Soft Set-Based Switching Faults Decision Making in DTC Induction Motor Drives

Soft Set-Based Switching Faults Decision

Making in DTC Induction Motor Drives¤

Veli Türkmenoğlu†

Vocational School of Technical Sciences,

University Department, Ordu University,Ordu 52200, Turkey

[email protected]

Mustafa AktaşEngineering Faculty,

Karab€uk University, Address,

Karab€uk 78100, Turkey

[email protected]

Serkan KarataşDepartment of Mathematics,

Faculty of Arts and Sciences,

Ordu University 52200 Ordu, Turkey

[email protected]

Halil İbrahim OkumuşEngineering Faculty,

Karadeniz Technical University,

Trabzon 61080, [email protected]

Received 23 October 2013

Accepted 17 September 2014Published 10 November 2014

This paper introduces a method for detection and identi¯cation of IGBT-based drive open-

circuit fault of DTC induction motor drives. The detection mechanism is based on soft set

theory and wavelet decomposition, if it is detailed, Z-product decision making method andsym2wavelet decomposition have been used in the detection mechanism. In this method, the

stator currents have been used as an input to the system. The stator current has been used for

the detection of the fault. The signal analysis has been performed up to the six level detailswavelets decomposition. Faulty switch is detected by applying soft set theory to sixth level

wavelets transformation. This is the ¯rst time applied to inverter in induction motor drives fault

*This paper was recommended by Regional Editor Masakazu Sengoku.†Corresponding author.

Journal of Circuits, Systems, and ComputersVol. 24, No. 2 (2015) 1550021 (14 pages)

#.c World Scienti¯c Publishing Company

DOI: 10.1142/S0218126615500218

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http://dx.doi.org/10.1142/S0218126615500218

detection. The results demonstrate that the proposed fault detection and diagnosis system has

very good capabilities.

Keywords: Soft set; wavelet transformation; fault decision making; induction motor drive;

inverter switch faults; Z-product of soft sets; DTC.

1. Introduction

There are various studies about wavelets-based fault diagnosis in the literature. As a

general view; as the failure observation has been constructed, new methods appeared

to watch the power di±culty of the power constructions enhance there is a powerful

drive to agreement for improving observation methods. Failure observation and

diagnosis for power construction is di±cult because of the large di®erences in power

elements mode of operating situation and e®ort caused by many di®erent restric-

tions. This requires the use of analysis methods su±ciently robust and versatile to

handle signals in terms of their time-frequency localization.1,2 The theory of wavelet

transforms (WT) application to fault detection and classi¯cation in a power system

has long been discussed.3,4

Most power signals of interest include a combination transients and noise for

which STFT and other conventional time-frequency methods are much less suited for

analysis. So WT can o®er a better compromise in terms of localization.5 The wavelet

transform is practical for analyzing power system transients by extracting the vital

information embedded.2,3,6 In this paper, the analysis of electrical transients arising

during the switch open circuit fault in a three phase power inverter feeding DTC

induction motor drives has been decomposed by using the wavelet transform. The

results demonstrate that the proposed fault detection and diagnosis system has very

good capabilities.

There are various theoretical and applied studies on the subject of soft set theory.

Problems in many ¯elds involve data that contains uncertainties. Uncertainties

might be dealt by using a wide range of existing theories such as probability theory,

fuzzy set theory,7 intuitionistic fuzzy sets,8 rough set theory,9 etc. Molodtsov10 in-

troduced the concept of soft set as a new mathematical tool for dealing with

uncertainties that is free from the di±culties such as long computation and com-

putation times.

At present, works on soft set theory and its applications are progressing rapidly.

The help of rough mathematics of Pawlak,9 Maji et al.11 de¯ned a parameter re-

duction on soft sets, and presented an application of soft sets in a decision making

problem. Chen et al.12 and Kong et al.13 presented a new de¯nition for the parameter

reduction. Xiao et al.,14 and Pei and Miao15 discussed the relationship between soft

sets and information systems. They showed that soft sets are a class of special

information systems.

In the soft set theory, the parameters are fuzzy concepts in real world from the

viewpoint of fuzzy set theory. The applications of the soft set theory generally solve

V. T€urkmeno�glu et al.

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problems with the help of the rough sets or fuzzy soft sets. It de¯nes the operations of

soft sets which are more functional to make theoretical studies of soft set theory in

more detail and improve several results in Ref. 16.

