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Incipient Fault Detection and Diagnosis of Induction

Motor using Fuzzy Logic

Abstract: Induction motors are critical components in manyindustrial processes. Online monitoring of induction motors is

becoming increasingly important. The main aim of this paper is to

perform the electrical fault analysis of a three phase induction motorusing simulation in MATLAB SIMULINK and to design a fuzzylogic algorithm for detecting and analyzing the electrical fault of themotor. Several types of electrical faults such as under voltage fault,unbalance fault, overload fault and earth faults are experienced in

three phase induction motor. This paper presents a systematicapproach to detect and analyze the electrical faults of an inductionmotor. The work is explained in three phases. The first phaseexplains the causes and after effects of different types of electrical

faults in an induction motor. The mathematical model and simulationof induction motor with different types of electrical faults areexplained in second phase .The design and simulation of fuzzy logicalgorithm for identification and analyzing electrical faults are

discussed in third part. In this work, fuzzy logic is used to makedecisions about the motor condition with high accuracy.

Key words: Induction Motor, Electrical Faults, Modeling,

Simulation, Diagnosis, Fuzzy logic, Stator current amplitude.

I. INTRODUCTION

Three phase induction motors are commonly used in

industrial applications due to their simple construction, high

reliability, low cost etc. Early detection of abnormalities will

helps avoiding the malfunction of the machine. So, condition

monitoring of three phase induction machine can significantly

reduce the maintenance cost and its performance is also

improved [1-3]. The induction motor performance is affected

by three types of faults such as electrical faults, mechanical

faults and environmentally related faults. Electrically related

faults consist of unbalanced faults, under voltage faults,

overload faults and earth faults. The rotor winding failure,

stator winding failure and bearing faults are included in

mechanically related faults. The external moisture,

contamination in the ambient temperature also affects theinduction motor performance. The faults due to these external

variation and vibration faults are included in the

environmentally related faults.

Electrical faults in three phase induction motor will

produce more heat on both stator winding and rotor winding.

Due to the electrical faults, life time of the motor will reduce.

The behavior of induction motor under electrically related

faults such as unbalanced supply voltage, over load, under

voltage and earth faults are explained in this paper. The fuzzy

logic algorithm for the identification and analysis of electrical

faults are also included in this paper.

The mathematical model of three phase induction motor

used for the fault analysis is developed and simulated using

MATLAB

SIMULINK toolbox .In fact, fuzzy logic isreminiscent of human thinking process and natural language

enabling decisions to be made based on the vague information.

In fuzzy logic, the fault condition of the motor are described

using linguistic variables. Fuzzy subsets and corresponding

membership functions describe the stator current amplitudes,

negative sequence components of stator currents and the

speed. A knowledge base comprising rules and data- base is

built to support the fuzzy inference. The induction motor

conditions are diagnosed using a compositional rule of fuzzy

inference.

The aim of this paper is to present a useful and straight

forward method to simulate electrical faults such as under

voltage fault, over load fault, unbalanced fault and earth faults.

A fuzzy logic algorithm is proposed for identifying and

analyzing the faults.

II. INFLUENCE OF ELECTRICAL FAULTS ON MOTOR

PERFORMANCE

Electrically related faults are frequently occurring in three

phase induction motors. Because of these electrical faults

more heat will produced on stator winding and rotor winding,

this will reduce the life time of the machine. In this subsection

causes and effects of different types of electrical faults such as

unbalanced supply voltage fault, under voltage fault, over

voltage fault, over load fault and earth faults are discussed [4-

6].

Causes and effects of electrical faults

Open delta transformers, unbalanced loading, unequal tap

settings of the transformer and shunted single phase load etc,

are the causes of unbalanced voltage faults. The effects of

unbalanced supply voltage faults are, reduction in motor

efficiency, increase in stator and rotor copper losses,

temperature rise and serious reduction in starting torque. The

Dr.S.UshakumariAsst. Professor

Department of Electrical EngineeringCollege of Engineering Trivandrum

Kerala, India

Mini.V.PSr. Lecturer

Department of Electrical EngineeringCollege of Engineering Trivandrum

Kerala, India

978-1-4244-9477-4/11/$26.00 2011 IEEE

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efficiency reduction in induction motor due to the unbalanced

supply voltage faults results in a higher electricity bill for the

same amount of work done.

