design of interval power system stabilizer

8/11/2019 Design of Interval Power System Stabilizer

http://slidepdf.com/reader/full/design-of-interval-power-system-stabilizer 1/8

Abstract — This paper presents the performance of an application

of latest development of type1 fuzzy logic which is interval type2

fuzzy logic as a Power System Stabilizer (PSS). Interval Type2 Fuzzy

Logic PSS (IT2FLPSS) is a proportional-derivative type fuzzy logic

PSS consists of interval type2 fuzzy logic controller and adjustable

proportional and derivative gain. IT2FLPSS uses rotor speed

deviation as a main input and armature power as auxiliary input.

Simulations are done with several fault tests at transmission line onK undur Test System. As reference Type1 Fuzzy Logic PSS

(T1FLPSS), IEEE PSS4B (Multi Band PSS) and IEEE PSS2B (dw

PSS) from IEEE std 421.5 have been used to be compared to

IT2FLPSS. The result shows that power transfer response using

IT2FLPSS has a settling time 5.36s and overshoot level 126.35 MW

in fault normally cleared simulation. For fault cleared with one line

outage simulation, the system has settling time 8.07s with overshoot

value 68.41 MW. Similarly, for voltage deviation and armature

power deviation responses, application IT2FLPSS shows great

improvement.

Keywords — Interval Type-2 Fuzzy Logic, Power System

Stabilizer.

I. I NTRODUCTION

LECTRICAL power system generally consists of some

generating unit, transmission line, and load center. The

fault is always occurred in the electrical power system,

whether it is a permanent one or temporary one. The fault in

electrical power system can caused deviation on system’s

variables, such as voltage, frequency and others. This

deviation can affect the stability of system. Stability in

electrical power system is defined as an ability of electrical

power system to maintain synchronization during and after

fault occurred.

Power System Stabilizer (PSS) has function to maintain

electrical power system stability [1, 2, 3]. Most PSS used in

electrical power system is developed from the classical linear

control theory. Linear control theory is based on a linear

model of a fixed power system configuration. In other words, a

fixed-parameters PSS, called a conventional PSS is optimum

for one set of operating conditions and may not be as effective

for drastically different set of operating condition [2].

Imam Robandi, PhD, is with Department of Electrical Engineering, Institut

Teknologi Sepuluh Nopember (ITS), K ampus ITS, Sukolilo, Surabaya 60111,

Indonesia (e-mail: [email protected]).

Bedy K harisma is senior student of ITS, and he is now under supervised by Dr. Imam Robandi in his final project.

Nowadays PSS has possibility to be designed and

implemented with a new controller based on a modern and

sophisticated technology such as artificial intelligent. In

artificial intelligent methods, fuzzy logic is really interesting,

because it does not need mathematical approach to give

control solution.

Fuzzy logic and fuzzy sets are fundamental element for

fuzzy systems, where their objective is to model brainmanipulates inexact information. So this method is suitable for

a complex system and non-linear [4, 5]. Fuzzy set is

introduced first time by Zadeh in 1965 to manipulate data and

information which unprobabilistic and uncertain.

Further development on type1 fuzzy set is interval type2

fuzzy set. Interval type2 fuzzy set is used to model uncertainty

and imprecision in a better way. Interval type2 fuzzy set is

introduced at the first time at 1975 by Zadeh and developed by

Mendel with characterizing interval type2 fuzzy set as

Footprint of Uncertainty (FOU). FOU is limited by superior

and inferior type1 membership function [6, 7]. The

development of fuzzy set from type1 to interval type2 in mostcases always shows a better result [8].

In order to obtain the performance improvement of the

electrical power system, Interval Type2 Fuzzy Logic PSS

(IT2FLPSS) is proposed. In the IT2FLPSS application,

K undur Test System is used as test plant in conditions of fault

normally cleared and fault cleared with one line outage. In this

paper, the application of IT2FLPSS is compared with the Type

1 Fuzzy Logic PSS (T1FLPSS), dw PSS, and Multi Band PSS

(MB PSS). Three parameters are observed, voltage deviation,

power armature deviation and power transfer deviation. A

good PSS is a PSS which can maintain system’s

synchronization with minimum overshoot and settling time at

each observed parameters. The result is quite promising that

power transfer response using IT2FLPSS has a settling time

5.36s and overshoot level 126.35 MW in fault normally

cleared simulation. For fault cleared with one line outage

simulation, the system has settling time 8.07s with overshoot

value 68.41 MW. From these result IT2FLPSS can greatly

improve the system stability. Similarly, for voltage deviation

and armature power deviation responses, application

IT2FLPSS shows great improvement.

