Electrical Fault Detection and Diagnosis of Induction Motor using

Fuzzy Logic

*V. P. Mini, **S. Ushakumari,

Department of Electrical Engineering, College of Engineering Trivandrum, Kerala, 695 016, INDIA

* vpminicet@yahoo.in, ** ushalal2002@yahoo.com

Abstract

Induction motors are critical components in many industrial processes and online monitoring

of the parameters of these high capacity induction motors is becoming increasingly important. The

motor experiences different type of faults, like electrical faults, mechanical faults etc. Objective of

the paper is to study the effects of various types of electrical faults such as stator winding faults and

external faults. It is also proposed to formulate fuzzy inference algorithms for detecting various

faults and analyzing their severity. The mathematical model of three phase induction motor, under

healthy condition is taken as the reference for fault detection and analysis. The asymmetrical

induction motor model is used for inter-turn short circuit fault detection. For the earth fault and

external fault detection, the symmetrical induction motor model is used. In this work, fuzzy logic

inference algorithms are used to formulate decisions about the motor condition with high degree of

accuracy.

Key words

Induction Motor, Electrical fault, Modeling, Fuzzy logic, Fault detection and diagnosis.

1. Introduction

Three phase induction motor is popular in industries due to the simple construction, high

reliability, low cost etc. Because of costly repair, external process down time, health and safety

problem are the areas focusing attention for fault detection and predictive maintenance strategies

for an industrial plant. For the past 25 years, substantial amounts of research have been carried out

for the formulation of new condition monitoring techniques for induction motor drives. Some fault

analysis methods for single phase and three phase induction motors are given by M. Chow et al.

(1991) and F. Filippetti et al. (1993). The induction motor faults are categorised into three viz.

internal, external and environmental related faults. Electrical and mechanical faults are the two

classifications of internal faults. Electrical faults are further sub divided into stator and rotor faults.

Mechanical faults are the faults associated with bearings of the machine.

Stator inter-turn short circuit fault detection method of three phase squirrel cage induction

motor, by analyzing the axial flux linkage of the machine is given by J. Penman et al. (1994). A

method for the detection of rotor fault and mechanical fault of a squirrel cage induction motor is

given by Tarek Aroul et al. (2009) and R. Samsi (2006).

Several techniques such as Fast Fourier Transform (FFT), spectrum analysis, vibration

analysis, temperature analysis etc. are explained by J. Penman et al. (2000), C. J. Dister et al.

(1998) and M. E. H. Benbouzid et al. (2000). The dynamic motor model is required for the

detection and analysis of faults of an induction motor using above methods. Due to the complexity

of the mathematical model, the computation cost and time is very high in the said techniques.

Currently, artificial intelligence based techniques such as fuzzy logic, genetic algorithm and Neural

network are introduced by M. E. H. Benbouzid et al. (2001), Lasurt et al. (2000), L. Cristaldi et al.

(2004), F. Flipperti et al. (1993), R. Saravanakumar et al. (2009) and V. P. Mini et al. (2010) due to

their simplicity, speed of computation and low computation cost. This paper applies fuzzy logic for

the diagnosis of stator conditions and open circuit conditions in phases of an induction motor, based

on the amplitude of stator currents. It is proposed to present a more realistic and straightforward

method to simulate external faults such as open circuit in any of stator phases, under voltage fault,

over load fault, unbalanced fault, earth faults and inter-turn short circuit fault in stator winding.

Two fuzzy logic algorithms are proposed for identifying and analyzing these faults. First algorithm

is used to detect and analyze the inter-turn stator short circuit faults and open circuit faults.

External faults of an induction motor are analyzed with the second fuzzy logic algorithm.

2. Causes and effects of electrical faults

Electrical related faults are frequent in three phase induction motors. Because of these, more

heat will be produced on both stator and rotor windings, which will reduce life of the machine. The

causes and effects of different type of electrical faults such as inter-turn short circuit faults, open

circuit faults, unbalanced supply voltage fault, under voltage fault, over voltage fault, over load

fault and earth faults are discussed here. The causes and after effects of stator faults of electric

motors are given by Ojo et al. (2002), Trutt et al. (2002). The incipient winding faults in a single

stator coil may have relatively little effect on the performance of the motor but may affect the

overall motor reliability and longevity.