The under voltage fault occurs when a reduced supply

voltage with a rated mechanical load on the motor. The

increased stator current, excess heating of machine and

increase in the stator and rotor copper losses are the after

effects of under voltage faults. When any one of the linevoltage is greater than 110% of the rated value, the over

voltage fault will occur, it will produce harmful effects to the

machine insulation.

The mechanical load on the motor is to increase beyond

the rated value at that time over load fault will occur. Due to

the high load torque motor begins to draw more current. The

effects of over load faults are increase in stator current and

overheating of the machine. Ground faults are more prevalent

in motors than other power system devices. The ground fault

is identified and analyzed by measuring leakage currents . The

effects of earth faults are thermal stress due to fault current

and hazards of human safety.

III INDUCTION MOTOR MODEL

The model of a symmetrical three- phase induction motor is

well known. To derive equations for symmetrical stator

winding, and rotor, the following assumptions are made:[1, 7-

11]

Each stator phase of the motor has same number of turns,and uniform spatial displacement .

Magnetic saturation is not present.With the appropriate subscripts as, bs, cs, ar, br and cr, the

voltage equations of the magnetically coupled stator and rotor

circuits can be written as :

)1(0,v sabcr

abc

r

abc

r

abc

s

abc

s

abc

s

abc pirpir +=+=

where p=d/dt. Applying a stationary reference frametransformation to this equation yields the corresponding qd0

equations and (1) becomes

)2(0

000

001

010

,v sqdo

=+

+=

r

qdo

r

qdor

r

qdo

r

qdo

s

qdo

s

qdo

s

qdo

pir

pir

In matrix notation, the flux linkages of the stator and rotor

windings may be written in terms of the winding inductances

and the current as

)3(rabcrr

abc

s

abc

rs

abc

r

abc

rabc

srabc

sabc

ssabc

sabc

iLiL

iLiL

+=

+=

The stator and rotor qd0 flux linkages are obtained byapplying transformation to the stator and rotor abc flux

linkages (3), that is

)4(r

qdo

rr

qdo

s

qdo

rs

qdo

r

qdo

r

qdo

sr

qdo

s

qdo

ss

qdo

s

qdo

iLiL

iLiL

+=

+=

Normally, an induction machine is connected to a three-

phase supply by a three-wire connection. The stator and rotorflux linkages in (4) may be expressed compactly as

)5(

0

0

222221

111211

22212221

12111211

=

rd

r

q

s

d

s

q

rrsrsr

rrsrsr

srsrssss

srsrssss

rd

r

q

s

d

s

q

i

i

i

i

LLL

LLL

LLLL

LLLL

A. Determination of InductancesIn order to define symmetrical machine inductances,

assume that the stator phases as, bs and cs have equal numberof winding turns given by Ns, and that the rotor phases ar, br

and cralso have equal number of winding turns given byNr.

The stator self-inductances for phases as, bs and cs can becalculated as

)6(3

2csc

+=== mlssbsbsasas LLLLL

The stator mutual inductances between phases as and bs, bsand cs, and cs and as can be derived as

( ) )7(3

1LmLLL csasbscsasbs

===

The rotor self and mutual inductances can be found by asimilar way. As the rotor is also symmetric, the total self-

inductances of rotor phases ar, brand crare equal. Therefore

)8(3

22

2

marlrm

s

r

lrcrcrbrbrarar LLLN

NLLLL +=+===

where ms

rmar L

NNL

2

2

32= . For the same reason, rotor mutual

inductances are also equal to each other and given by

)9(3

2

2

12

2

=== m

s

rcrarbrcrarbr L

N

NLLL

Because of the rotor and stator symmetry the stator to

rotor mutual inductances are equal

ieLasar = Lasbr= Lascr,= Lbsar = Lbsbr = Lbscr = Lcsar = Lcsbr =

Lcscr.The rotor phase mutual inductances will be

)10(32

=== m

s

r

ascrasbrasar LNNLLL

wherem

s

rmsr L

N

NL

23

2= .