II. K UNDUR TEST SYSTEM AND POWER SYSTEM STABILIZER

K undur Test System is a system known worldwide as a

simple system on behalf of a general electricity system.

Design of Interval Type-2 Fuzzy Logic Based

Power System StabilizerImam Robandi, and Bedy K harisma

E

PROCEEDI NGS OF WORLD ACADEMY OF SCIE NCE, E NGI NEERI NG A ND TECH NOLOGY VOLUME 31 JULY 2008 ISS N 1307-6884

PWASET VOLUME 31 JULY 2008 ISS N 1307-6884 683 © 2008 WASET.ORG

International Journal of Electrical and Electronics Engineering 3:10 2009

593



Despite its small size, it mimics very closely the behavior of

typical systems in actual operation. The K undur Test System is

used as a plant for PSS implementation.

A. Kundur Test System

The K undur Test System is shown in Fig. 1 that consists oftwo fully symmetrical areas linked together by two 230 kV

lines of 220 km length. Each area is equipped with two

identical round rotor synchronous acts as thermal plant

generators rated 20kV/900MVA connected to transformer (T1,

T2, T3, and T4) . The synchronous machines (G1, G2, G3, and

G4) in all area have identical parameters, except for inertia

which is H = 6.5s for all generators in Area 1 and H = 6.175s

for all generators in Area 2. Thermal generating plants having

identical speed regulators and fast static exciters with a 200

gain at all locations. Each generator produces 700 MW. The

loads are assumed everywhere as constant impedance load.

The Area 1 and Area 2 loads are 967 MW (L1) and 1767 MW(L2) respectively. The load voltage profile was improved by

installing 187 MVAr capacitors (C1 and C2) in each area to

make closer to unity. Area 1 is exporting to Area 2 through

two tie-lines and a single tie-line with power transfer level 413

MW and 353 MW, respectively. [2,3,9].

Fig. 1 K undur Test System

B. dw PSS

The dw PSS provides an auxiliary signal control to

excitation system based on moderate phase advance at

frequencies in order to compensate inherent lag between the

field excitation and the electrical torque . The dw PSS consists

of Sensor Time Constant, Gain, Wash Out Filter, Lead-Lag

Compensator, and a limiter. The dw PSS model is shown in

Fig. 2.

Fig. 2 dw PSS [9]

The model consists of a low-pass filter, a general gain, a

washout high-pass filter, a phase-compensation system, and an

output limiter. Functions of each block are explained as

follows:

1) Sensor

Sensor block is a first order low-pass filter. Its function is

to filter input signal.

2) Overall Gain

Overall Gain’s function to regulate amplifying level of

input signal.3) Wash-out

Washout is a filter works as high pass filter for the input

signal.

4) Lead-Lag Compensator

Lead-lag compensator works as phase-lead and phase–lag

compensator of excitation system.

5) Limiter

Limiter works to limit the output of PSS before the output

signal goes to excitation Systems.

Values of dw PSS’s parameters are presented in Table I.

TABLE IDW PSS’S PARAMETER

Parameter Value

Sensor time constant (Ts) 15 10-3s

Wash-Out time constant (Tw) 10s

Overall Gain (K ) 30

Lead-Lag #1Time constant (T1n) 50 10-3s

Lead-Lag #1 Time constant (T1d) 20 10-3s

Lead-Lag #2 Time constant (T2n) 3s

Lead-Lag #2 Time constant (T2d) 5.4s

Limiter -0.15 to 0.15

C.

MB PSS

Multi Band PSS (MB PSS) is designed to damp all the

disturbances occurring in an electrical power system. The

disturbance induces electromechanical oscillations to electrical

generators on system. Electromechanical oscillations can be

classified in four main categories as explained as follows:

1) Local oscillations: it is caused by a fault occurred between

a unit and the rest of the generating station and between the

latter and the rest of the power system. Their frequencies

typically range from 0.8 to 4.0 Hz.