Open delta transformers, unbalanced loading, unequal tap settings of the transformer etc. are

the causes of unbalanced voltage faults. The effects are reduction in motor efficiency, temperature

rise and reduction in starting torque. The under voltage fault occurs when a reduced supply voltage

is applied to the motor with a rated mechanical load. Increased stator current, excess heating of

machine are the effects of under voltage fault. When the mechanical load on the motor is increased

beyond the rated value, over load fault will occur. 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 to human safety. The

protection scheme for three phase induction motor from incipient faults is discussed by M. Sudha et

al. (2009).

3. Induction motor model under healthy condition

Model of an induction motor is the circuit representation of the motor. As per the explanation

given by R.M. Tallam et al. (2000), M. Arkan et al. (2005) and V. P. Mini et al. (2011), the model

of the induction motor can be used for fault detection and its analysis. Asymmetrical induction

motor model is used as the reference for inter-turn short circuit fault analysis and symmetrical

induction motor model is used for external fault analysis.

3. a. Asymmetrical Induction motor model Mathematical equations of an asymmetrical induction machine are explained by P. Krause et

al. (1995). The performance evaluation of a three phase induction motor and its fault analysis is

given by V. P. Mini et al. (2010). To derive voltage equations for asymmetrical stator winding and

rotor, following assumptions are made.

Each stator phase of the motor has a different number of turns, but with uniform spatial

displacement.

Magnetic saturation is not present.

With the appropriate superscripts as, bs, cs, ar, br and cr, the voltage equations of the magnetically

coupled stator and rotor circuits can be written as, rabc

rabc

rabc

sabc

sabc

sabc pirpir 0,vs

abc where p=d/dt. (1)

Applying a stationary reference frame transformation to the above equation yields the

corresponding qd0 equation, then (1) becomes

0000001010

,v sqdo

rqdo

rqdor

rqdo

rqdo

sqdo

sqdo

sqdo

pir

pir

(2)

In matrix notation, the flux linkages of the stator and rotor windings can be written in terms of the

winding inductances and the current as

rabc

rrabc

sabc

rsabc

rabc

rabc

srabc

sabc

ssabc

sabc

iLiLiLiL

(3)

The stator and rotor flux linkages in qd0 frame are obtained by applying transformation to the stator

and rotor abc flux linkages in (3),

rqdo

rrqdo

sqdo

rsqdo

rqdo

rqdo

srqdo

sqdo

ssqdo

sqdo

iLiL

iLiL

(4)

Normally, an induction machine is connected to a three phase supply by a three-wire connection.

The stator and rotor flux linkages in (4) may be expressed compactly as

rd

rq

sd

sq

rrsrsr

rrsrsr

srsrssss

srsrssss

rd

rq

sd

sq

iiii

LLLLLL

LLLLLLLL

222221

111211

22212221

12111211

00

(5)

3. a. i. Determination of Inductances

To define asymmetrical machine inductances, as per the explanation given by M. Arkan et al.

(2005) and V. P. Mini et al. (2011), it is assumed that the stator phases as, bs and cs have number

of winding turns Na, Nb, and Nc respectively and the rotor phases ar, br and cr have number of

winding turns Nar = Nbr = Ncr = Nr. The new parameters of an asymmetrical machine stator self

inductance, stator mutual inductances and rotor self and mutual inductances can be defined from

the known parameters of symmetrical machine with reference number of stator turns Ns.

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

mlsLbNmLlsL

sN

bNbsbsLmlsamls

s

aasas LNLL

NNL 2

3

22

2

, 32 2

2

2

(6)

mlscmlss

c LNLLNN 2

2

2

32

where

mls

smls LL

NL

321

2

(7)

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

mssbas

mbabsasasbs LNN

NLNNLL

23

221

(8)

msscbs

mcbcsbsbscs LNN

NLNNLL

23

221

(9)

msscas

mcacsasascs LNN

NLNNLL

23

221 where

23

1 s

mmss N

LL (10)

The rotor self and mutual inductances can be found by a similar way. Because the rotor is assumed

symmetric, the total self-inductances of rotor phases ar, br and cr are equal. Therefore,