This paper aims to present the investigation of a method for detection and

identi¯cation of IGBT-based drive open-circuit fault of DTC induction motor drives.

The detection mechanism is based on soft set theory and wavelet decomposition, if it

is detailed, they have been used Z-product decision making method and sym2

wavelet decomposition in the detection mechanism. Simulated results verify the

feasibility of proposed strategies.

2. Wavelet Trasform

The wavelet analysis does not need to use a single window, function in all frequency

components, or has linear resolution in the whole frequency domain that are weak

points for Fourier analysis. Much of this interest concentrates wavelet in time-fre-

quency analysis Ref. 17.

Wavelet analysis provides a basis for L2ðRÞ and in many wavelet systems the

elements of this basis are orthogonal to each other and normalized. Wavelet analysis

that provides a basis for L2ðRÞ is similar to the set fcosðnw0tÞ; sinðnw0tÞ : n 2 Zgforming an orthogonal basis for periodic functions having frequency !0. Using a

wavelet expansion, any function in L2ðRÞ can be expressed as a sum of the basis

elements

fðtÞ ¼X1

k¼�1ck’ðt� kÞ þ

X1k¼�1

X1j¼0

dj;k2j=2 ð2jt� kÞ : ð1Þ

Parameter j determines the scale or the frequency range of each wavelet basis

function . Parameter k determines the time translations. The de¯ning characteristic

of a wavelet or multi-resolution system is that ðtÞ satis¯es a scaling equation, such as

�ðtÞ ¼X1k¼�1

h½k�ffiffiffi2

p�ð2t� kÞ ð2Þ

for some sequence h½k� that is usually ¯nite. The wavelet function ðtÞ is derived from

’ðtÞ. Each coe±cient can be calculated as the inner products between fðtÞ and the

respective basis element. The L2 inner products and alternative notation for the

coe±cients in Eq. (1) are:

c½k� � ck ¼Z 1

�1fðtÞ’ðt� kÞdt ;

dj½k� � dj;k ¼Z 1

�1fðtÞ2j=2 ð2jt� kÞdt ;

ð3Þ

c½k� is called approximation coe±cients and the dj½k� are called detail coe±cients.18,19

Soft Set-Based Switching Faults Decision Making

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Selecting an adequate wavelet ¯lter is crucial to identify the features of the fault

voltage and current signals. The \optimal" wavelet for extracting a given signal is

the one that can generate the most coe±cients with maximal values within the time-

scale domain, to represent the feature of a signal. Figure 1 shows the principle of the

implementation procedure of the discreet wavelet transform (DWT), where f is the

original signal, cA1 and cD1 denote low-pass and high-pass ¯lters, respectively. In

each resolution level, the input signal in the upper resolution nth level is split into the

approximation by a low-pass ¯lter and the detail by the high-pass ¯lter in the lower

resolution ðnþ 1Þth level. Both of output approximation and details signal are then

decimated by 2. This procedure is repeated until the signal has been decomposed to

the desired level. In this study, the stator phase currents are used as the input signals

of the wavelet diagram. Symlet wavelet, a modi¯ed member of the Doubechies

wavelets family, and sym2, symbolization of the symlet wavelet in the MATLAB

environment, are employed since it has been demonstrated to perform well and

satisfy the above mentioned conditions. The transients of the study cases are ana-

lyzed through wavelet transform at the level six.6 Both approximation and details

information related stator phase currents are extracted from the original signal with

the multiresolution analysis.

3. Soft Set Theory

Symbol list

U Initial universe

E Parameter universe

FA Soft Set

P ðUÞ Power set of U(or all subsets of U)

A� B Cartesian product of A and B

fA Approximate function

SðUÞ Set of all soft set over U

FA~\FB Soft intersection of FA and FB

F� Soft empty set

Fig. 1. Wavelets decomposition.


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(Continued )

Symbol list

F cA Soft complement set of FA

FA ^ FB And-Product of FA and FB

FAZFB And-Not-Product of FA and FB

In this section, it is given some new de¯nitions and various results on soft set theory

in Ref. 16. Throughout this work, U refers to an initial universe, E is a set of

parameters, P ðUÞ is the power set of U (i.e., P ðUÞ is set of all subsets of U), and

A � E.