2) Interplant oscillations: it is caused by a fault occurred

between two electrically close generation plants.

Frequencies can vary from 1 to 2 Hz.3) Inter-area oscillations: it is caused by a fault occurred

between two major groups of generation plants.

Frequencies are typically in a range of 0.2 to 0.8 Hz.

4) Global oscillation: characterized by a common in-phase

oscillation of all generators as found on an isolated system.

The frequency of such a global mode is typically under 0.2

Hz.

These oscillations, also called power swings, must be

effectively damped to maintain the system's stability. Multi

Band PSS (MB PSS) provides damping action using three

separate working bands to damp all oscillation frequency

spectrums that may be occurred at electrical power system.




594



Three separate bands are used, respectively dedicated to the

low-, intermediate-, and high-frequency modes of those

oscillations: the low band is typically associated with the

power system global mode, the intermediate with the inter-area

modes, and the high with the local modes. MB PSS model is

shown in Fig. 3.

Fig. 3 Multi Band PSS

Each of the three bands is made of a differential band pass

filter, a gain, and a limiter. Functions of each block are

explained as follows:

1) Speed Transducers

Speed Transducer’s function is to change rotor speed

deviation as input signal into frequency.

2) Low Frequency Band [FL K L]

Low Frequency Band is a high pass filter. Its function is to

filter low frequency oscillation mode.

3) Intermediate Frequency Band [FI K I]

Intermediate Frequency Band is a high pass filter. Its

function is to filter Intermediate frequency oscillation

mode.

4) High Frequency Band [FH K H]

High Frequency Band is a high pass filter. Its function is to

filter high frequency oscillation mode.

5) Signal Limiter [VLMAX-MIN VlMAX-MIN VHMAX-MIN]

Signal Limiter’s function is to limits the output signal of

each band pass filter and MB PSS final limiter

6) Final Limiter [VSTMAX-STMIN]

Final Limiter’s function is to limit total sum of band pass

filter outputs.

Values of MB PSS’s parameters are presented in Table II.

TABLE II

MB PSS’S PARAMETERS

Parameter Value

FL 0.2Hz

K L 30

FI 1.25Hz

K I 40

FH 12.0Hz

K H 160

VLMAX-MIN -0.075 to 0.0175

VlMAX-MIN -0.15 to 0.15

VHMAX-MIN 0.15 to 0.15VSTMAX-MIN 0.15 to 0.15

III. PROPOSED I NTERVAL TYPE2 FUZZY LOGIC PSS I N

APPLICATION

An Interval Type2 Fuzzy Logic PSS is similar with Type1

Fuzzy Logic PSS, but instead using type1 Fuzzy Logic as a

controller IT2FLPSS uses Interval Type2 Fuzzy Logic as the

controller. The explanation about Interval Type2 Fuzzy Logic

and its application, IT2FLPSS, are explained as follows:

A. Interval Type2 Fuzzy Logic

Membership function in interval type2 fuzzy logic set as an

area called Footprint of Uncertainty (FOU) which limited by

two type1 membership function those are: Upper membership

Function (UMF) and Lower Membership function (LMF)

[6,7]. Interval type2 membership function is shown in Fig. 4.

Fig. 4 Membership Function Interval Type2 Fuzzy Logic Set

Operation at Interval type-2 fuzzy set is identical with an

operation on type-1 fuzzy set, however on interval type-2

fuzzy system; fuzzy operator is done at two type1 membership

function which limits the FOU, UMF and LMF to produce

firing strenght. Operation on interval type2 fuzzy logic is

shown in Fig. 5.

Fig. 5 Operation on Interval Type2 Membership Function

Fuzzy Inference System (FIS) which used in this paper is

Mamdani method, or used to call Max-Min method. On

Mamdani FIS it needs 5 steps to produce an output:

Fuzzyfication, Membership function operation, Implication

function, Aggregation, and Defuzzyfication. A simple example

of Mamdani Fuzzy Inference System on “dinner for two” [10]

on interval type2 fuzzy logic system is shown in Fig. 6.