B.Simulation of the symmetrical Induction MotorIn this subsection, equations are rearranged for the

symmetrical induction motor model that has been developed

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[12-14]. Flux linkages obtained from (2) for a three- wire

system is

( )

( )

( )

( ) )11(

2221

1211

dtir

dtir

dtirirv

dtirirv

r

d

r

r

r

qr

r

d

r

q

r

r

r

dr

r

q

s

d

ss

q

ss

d

s

d

s

d

ss

q

ss

q

s

q

+=

=

=

=

Fig. 1. Block Diagram of fault detection system with induction motor model

The stator current is obtained by inverting (5) and the speed of

the machine is obtained from the torque equation as

( ) ( ) )12(2

= dtTTTJ

Pt dampmechemr

Tem is the electromagnetic torque impressed on the shaft of the

machine and can be expressed as

( ) )13(22

3 sd

s

q

s

q

s

dem iiP

T =

Tmech is the externally applied mechanical torque , Tdamp is the

damping torque andJis inertia.

Using (11)(13) with resistances and inductances, a motor

with symmetrical windings can be simulated. The blockdiagram representation of the model for the simulation of the

fault detection system for symmetrical induction motor is

shown in Fig.1.

IV. FUZZY LOGIC BASED DIAGNOSIS APPROACH

Fuzzy systems rely on a set of rules. These rules, while

superficially similar, allow the input to be fuzzy, i.e. more likethe natural way that humans express knowledge. Thus, a

power engineer might refer to an electrical machine assomewhat secure or a little overloaded. This linguistic

input can be expressed directly by a fuzzy system. Therefore,

the natural format greatly eases the interface between the

engineer knowledge and the domain expert [15-16].

A. Fuzzy System Input-Output Variables

As stated, the induction motor condition can be deduced

by observing the stator current amplitudes and speed are input

variables. Interpretation of result is difficult as relationships

between the motor condition and the current amplitudes are

vague. Therefore, using fuzzy logic, numerical data arerepresented as linguistic information.

In this case, the stator current amplitudes Ia, I

b, and I

c,,negative sequence currentIneg and speedNare considered as

the input variables to the fuzzy system. The motor condition,MC, is chosen as the output variable. All the system inputs and

outputs are defined using fuzzy set theory.

B. Linguistic Variables

Basic tools of fuzzy logic are linguistic variables. Their

values are words or sentences in a natural or artificial

language, providing a means of systematic manipulation ofvague and imprecise concepts.

For instance, the term set T(MC), interpreting motorcondition,MC, as a linguistic variable, could be

T(MC )= {NR, AEF, BEF, CEF ABEF ,BCEF, ACEF ,ABCEF,

MOL, HOL, MUB, HUB, VHUB, MUVF, HUVF }

Similarly, the input variables stator current amplitudesIa,Ib, and Ic , Ineg and speed N are interpreted as linguisticvariables, with T(Q)= {Normal (NR) Slightly high (SLH)

medium (M), positive medium (PM), High (H) Very high

(VH)}, T(Ineg)= {Very very small, very small, small, medium,

large, very large}, T(N )= {Very very low, very low, low,

medium, positive medium , Normal}

where Q= ia, ib, icrespectively

C.Fuzzy Membership Functions ConstructionFuzzy rules and membership functions are constructed by

observing the data set. For the measurements related to thestator currents and speed, more insight into the data is needed,

so membership functions will be generated for all input andoutput variables. The optimized input membership functions

for this problem are shown in Fig.2. The output fuzzylinguistic variables and their membership function value

ranges are given in Appendix B for different types of motor

condition.

.

NR M PM H VH

Fig.2. Input fuzzy sets for ia , ib &ic

SLH

Motor model dqto abc

detection

algorithm

condition

Vaabcto

dqVb

Vc

Calculation ofind.&

reis.

Ns

Nr

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VI. SIMULATION RESULTS

The mathematical model of induction motor is developed

and simulated by MATLAB

SIMULINK tool box. The

simulation results are given below for a 2 hp motor [1] withparameters given in Appendix A. The results are taken during

acceleration from standstill to full speed.