De¯nition 1. A soft set FA on the universe U is de¯ned by the set of ordered pairs

FA ¼ fðx; fAðxÞÞ : x 2 E; fAðxÞ 2 P ðUÞg ;where fA : E ! P ðUÞ such that fAðxÞ ¼ ; if x 62 A. Here, fA is called the

approximate function of the soft set FA. From now on, it is used SðUÞ for the set

of all soft sets over U .

Example 1. A soft set FA describes the capability of the candidates who are wanted

to ¯ll a position for a company. Suppose that there are six candidates in the universe

U ¼ fu1;u2;u3;u4;u5;u6g :Under consideration, and E ¼ fx1;x2;x3;x4;x5g is the set of parameters. The xi

(1 � i � 5) stand for the parameters \experience", and \computer knowledge", and

\young age", and \higher education", and \good health", respectively. In this case, to

de¯ne a soft set means to point out experienced workers, computer knowledge

workers, and so on. Assume that A ¼ fx1;x3;x4g � E, and fAðx1Þ ¼ fu2;u4g, andfAðx3Þ ¼ U , and fAðx4Þ ¼ fu1;u3;u5g. Then we can view the soft set FA as consisting

of the following collection of approximations:

FA ¼ fðx1; fu2;u4gÞ; ðx3;UÞ; ðx4; fu1;u3;u5gÞg :

De¯nition 2. If FA;FB 2 SðUÞ, then soft intersection, soft empty set and soft

complement de¯ned by16:

FA~\FB ¼ fðx; fA ~\BðxÞÞ : fA ~\BðxÞ ¼ fAðxÞ \ fBðxÞ;x 2 Eg ;F� ¼ fðx; fAðxÞÞ : fAðxÞ ¼ ;;x 2 Eg ;F c

A ¼ fðx; fAcðxÞÞ : fAcðxÞ ¼ U � fAðxÞ;x 2 Eg ;where f c

AðxÞ is complement of fAðxÞ.

Example 2. Let U ¼ fu1;u2;u3;u4g be a universal set and E ¼ fx1;x2;x3;x4g be

the set of all parameters. Assume that A ¼ fx1;x2;x4g and B ¼ fx1;x2;x3g are two

subsets of E. Then we can write the following soft sets.


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FA ¼ fðx1; fu1;u2gÞ; ðx2; fu3gÞ; ðx4; fu2;u4gÞg ;FB ¼ fðx1; fu1;u4gÞ; ðx2; fu4gÞ; ðx3;UÞg :

Then, FA~\FB ¼ fðx1; fu1gÞg and

F cA ¼ fðx1; fu3;u4gÞ; ðx2; fu1;u2;u4gÞ; ðx4; fu1;u3gÞg :

It is possible that every soft set represent as a matrix. U ¼ fu1;u2; . . . ;umg and

E ¼ fx1;x2; . . . ;xng, lets consider FA soft set, where

Example 3. Let consider Example 2. Then we can writeFA, FB, FA~\FB and F c

A soft

sets respectively as following matrix forms

1 0 0 0

1 0 0 1

0 1 0 0

0 0 0 1

2664

3775;

1 0 1 0

0 0 1 0

0 0 1 0

1 1 1 0

2664

3775;

1 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

2664

3775 and

0 1 1 1

0 1 1 0

1 0 1 1

1 1 1 0

2664

3775:

3.1. Products of soft sets

Now, we de¯ne the binary operations on soft sets which depend on the approximate

function of one variable. We de¯ne products of the soft sets which are binary

operations of soft sets depending on an approximate function of two variables. We

have two kinds of products in the soft set theory. They are And-product and And-

Not-product that are denoted by ^-product and Z-product, respectively.

De¯nition 3 (see Ref. 16). If FA;FB 2 SðUÞ, then ^-product of two soft sets FA

and FB, denoted by FA ^ FB, is a soft set de¯ned by the approximate function for all

x 2 A and all y 2 B

fA^B : E � E ! P ðUÞ; fA^Bðx; yÞ ¼ fAðxÞ \ fBðyÞ :De¯nition 4. If FA;FB 2 SðUÞ, then Z-product of two soft sets FA and FB, denoted

by FAZFB, is a soft set de¯ned by the approximate function for all x 2 A and all

y 2 B

fAZB : E � E ! P ðUÞ; fAZBðx; yÞ ¼ fAðxÞ \ f cBðyÞ :

Example 4. U ¼ fu1;u2;u3;u4;u5g be a soft set and E ¼ fx1;x2;x3;x4g be the set

of all parameters. Assume that A ¼ fx2;x3;x4g and B ¼ fx1;x3;x4g are two subsets

of E. Then we can write the following soft sets.