32

2

2

marlrms

rlrcrcrbrbrarar LLL

NNLLLL

Where

ms

rmar L

NNL

2

2

32

(11)

For the same reason, rotor mutual inductances are also equal to each other and given by

m

s

rcrarbrcrarbr L

NNLLL 2

2

32

21

(12)

Because of rotor symmetry, the stator to rotor mutual inductances will be Lasar = Lasbr = Lascr,

Lbsar = Lbsbr = Lbscr and Lcsar = Lcsbr = Lcscr. The rotor phase mutual inductances will be

msrms

raascrasbrasar LL

NNNLLL a2 N

32

where m

s

rmsr L

NNL

2

2

32 (13)

N and N ccscb msrrcsbrcsarmsrbscrbsbrbsar LLLLLLLL (14)

3. b. Symmetrical Induction motor model

To derive symmetrical induction machine model, it is assumed that the winding turns in the

three stator phases of an asymmetrical induction machine are equal and it is taken by Ns. The

parameters of a symmetrical machine stator self inductance, stator mutual inductances between the

phases and rotor self and mutual inductances can be expressed as

mls LL

32L L L cscsbsbsasas

(15)

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

LmLLL csasbscsasbs

31

(16)

The rotor self and mutual inductances can also be found by a similar manner. As the rotor is also

symmetric, the total self-inductances of rotor phases ar, br and cr are equal. Therefore,

ms

rmarmarlrm

s

rlrcrcrbrbrarar L

NNLLLL

NNLLLL 2

2

2

2

32 where,

32

(17)

For the same reason, rotor mutual inductances are also equal to each other and is given by

m

s

rcrarbrcrarbr L

NNLLL

2

2

32

21 (18)

Because of the rotor and stator symmetry the stator to rotor mutual inductances are equal

32

csc

m

s

rrcsbrcsarbsbrbsar L

NNLLLL

(19) 4. Simulation of the Induction Motor model

Here the induction motor model equations are rearranged and flux linkages obtained from (2)

for a three-wire system can be written as

dtir

dtir

dtirirv

dtirirv

rd

rr

rqr

rd

rq

rr

rdr

rq

sd

ssq

ssd

sd

sd

ssq

ssq

sq

2221

1211

(20)

The stator currents can be found by inverting (5). The speed of the machine can be obtained

from the torque equation as

dtTTTJ

Pt dampmechemr 2

(21)

Tem is the electromagnetic torque impressed on the shaft of the machine and can be expressed as

sd

sq

sq

sdem iiPT

223

(22) Tmech is the externally applied mechanical torque in the direction of the rotor speed, Tdamp is

the damping torque in the opposite direction of the rotor speed and J is the inertia. By using (20) -

(22) with resistances and inductances, a motor with symmetrical windings can be simulated. The

block diagram representing the model for simulation for the fault analysis of the symmetrical motor

is shown in Fig. 1.

Fig. 1. Block Diagram of fault detection system for a symmetrical induction motor model

5. Induction motor model with inter-turn stator short circuit faults The causes and after effects of stator inter-turn short circuit fault of three phase induction

motor and its modeling is given by Gojko M. et al. (2000). One phase group of three coils in a three

phase induction motor is shown in fig. 2. For explaining inter-turn short circuit fault, it is assumed

that inter-turn short circuit arises between points ‘a’ and ‘b’ of the coil AX. From simple theory, it

is clear that the current flow path from the point A to X is divided into two independent circuits

such as the phase current and the current which flows through the short circuit path. Firstly, when a

short circuit occurs, the MMF is reduced due to the decrease in the number of turns in the phase

winding. Secondly, short-circuit current MMF is opposite to the MMF of the phase winding.

Therefore, inter-turn short circuits have a cumulative effect in decreasing the MMF in the vicinity

of the short-circuited turns.

Fig. 2. One phase of three coils with Inter-turn short circuit between points a and b

In three phase induction motors, the inter-turn short circuits are commonly occurred in

between the turns of the same coil, because the coils of commercially available induction motors

are insulated from one another in slot region and end winding region.