Fig.3 shows the speed and torque variation of symmetrical

machine under normal conditions. In this condition, thestarting torque is about 80Nm and the speed is about 155

rad/sec and the motor will maintain the constant speed within0.5seconds. Fig .4, shows the amplitude of stator current and

negative sequence current of the motor under normal working

condition.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-50

0

50

100

150

200

Time(Sec)

Torque(N

m

),

Speed(rad/sec)

Speed

Torque

Fig. 3. Speed and Torque Variation under normal condition

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

10

15

20

25

30

Time(Sec)

Curren

t(A)

ic

ib

ia

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.005

0.01

0.015

0.02

0.025

0.03

Time(Sec)

Ineg(A)

Fig.4. Stator and negative sequence currents under normal condition

Fig.5 shows the torque and speed response of the machine

under unbalanced fault condition(Va = 230V, Vb= 190V and

Vc = 160V). Due to unbalance in supply voltage the motorwill take more time (about 3.5sec) to attain the steady state

speed and the starting torque gets reduced and also the torque

response consists ripples.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-20

0

20

40

60

80

100

120

140

160

Time(Sec)

Torque(Nm

),Speed(rad/sec)

Speed

Torque

Fig. 5. Speed and Torque under unbalanced fault condition

Fig.6. shows the stator phase currents ia, ib and ic underunbalanced fault condition. Due to this unbalanced supply

voltage fault the currents are in unbalanced condition, Because

of these unbalanced full load current and low starting torque,

the premature failure of motor winding and nuisance of overload tripping will occur.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

2

4

6

8

10

12

14

16

18

Time(Sec)

Current(A)

Ia

Ib

Ic

Fig. 6. Stator currents i a , ib and i c underunbalanced fault condition

Fig.7.and Fig.8 show the torque speed characteristics and

stator current waveforms of the induction motor in under

voltage fault condition. The supply maximum voltage isreduced to 60% of rated voltage on all three phases forsimulating the under voltage fault. During under voltage fault

the stator current become highly increasing, due to these high

current more heat is produced and it will take very large time

to attain the steady state speed.

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-20

0

20

40

60

80

100

120

140

160

Time(Sec)

Torqu

e(Nm

),

Speed(rad/sec)

Speed

Torque

Fig. 7. Speed and Torque variation on under voltage fault condition.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

2

4

6

8

10

12

14

16

Time(Sec)

Current(A

)

ia

ib

ic

Fig. 8. currents ia , ib and i c onunder voltage fault condition

The speed and torque characteristics of three phase

induction motor under single phase to ground fault is shown

fig.9.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-100

-50

0

50

100

150

200

Time(Sec)

Torque(Nm

),Speed

(rad/sec)

Speed

Torque

Fig. 9. Speed and Torque when single phase to ground fault occurs

Corresponding currents in three phases such as a, b and c and

leakage current Ineg are shown in fig.10and fig.11 respectively.During normal running condition, at 1sec phase A is earthed

and cleared at 2sec for simulating the single phase to groundfault. Due to single phase to ground fault more pulsation is

occurred in speed and torque this will reduce the life time of

the motor. Due to single phase to ground fault the unbalance

is obtained in the stator currents, because of these unbalance in

stator current turn to turn insulation failure and motor

insulation failure will also occurred.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

10

15

20

25

30

Time(Sec)

Current(A)

ia

ib

ic

Fig. 10. currents ia , ib and i c onsingle phase to ground fault condition

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.01

0.02

0.03

0.04

0.05

0.06

Time(Sec)

Ineg(A)

ineg

Fig. 11. currents I neg for single phase to ground fault condition

The over load fault is created by increasing the

mechanical torque on the motor by changing the load torque

value in the simulation environment. Fig.12 shows theamplitudes of phase currents under the overload fault

condition. Due to the overload fault, the phase current isincreased to more than 7 times of the rated current. Due to the

high current, the motor will over heat.

0 0.5 1 1.5 2 2.5 30

5

10

15

20

25

30

Time(Sec)

Current(A)

ia

ib

ic

Fig. 12. Currents i a , ib and ic on over load fault condition

The stator current rms amplitudes, speed and leakage

current amplitudes have been applied to the fuzzy logic fault

detection algorithm and the corresponding fuzzy rule viewer

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for different fault conditions of the motor is shown in Figs.