Defuzzyfication is a mapping process from fuzzy logic

control action area to a non-fuzzy (crisp) control action area.

Defuzzyfication on an interval type2 fuzzy logic system thatuse centroid method has been proposed by K arnik and




595



Mendel, known as K arnik-Mendel Algorithm [9]. The K arnik-

Mendel Algorithm flow chart is shown at Fig. 7.

Fig. 6 Mamdani Fuzzy Inference System on Interval Type2 Fuzzy

Logic

Fig. 7 K arnik-Mendel Algorithms to locate Centroid on Interval

Type2 Fuzzy Logic System

The K arnik-Mendel Algorithm flow chart at Fig. 7 can be


The cl determination

1) Initialization ofi

θ , through equation (1)

[ ] N1,...,i ,)(xµ)(xµ2

1θ iii =+= (1)

2) Calculate 'c through equation (2)

∑

∑

=

=== N

1i

i

N

1i

ii

Ni

θ

θx

)θ,...,c(θc' (2)

3) Calculate K value, so it fulfills equation (3)

1k k xc'x+

≤≤ (3)

4) Calculate "c through equation (4)

∑∑

∑∑

+==

+==

+

+

= N

1k i

iA

k

1i

iA

N

1k i

iAi

k

1i

iAi

)(xµ)(xµ

)(xµx)(xµx

c" (4)

5) Check, if c'"cl = than stop. If not, set "cc' l= then return

to step number 2.

The cr determination1) Initialization

iθ , through equation (1)

2) Calculate 'c through equation (2)

3) Calculate k value, so it fulfills equation (3)

4) Calculate "c through equation (5)

∑∑

∑∑

+==

+==

+

+

= N

1k i

iA

k

1i

iA

N

1k i

iAi

k

1i

iAi

)(xµ)(xµ

)(xµx)(xµx

c" (5)

5) Check, if c'"c r = than stop. If not, set "cc' r

= then

return to step number 2.

Centroid Calculation

The cl and cr are important in centroid calculation. The

centroid can be obtained through equation (6).

Centroid = (cl+cr )/2 (6)

Even though centroid calculation is an iteration process, the

number of iteration will not exceeds N, where N equals the

number of sampled values of the primary variable [11].

B. Interval Type2 Fuzzy Logic PSS

The model of IT2FLPSS refers [2] with a type development

on fuzzy logic controller block, and to simplify modelintegrator block is also removed. IT2FLPSS model is as shown

in Fig. 8.

Fig. 8 IT2FLPSS Model

Fig. 8 shows that IT2FLPSS consists of blocks, those arewash-out, gain (K w, K p, K s1), and limiter. Each part is




596




1) Wash Out

This block consists of two wash-out filter with time

constant 10 second.

2) Gain [K w K p K s1]

Gain is needed to normalize the input and output of fuzzylogic controller.

3) Fuzzy Logic Controller

Fuzzy Logic Controller has a function to produce control

signal as an output appropriate with the input.

4) Limiter [Vsmin Vsmax]

Limiter gives limitation of the PSS output.

In order to set fuzzy logic controller, input membership

function, output membership function, rules, and gain tuning

are definitive. Detail of input membership function, output

membership function, rules, and gain tuning are as follows:

Input Membership Function

Each of input variables are classified by Input membership

function consists of trapezoidal membership function and

triangular membership function, described in Fig. 9.

-6 -4 -2 0 2 4 60

0.5

1

Fig. 9 Input Membership Function

The linguistic variable of input membership shown in Fig. 9

can be described as follows:

IBN _ UMF =[-5-0.25 -1 -0.2 0.1+0.25 ];

IBN _ LMF =[-5+0.25 -1 -0.2 0.1-0.25 ];

IMN _ UMF =[-1-0.25 -0.15 0.2+0.25 ];

IMN _ LMF =[-1+0.25 -0.15 0.2-0.25 ];

ILN _ UMF =[-1-0.25 -0.065 1+0.25 ];

ILN _ LMF =[-1+0.25 -0.065 1-0.25 ];

IZ_ UMF =[-1-0.25 0 1+0.25 ];