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FA ¼ fðx2; fu2;u3;u4;u5gÞ; ðx3; fu1;u2;u3gÞ; ðx4;UÞg ;FB ¼ fðx1; fu1;u2gÞ; ðx3; fu3;u4;u5gÞ; ðx4;UÞg :

Now we can ¯nd FA ^ FB and FAZFB as follows:

FA ^ FB ¼ fððx2;x1Þ; fu2gÞ; ððx2;x3Þ; fu3;u4;u5gÞ; ððx2;x4Þ; fu2;u3;u4;u5gÞððx3;x1Þ; fu1;u2gÞ; ððx3;x3Þ; fu3gÞ; ððx3;x4Þ; fu1;u2;u3gÞ;ððx4;x1Þ; fu1;u2gÞ; ððx4;x3Þ; fu5gÞ; ððx4;x4Þ;UÞg

and

FAZFB ¼ fððx2;x1Þ; fu3;u4;u5gÞ; ððx2;x3Þ; fu2gÞ; ððx3;x1Þ; fu3gÞ;ððx3;x3Þ; fu1;u2gÞ; ððx4;x1Þ; fu5gÞ; ððx4;x3Þ; fu1;u2gÞg :

4. Direct Torque Control Principles

Technological advances in power semiconductor and microprocessor technology have

made possible the application of advanced control techniques to ac motor drive

systems.20 Direct Torque Control (DTC) is one of the most popular techniques for

the control of induction motor drives as it provides a fast dynamic torque response

and robustness to machine parameter variations without the use of current

regulators.

In general, in a symmetrical three-phase induction machine, an instantaneous

electromagnetic torque is a cross product of the stator and rotor °ux linkage space

vector or stator current space vector and stator °ux linkage space vector

Te ¼3

2P�s � �I s ; ð4Þ

where �s is the stator °ux linkage space vector and �I s is the stator space vector. In

Eq. (4), both space vectors are expressed in the stationary reference frame. By

considering that �s ¼ Ls�I s þ Lm

�I0r�

0r ¼ Lr

�I r þ Lm�I s where the primed rotor

quantities are expressed in the stationary reference frame, it follows that

�I s ¼ �s=L0s � ½Lm=ðLrL

0sÞ�� 0

r. Thus, Eq. (4) takes the following form:

Te ¼3

2P

Lm

L 0sLr

j� 0rjj�sjsin � : ð5Þ

The electromagnetic torque given by Eq. (5) is a sinusoidal function of �, the angle

between the stator and rotor °ux linkage space vector.

The magnitude of the stator °ux is normally kept constant and the motor torque

is controlled by means of the angle �. The rotor time constant of the standard

induction machine is typically larger than 100ms. Thus, the rotor °ux is stable and

its stability and variations are slow compared with the stator °ux. It is therefore


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possible to achieve the required torque very e®ectively by rotating the stator °ux

vector directly in a given direction as fast as possible.

Controlling the stator °ux and electromagnetic torque control achieved by using

the appropriate stator voltages can quickly change the electromagnetic torque.

Choosing suitable voltage vectors those increases or decreases � causes the electro-

magnetic torque to increase or to decrease.21,22

The core of the system consists of a °ux and torque estimator, a speed controller, a

°ux controller, a torque controller and an optimum switching table. The estimator

estimates the actual stator °ux and torque by using two measured motor stator

phase currents, the dc voltage and the states of the power switches. Torque and °ux

references are compared with the actual values and a two-level for °ux and a three-

level for torque hysteresis control method produce control signals.21,22

In Fig. 2, the block scheme of the induction motor drive with the proposed sen-

sorless DTC is presented. Here the PI controller is used to transfer the speed feedback

into the torque value. By this way the system is able to check the speed control. That

is, besides the moment control the speed control is also done.