13-17.

Fig.13. shows the result of fuzzy detection with certain

output membership function value (0.875) for the healthy

condition of the motor when all the stator currents and speedare in normal position and the negative sequence current is

almost zero. Figs. 14, 15, and 16 show the fuzzy rule viewer

for double phase to ground fault in an induction motor ,

unbalanced fault and under voltage fault of the motorrespectively.

Fig.13. Fuzzy inference diagram for healthy condition

The motor condition will be decided according to the

output membership function value considered in the design offuzzy logic detection algorithm. The output membershipfunction value ranges are given in Appendix B for different

types of motor fault condition.

Fig.14. Fuzzy inference diagram for double phase to ground fault.

For example fig.14 shows the result of the fuzzy ruleviewer with certain output member function value (16.4) for

double phase to ground fault (ACEF). Fig.15. Shows the fuzzy

rule viewer for certain output membership value (27.3) then

the motor is in unbalanced fault condition (MUB). In fig. 17

the output is 32.9 then the motor is in under voltage fault

condition (VHUVF).

Fig. 15. Fuzzy inference diagram for unbalance fault.

Fig.16. Fuzzy inference diagram for under voltage fault.

Fig.17.shows the result of fuzzy detection with certain

output membership function value (24) for the over loadcondition of the motor when all the stator currents are very

high, speed is in very very low position and the negative

sequence current is very small.

Fig. 17. Fuzzy inference diagram for over load fault.

VII. CONCLUSION AND FUTURE SCOPE

The symmetrical induction motor model has been adopted

for analyzing different types of electrical faults. The model isbased on general machine parameters so that it is not

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necessary to know detailed geometry or physical layout of the

windings.

The electrical faults such as earth fault, unbalanced fault,

under voltage faults and overload faults can be easily

simulated by using the developed model. Fault severity can be

analyzed by varying the supply voltage for under voltage and

unbalanced fault conditions, The results from the simulationsuch as stator current rms amplitudes, leakage current and

speed amplitudes have been used as inputs of the fuzzy faultdetection algorithm to detect the type of fault. The earth fault

also can be done easily with the model. Simulation results of

stator current have been used as inputs to the fault detection

algorithms to detect the condition of the motor.

A method of using fuzzy logic to interpret stator current

signal, speed and leakage current signals of induction motor

for its electrical fault condition monitoring was presented. The

fuzzy decision system achieved with high diagnosis accuracy.

The work done can be extended to identify and analyze the

rotor fault of an induction motor by fuzzy logic algorithm or

by any other diagnostic techniques.

Appendix A: Motor Parameters

Line Voltage = 400 V

Horse power = 2 hpRated speed = 1500 rpm at 50 HzNo. of Poles = 4Total no. of turns per phase = 252

Stator winding resistance = 4.05 ohmStator leakage inductance = 13.97 mHRotor leakage inductance = 13.97 mHRotor resistance = 2.6 ohmMagnetizing inductance = 538.68 mH

Appendix B: Fuzzy output membership function value ranges andcorresponding motor condition

Outputmembershipvalue range

Faultcondition

Outputmembershipvalue range

Fault condition

-2 to 2 Normal 20.2 to 22.6 MOL(Medium overload)

2.2 to 4.6 AEF(Earth fault

at A Phase)

22.8 25.2 HOL(Heavy over

load)

4.8 to 7.2 BEF(Earth faultat B Phase)

25.4 to 27.8 MUB(Mediumunbalance)

7.4 to 9.8 CEF(Earth faultat C Phase)

27.9 to 29.1 HUB(Highlyunbalance)

10 to 12.4 ABEF(Earth faultat A B Phase)

29.2 to 20.4 VHUB(Very highunbalance)

12.6 to 15.0 BCEF(Earth faultat BC Phase)

30.5 to 31.7 MUVF(Mediumunder voltage fault)

15.2o 17.6 ACEF(Earth fault

at AC Phase)

31.8 to 34 VHUVF(Very high

under voltage fault)

17.8 20.2 ABCEF(Earthfault at all Phase)

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