IZ_ LMF =[-1+0.25 0 1-0.25 ];

ILP _ UMF =[-1-0.25 0.065 1+0.25 ];

ILP _ LMF =[-1+0.25 0.065 1-0.25 ];IMP _ UMF =[-0.2-0.25 0.15 1+0.25 ];

IMP _ LMF =[-0.2+0.25 0.15 1-0.25 ];

IBP _ UMF =[-0.1-0.25 0.2 1 5+0.25 ];

IBP _ LMF =[-0.1+0.25 0.2 1 5-0.25 ];

Output Membership Function

Output membership function also consists of triangular

membership function, described in Fig. 10.

-1.5 -1 -0.5 0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Fig. 10 Output Membership Function

The linguistic variable of output membership shown in Fig.

10 can be described as follows:

OBN _ UMF =[-1-0.005 -0.51 -0.439+0.005 ];

OBN _ LMF =[-1+0.005 -0.51 -0.439-0.005 ];

OMN _ UMF =[-0.515-0.005 -0.439 -0.302+0.005];

OMN _ LMF =[-0.515+0.005 -0.439 -0.302-0.005];

OLN _ UMF =[-0.439-0.005 -0.302 0+0.005 ];

OLN _ LMF =[-0.439+0.005 -0.302 0-0.005 ];

OBZ_ UMF =[-0.302-0.005 0 0.302+0.005 ];

OBZ_ LMF =[-0.302+0.005 0 0.302-0.005 ];

OLZ_ UMF =[-0.0015-0.0005 0 0.0015+0.0005 ];

OLZ_ LMF =[-0.0015+0.0005 0 0.0015-0.0005 ];

OLP _ UMF =[0-0.005 0.302 0.439+0.005 ];

OLP _ LMF =[0+0.005 0.302 0.439-0.005 ];

OMP _ UMF =[0.302-0.005 0.439 0.515+0.005 ];

OMP _ LMF =[0.302+0.005 0.439 0.515-0.005 ];

OBP _ UMF =[0.439-0.005 0.515 1+0.005 ];

OBP _ LMF =[0.439+0.005 0.515 1-0.005 ];

Rules

Rules used by IT2FLPSS are identical with T1FLPSS [2].

The Rules are shown in Table III.

TABLE III

FUZZY LOGIC R ULES

dw\dPa BP MP LP Z LN MN BN

BN BZ LN MN MN BN BN BN

MN LP BZ LN MN MN BN BN

LN MP LP BZ LN LN MN BN

Z BP MP LP LZ LN MN BN

LP BP MP LP LP BZ LN MN

MP BP BP MP MP LP BZ LN

BP BP BP BP MP MP LP BZ

Gain Tuning

The gains of the proportional and derivative actions of the

IT2FLPSS are given by the following relations:

K PR = K s1× (F{K p} + F{K w})

K DER = K s1 × F{K P}

With K PR , K DER , and F{} are proportional gain, derivative

gain, and fuzzy operation, respectively. To obtain the gains

K w, K p, and K s1 a two steps method has been used. These

two steps consist of adjusting K p and K w in order to normalize

input and then tuning K s1 to obtain best result. The value of

K w, K p, and K s1 are 0.55, 50 x K p, and 3, respectively.




597



IV. R ESULT AND A NALYSIS

To see the performance of PSS on electrical power system,

fault simulation is demonstrated with connecting a 3 phase-

ground fault block at the middle of transmission line (Fault

Point A) for 8 cycles, in normally cleared condition and

cleared with one line outage condition.

A. Fault Normally Cleared

In this simulation, K undur Test System is demonstrated

under a fault simulation and then cleared without any line

outage. While fault occurred in electrical power system, it can

deviates power armature that can cause swing on generator,

affect generator voltage output and area power transfer level

until the fault is cleared [1]. When fault is cleared, system will

oscillate to return on its stable point. Electrical power transfer

level from Area1 to Area2, voltage deviation response at G1,

and power armature deviation response at G1 are shown in

Fig. 11 until Fig. 13.