5. Fault Detection Process

The MATLAB program has been used to process of DTC induction motor simulation

and DWT of the signals. Research topic is asynchronous motor power circuit that is

given in Fig. 3. When a fault occurs in the power switch, stator currents show

unstable vibration in Fig. 3(a)–3(c). These phase signals are applied wavelets de-

composition. It can be seen in Figs. 4(a)–4(c) that variation within the decomposi-

tion coe±cient of the current signals contains useful fault signatures. The sharp

signal variations can be regarded as features of the faults. The objective of this work

is to detect and classify the switches faults in power inverter using the level six

Fig. 2. Block diagram of the proposed sensorless DTC induction motor drive system.


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(a)

(b)

(c)

Fig. 3. IGBT1 open circuit fault stator time domain currents. (a) Induction motor stator current (ia),

(b) Induction motor stator current (ib), (c) Induction motor stator current (ic).


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(a) ia

(b) ib

(c) ic

Fig. 4. IGBT1 open circuit fault, sym2 wavelets level 6 decomposition of stator currents ia, ib and ic,

respectively.


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approximation and details from the multi resolution analysis output of the stator

three-phase currents.

At time domain studies, the faulty system can be easily separated from the

healthy one. In fact detailed levels, such as d5 and d6 are distinguishable. Moreover,

the fault appears at low frequency area which can be observed on the approximation

level 6 (a6). On the other hand, the comparison of the various levels of the details and

approximations in both healthy and faulty operating system demonstrates that the

signal is increased in certain frequency area or decreased in another region.

It is seen that stator phase currents sym2 wavelets sixth level decomposition

energy mean values, which are calculated in the MATLAB environment, listed in

Tables 1 and 2.

Table 3 shows di®erent values from No/Fault than faulty one. These values help

us to ¯nd faulty phase and power switch. On the other hand, we organize Table 3 to

make a decision about faulty switch via error values ea6, ed5, ed6 and eE, respectively.

Table 1. Wavelets decomposition Ias energy mean values.

Ias a6 d1 d2 d3 d4 d5 d6 E

No/Fault 31.7456 1.4663 0.5802 0.4461 2.5709 22.9859 40.205 11.3757

IGBT1 28.3925 0.5368 0.3916 0.6268 3.0773 21.8511 45.1239 11.9346

IGBT2 62.2184 0.9304 0.6275 0.8332 2.4775 7.8385 25.0743 6.2969IGBT3 24.1961 0.6959 0.4556 0.8056 3.9856 21.2424 48.6187 12.634

IGBT4 34.114 0.6364 0.3938 0.5823 3.5043 24.8812 35.8879 10.981

IGBT5 29.0044 0.5202 0.332 0.5273 3.3857 20.9754 45.255 11.8326

IGBT6 35.276 0.6346 0.4023 0.5495 2.9688 21.1776 38.9911 10.7873

Table 2. Wavelets decomposition Ibs energy mean values.

Ibs a6 d1 d2 d3 d4 d5 d6 E

No/Fault 32.3868 1.5366 0.5792 0.4457 2.6281 18.8714 43.5521 11.2689IGBT1 32.7711 0.5838 0.4084 0.6387 3.1125 17.118 45.3676 11.2048

IGBT2 47.6789 0.9467 0.5948 0.9439 3.6018 14.3477 35.8862 9.3869

IGBT3 33.1271 0.5853 0.4002 0.6602 3.1246 19.2704 43.8322 11.3122IGBT4 31.003 0.5922 0.3728 0.5779 3.0194 18.6171 43.8175 11.1662

IGBT5 25.0671 0.5999 0.3826 0.773 3.9223 20.937 48.3181 12.4888

IGBT6 33.1405 0.7017 0.4442 0.6496 3.3952 20.8535 40.8153 11.1433

Table 3. Wavelets decomposition Ias error values.

Ias ea6 ed1 ed2 ed3 ed4 ed5 ed6 eE

IGBT1 3.3531 0.9295 0.1886 �0.181 �0.506 1.1348 �4.9189 �0.5589IGBT2 �30.473 0.5359 �0.047 �0.387 0.0934 15.1474 15.1307 5.0788

IGBT3 7.5495 0.7704 0.1246 �0.36 �1.415 1.7435 �8.4137 �1.2582

IGBT4 �2.3684 0.8299 0.1864 �0.136 �0.933 �1.8953 4.3171 0.3948

IGBT5 2.7412 0.9461 0.2482 �0.081 �0.815 2.0105 �5.05 �0.4569IGBT6 �3.5304 0.8317 0.1779 �0.103 �0.398 1.8083 1.2139 0.5884


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6. Proposed Soft Set-Based Decision Making Method

Now the key corresponding to hand in our keys and our failure data creates soft set.

