential evolution algorithm”,
International Journal of Electrical Power and Energy Systems, Vol. 62,
pp. 19-28, 2014

[12] S. Kamel, B. Ziyad, H. M. Naguib, A. Mouloud, R. Mohamed, “An
indirect adaptive type-2 fuzzy sliding mode PSS design to damp power
system oscillations”, 7th International Conference on Modelling,
Identification and Control, Sousse, Tunisia, December 18-20, 2015

[13] A. Abbadi, L. Nezli, D. Boukhetala, “A nonlinear voltage controller
based on interval type 2 fuzzy logic control system for multimachine
power systems”, International Journal of Electrical Power and Energy
Systems, Vol. 45, No. 1, pp. 456-467, 2013

[14] M. Tripathy, S. Mishra, “Interval type-2-based thyristor controlled series
capacitor to improve power system stability”, IET Generation,
Transmission & Distribution, Vol. 5, No. 2, pp. 209-222, 2011

[15] N. Karnik, J. Mendel, Q. Liang, “Type-2 fuzzy logic systems”, IEEE
Transactions on Fuzzy Systems, Vol. 7, No. 6, pp. 643-658, 1999

[16] K. Sebaa, M. Boudour, “Optimal locations and tuning of robust power
system stabilizer using genetic algorithms”, Electric Power Systems
Research, Vol. 79, No. 2, pp. 406-416, 2009

[17] G. Rogers, Power System Oscillations, Springer, 2000

[18] P. Kundur, Power System Stability and Control, EPRI, 1994

[19] K. Sebaa, H. Gueguen, M. Boudour, “Mixed integer non-linear
programming via the cross-entropy approach for power system
stabilisers location and tuning”, IET Generation, Transmission &
Distribution, Vol. 4, No. 8, pp. 928-939, 2010