0 200 400 600 800 1000 1200 1400 1600 1800 2000150

200

250

300

350

400

450

500

550

600

time (1/100 s)

M e g a W a t t ( M W )

Electrical Power Transfer Level

dw PSS

MB PSS

T1FLPSS

IT2FLPSS

Fig. 11 Electrical Power Transfer Response on Fault Normally

Cleared Simulation

0 200 400 600 800 1000 1200 1400 1600 1800 20000.9

0.95

1

1.05

1.1

1.15

time (1/100 s)

p e r u n i t ( p u )

Voltage Output at G1

dw PSS

MB PSS

T1FLPSS

IT2FLPSS

Fig. 12 Voltage Output Response on Fault Normally Cleared

Simulation

0 200 400 600 800 1000 1200 1400 1600 1800 2000-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

time(1/100 s)


Power Armature at G1

dw PSS

MB PSS

T1FLPSS

IT2FLPSS

Fig. 13 Power Armature Response on Fault Normally Cleared

Simulation

B. Fault Cleared with One Line Outage

In this simulation, K undur Test System is demonstratedunder a fault simulation and then cleared with opening breaker

on line which fault occurred. Disconnecting one of two tie-line

transmission lines can change the area power transfer level

into single-line power transfer level [1]. System will oscillate

to its new stable point, during that time system parameters will

deviate. Power transfer from Area1 to Area2, voltage deviation

response at G1, and power armature deviation response at G1

are observed and shown in Fig. 14 until Fig. 16.

0 200 400 600 800 1000 1200 1400 1600 1800 2000150

200

250

300

350

400

450

500

time(1/100 s)

M e g a W a t t ( M W )

Electrical Power Transfer Level

dw PSS

MultiBand PSS

T1FLPSS

IT2FLPSS

Fig. 14 Electrical Power Transfer Response on Fault Cleared With

One Line Outage Simulation




598



0 200 400 600 800 1000 1200 1400 1600 1800 20000.9

0.95

1

1.05

1.1

1.15

time(1/100 s)


Voltage Output at G1

dw PSS

MB PSS

T1FLPSS

IT2FLPSS

Fig. 15 Voltage Output Response on Fault Cleared With One Line

Outage Simulation

0 200 400 600 800 1000 1200 1400 1600 1800 2000-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

time (1/100 s)


Power Armature at G1

dw PSSMB PSS

T1FLPSS

IT2FLPSS

Fig. 16 Power Armature Response on Fault Cleared With One Line

Outage Simulation

To evaluate the overshoot value and settling time clearly,

the data of PSS performances are shown on Table IV and

Table V.

TABLE IV

FAULT NORMALLY CLEARED

Power

Transfer Level

Voltage

Output at G1

Armature Power

at G1PSS

Typeovershoot Settling

time

overshoot Settling

time

overshoot Settling

time

dw PSS 137.27 3.54 0.1112 2.68 0.3322 2.98

MB PSS 158.6083 14.34 0.1360 2.40 0.3321 3.26

T1FLPSS 143.0345 5.88 0.1197 2.56 0.3257 3.14

T2FLPSS 126.3580 5.36 0.1056 2.31 0.3257 2.81

TABLE V

FAULT CLEARED WITH O NE LINE OUTAGE

Power Transfer

Level Voltage

Output at G1 Armature Power

at G1 PSS

Typeovershoot Settling

time

overshoot Settling

time

overshoot Settling

time

dw PSS 74.7314 >20 0.1222 >20 0.3322 3.61

MB PSS 63.7735 10.42 0.1511 6.53 0.3321 3.20

T1FLPSS 71.2886 10.87 0.1346 9.29 0.3257 2.92

T2FLPSS 68.4138 8.07 0.1246 6.39 0.3257 2.75

V. CONCLUSION

The IT2FLPSS proposed in this paper has been verified by

means of digital simulations of a K undur Test System in two

fault simulations. From the simulations IT2FLPSS shows

better performance than dw PSS, Multi Band PSS and

T1FLPSS. For power transfer response IT2FLPSS able to

return system to its stable points at 5.36 second with overshoot

value 126.35 MW in fault normally cleared simulation and it

achieves its new stable point at 8.07 second with overshoot

value 68.41 MW in fault cleared with one line outage.