E ¼ fIGBT1; IGBT2; IGBT3; IGBT4; IGBT5; IGBT6gand

U ¼ fa1; a2; a3; a4; a5; a6; a7; a8; a9; a10; a11; a12gshows set of keys and set of faults occurred in the keys accordingly. From here, our

soft set is

FA ¼ fðIGBT1; fa1; a2; a6; a8; a9; a10gÞ; ðIGBT2; fa2; a3; a4; a6; a7; a8; a10; a11; a12gÞðIGBT3; fa1; a2; a9; a10gÞ; ðIGBT4; fa3; a4; a5; a6; a8; a10; a11; a12gÞðIGBT5; fa1; a2; a5; a10gÞ; ðIGBT6; fa2; a3; a4; a7; a8; a9; a10; a12gÞg :

Given any data, from a soft set expressed as FB ¼ fðxi; ffBðxiÞgÞ : i ¼1; 2; 3; 4; 5; 6g (IGBTi ¼ xi), the defects in the switch can be detected by using

Z-product. For 1 � k � 6 and 1 � i � 6 so that fAðIGBTkÞ \ f cBðxiÞ ¼ ; conditions

are met, the switch is defective.

Decision making process chart

(1) Obtaining data

(2) Wavelets transformation

(3) Wavelets coe±cients selection

(4) Produce error tables

(5) FA soft set is created for faulty situation of switches

(6) The corresponding soft set FA matrix is written

(7) FB soft set is created for obtained phase currents

(8) The corresponding soft set FB matrix is written

(9) Soft Z is implemented with MATLAB software between FA and FB

(10) The faulty switches are determined by the software algorithm

Decision making process chart is produced via using Table 4 accordingly by

threshold value method. Positive values are considered \1" and negative values are

considered \0" in Table 4 accordingly. FA is obtained for possible faulty switch of

inverter in Table 4. It is carried out Z procedure between faulty FA and real time data

of FB to attain a goal. This operation gives us whether there is any faulty switch and

which one of them is faulty. The study aimed to detect faulty switch by using the

data gained from MATLAB-based simulations. The decision-making process chart

regarding this procedure is given above.


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7. Conclusion

In this paper, the analysis of electrical transients arising during the switch open

circuit fault in a three phase power inverter feeding an DTC induction motor has

been decomposed using the wavelets transform and analyzed by soft set theory. Both

the power and the mean value coe±cients of the wavelet transform are calculated in

order to distinguish from No/Fault to faulty values. It is the ¯rst time this approach,

WT combined with soft set theory, has been used for detecting the faulty switch. We

used this approach at present study for the ¯rst time. With this proposed strategy,

major faults in the DTC induction motor drive can be prevented. The results

demonstrate that the proposed fault detection and diagnosis system has very good

capabilities.

References

1. M. Kezunovic and Z. Galijasevic, New software framework for automated analysis ofpower system transients, Proc. Int. Conf. Power System Transients, IPST (Rio deJaneiro, Brazil, 2001).

2. F. Char¯, K. Al-Haddad, B. Franqois, M. B. Messaoud and F. Sellami, Power systemfault monitoring using wavelet transform, 2004 35th Ann. IEEE Power ElectronicsSpecialists Conference Aachen, Germany (2004), pp. 919.

3. F. Char¯, F. Sellami and K. Al-Haddad, Fault diagnostic in power system using wavelettransforms and neural networks, IEEE ISIE 2006, Montreal, Quebec, Canada, July 9–12,2006.

4. S. Yeow Hong and W. Qin, A wavelet based method to discriminate between inrushcurrent and internal fault, power system technology, Proc. Int. Conf. Power Con 2000Vol. 2, 4–7 December 2000, pp. 927–931.

5. M. Thuillard, A review of wavelet networks, wavelets, fuzzy wavelets and their appli-cations, Proceeding ESIT 2000, Aachen, Germany, 14–15 September 2000.