For voltage output at G1 response IT2FLPSS able to return

system to its stable points at 2.31 second with overshoot value

0.1056 pu in fault normally cleared simulation and it achieves

its new stable point at 6.39 second with overshoot value

0.1246 in fault cleared with one line outage.

For armature power at G1 response IT2FLPSS able to

return system to its stable points at 2.81 second with overshoot

value 0.3257 pu in fault normally cleared simulation and itachieves its new stable point at 2.75 second with overshoot

value 0.3257 in fault cleared with one line outage.

R EFERENCES

[1] Imam Robandi, “Modern Power System Design” (Desain System

Tenaga Modern, in Bahasa Indonesia), Andi Offset Publisher: 2006.

[2] M. Dobrescu, I. K amwa, “A New Fuzzy Logic Power System Stabilizer

Performances”, IEEE, 2004.

[3] P. K undur, “Power System Stability and Control”, McGraw-Hill,1993.

[4] Timothy J. Ross, “Fuzzy Logic with engineering Applications”,

McGraw-Hill, 1997.

[5] ...., “Fuzzy Logic Toolbox for Use with MATLAB”, The Mathworks,

2002.[6] QilianLiangand, Jerry M. Mendel, “Interval Type-2 Fuzzy Logic System

Theory and Design”, IEEE, October, 2000.

[7] Jerry M. Mendel, Robert I.Bob John, “Type-2 Fuzzy Sets Made

Simple”, IEEE, April, 2002.

[8] Juan R. Castro, Oscar Castillo, “Interval Type-2 Fuzzy Logic for

Intelligent Control Applications”, IEEE, 2007.

[9] . ……, MATLAB help version 7.1.0.246 (R14) Service Pack 3, 2005.

[10] . ……, Fuzzy Logic Toolbox for use with MATLAB user’s guide,

version 2, 1998.

[11] Jerry M.Mendel, Feilong Liu, “Super-Exponential Convergence of the

K arnik–Mendel Algorithms for Computing the Centroid of an Interval

Type-2 Fuzzy Set”, IEEE, April 2007.




599



LIST OF ABREVIATION

Abbreviation Contraction

IBN _ UMF Input Big Negative Upper Membership Function

IBN _ LMF Input Big Negative Lower Membership Function

IMN _ UMF Input Medium Negative Upper Membership Function

IMN _ LMF Input Medium Negative Lower Membership Function

ILN _ UMF Input Low Negative Upper Membership Function

ILN _ LMF Input Low Negative Lower Membership Function

IZ_ UMF Input Zero Upper Membership Function

IZ_ LMF Input Zero Lower Membership Function

ILP _ UMF Input Low Positive Upper Membership Function

ILP _ LMF Input Low Positive Lower Membership Function

IMP _ UMF Input Medium Positive Upper Membership Function

IMP _ LMF Input Medium Positive Lower Membership Function

IBP _ UMF Input Big Positive Upper Membership Function

IBP _ LMF Input Big Positive Lower Membership Function

OBN _ UMF Output Big Negative Upper Membership Function

OBN _ LMF Output Big Negative Lower Membership Function

OMN _ UMF Output Medium Negative Upper Membership Function

OMN _ LMF Output Medium Negative Lower Membership Function

OLN _ UMF Output Low Negative Upper Membership Function

OLN _ LMF Output Low Negative Lower Membership FunctionOBZ_ UMF Output Big Zero Upper Membership Function

OBZ_ LMF Output Big Zero Lower Membership Function

OLZ_ UMF Output Low Zero Upper Membership Function

OLZ_ LMF Output Low Zero Lower Membership Function

OLP _ UMF Output Low Positive Upper Membership Function

OLP _ LMF Output Low Positive Lower Membership Function

OMP _ UMF Output Medium Positive Upper Membership Function

OMP _ LMF Output Medium Positive Lower Membership Function

OBP _ UMF Output Big Positive Upper Membership Function

OBP _ LMF Output Big Positive Lower Membership Function

BN Big Negative

MN Medium Negative

LN Low Negative

Z Zero

LP Low Positive

MP Medium PositiveBP Big Positive

BZ Big Zero

LZ Low Zero




600

design of interval power system stabilizer

Documents