6. F. Char¯, K. Al Haddad and F. Sellami, Analysis and identi¯cation of embedded powersystem faults using wavelet transform, Proc. Electric Vehicle Symp. EVS Monaco, 21April 2005.

7. Y. Zou and Z. Xiao, Data analysis approaches of soft sets under incomplete information,Knowledge-Based Syst. 21 (2008) 941–945.

8. K. Atanassov, Intuitionist fuzzy sets, Fuzzy Sets Syst. 20 (1986) 87–96.9. Z. Pawlak, Rough sets, Int. J. Inform. Comput. Sci. 11 (1982) 341–356.

Table 4. Decision making table.

FA ea6 ad5 ed6 eE ea6 ad5 ed6 eE ea6 ad5 ed6 eE

IGBT1 1 1 0 0 0 1 0 1 1 1 0 0

IGBT2 0 1 1 1 0 1 1 1 0 1 1 1

IGBT3 1 1 0 0 0 0 0 0 1 1 0 0IGBT4 0 0 1 1 1 1 0 1 0 1 1 1

IGBT5 1 1 0 0 1 0 0 0 0 1 0 0

IGBT6 0 1 1 1 0 0 1 1 1 1 0 1


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IRC

UIT

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ST C

OM

P D

ownl

oade

d fr

om w

ww

.wor

ldsc

ient

ific

.com

by M

ON

ASH

UN

IVE

RSI

TY

on

11/2

6/14

. For

per

sona

l use

onl

y.

10. D. Molodtsov, Soft set theory-¯rst results, Comput. Math. Appl. 37 (1999) 19–31.11. P. K. Maji, A. R. Roy and R. Biswas, An application of soft sets in a decision making

problem, Comput. Math. Appl. 44 (2002) 1077–1083.12. D. Chen, E. C. C. Tsang, D. S. Yeung and X. Wang, The parameterization reduction of

soft sets and its applications, Comput. Math. Appl. 49 (2005) 757–763.13. Z. Kong, L. Gao, L. Wang and S. Li, The normal parameter reduction of soft sets and its

algorithm, Comput. Mathe. Appl. 56 (2008) 3029–3037.14. X. Yang, D. Yu, J. Yang and C.Wu, Generalization of soft set theory: From crisp to fuzzy

case, Proc. ICFIE Fuzzy Information and Engineering, Guangzhou, China, 2007,B.-Y. Cao (ed.), Advances in Soft Computing, Vol. 40 (Springer, 2007), pp. 345–355.

15. D. Pei and D. Miao, From soft sets to information systems, Proc. Granular ComputingX. Hu, Q. Liu, A. Skowron, T. Y. Lin, R. R. Yager and B. Zhang (eds.), Vol. 2 (IEEE2005), pp. 617–621.

16. N. Çağman and S. Enginoğlu, Soft set theory and soft decision makings, Eur. J. Oper.Res. 207(2) (2009) 848–855.

17. Omar A. S. Youssef, A wavelet-based technique for discrimination between faults andmagnetizing inrush currents in transformer, IEEE Trans. Power Delivery 18(1) (2003)170–176.

18. S.-H. C. Henry, S. Y. R. Hui and K. Y. Mak, Time domain simulation of power electronicscircuits using embedded companion models, ISIE'99, Bled, Slovenia, pp. 226–232.

19. L. Jacovides, Analysis of induction motor drives with a non-sinusoidal supply voltageusing fourier analysis, IEEE Trans. Ind. App. A-9 (1973) 741–747.

20. B. K. Bose, An adaptive hysteresis-band current control technique of a voltage-fed PWMinverter for machine drive system, IEEE Trans. Industrial Electronics 37 (1990) 402–408.

21. M. Aktaş, TMS320C6711 based speed sensorless DTC induction motor drive, Ph.d.thesis, Black Sea Technical University, Turkiye (2006).

22. H. İ. Okumuş and M. Aktaş, M, Adaptive hysteresis band control for constant switchingfrequency in DTC induction machine drives, Turkish J. Elect. Eng. Comput. Sci. 18(2010) 59–69.


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Soft Set-Based Switching Faults Decision Making in DTC Induction Motor Drives

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Transcript of Soft Set-Based Switching Faults Decision Making in DTC Induction Motor Drives