Fig. 3. Stator star and delta winding configuration with an inter-turn short circuit fault

The stator star winding and delta winding arrangement with an inter-turn short circuit fault is

shown in fig. 3. As a result of the inter-turn short circuit fault, an independent circuit with fault

current Ish is established. To develop an induction motor model with a stator inter-turn short circuit,

it is assumed that the phase ‘as’ has two windings in series comprising of un-shorted turns Nus

turns and Nsh shorted turns, where Nas = Nus+Nsh, the overall number of turns is Ns. Nbs = Ncs = Ns.

The motor winding model in qd0 axis representation with an inter-turn short circuit fault occurs in

stator winding is shown in Fig. 4. The inter-turn short fault affects only the part of the q-axis stator

winding. An external resistance known as external short circuit current limiting resistance (rext) is

connected across the short circuited stator winding to limit the short circuit current. It may be noted

that the voltage vqsh will be zero when the external resistance rext is zero.

Fig. 4. Motor winding model in dq0 axis with inter-turn short circuit

The fault severity can be changed by varying the number of shorted turns and by a current

limiting resistance across the short circuit windings. The same assumptions that were made for the

first model are valid for this model also. The self-inductances for the phases as, bs and cs in (6) and

(7) can be written as

cscs2' L and mlssbsbsshshshususshususasas LNLLLLLL (23)

As it can be seen from (23), the self-inductance in phase ‘as’ contains the un-shorted self-

inductance Lusus, the mutual inductance between un - shorted and shorted turns Lussh, and the shorted

turns self-inductance Lshsh.

The stator mutual inductances for symmetrical case can be written as

mcsbsbscsascsshbsusbsasbs LLLLLLL31 , '

(24)

The stator-to-rotor mutual inductances for symmetrical case can be re-written as

ms

rscsrbsrsharusarm

s

raascrasbrasarasr L

NNNLLLLL

NNNLLLL 22 3

2 , 32

(25)

Stator and rotor flux linkages and stator resistances for the new model of a squirrel cage induction motors is written as

, and

00000

0000000

'scsbsshasas

rd

rq

sd

sq

shq

rrd

srd

rrq

srq

shrq

srd

ssd

srq

ssq

sshq

shrq

sshq

shq

rd

rq

sd

sq

shq

rrrrrr

iiiii

LLLLL

LLLLLLLL

(26)

Flux linkages may be obtained from (2) for a three-wire system in the stationary reference frame to give

dtir

dtir

dtirirv

dtirirvv

dtirv

rd

rr

rqr

rd

rq

rr

rdr

rq

sd

ssq

ssd

sd

sd

ssq

sshq

sq

sq

shqsh

shq

shq

2221

1211

(27)

6. Induction motor model with external faults In order to develop the model of induction motor with external faults such as open circuit,

unbalance, under voltage and earth faults etc., the symmetrical machine model is considered. The

external faults are applied during running condition, the open circuit fault is applied by opening any

one phase or more than one phases of symmetrical induction motor, the earth fault is applied by

grounding any one phase or more than one phases of the motor and under voltage faults and

unbalanced faults are applied by changing the supply voltage.

7. Fuzzy logic based diagnosis approach Fuzzy logic is known as a multi-valued logic derived from fuzzy sets for approximate

reasoning. The application of fuzzy logic system in condition monitoring of electrical machines is

given by Lasurt. et al. (2000) and M. E. H. Benbouzid et al. (2001). During the fault diagnosis,

there may arise situations where the fault may fall into some range which cannot be categorized as

“good" or “bad" perse. Since fuzzy logic mimics human thinking, it can be used for fault diagnosis

from vague information. A diagnostic technique can be developed by integrating human knowledge

and experience with fuzzy sets and fuzzy rules (which are obtained from the amplitude features of

the stator current). These fuzzy rules and fuzzy sets which help in the formulation of the knowledge

database that from the basis for fuzzy inference. The induction motor condition can then be

diagnosed using a compositional rule of fuzzy inference. This fuzzy inference system comprises the

fuzzy system input output variables and linguistic variables. A summary is added in the following

sections.

7. a. Fuzzy system input-output variables

The stator current, negative sequence current and speed are taken as the input variables for

condition monitoring algorithm. The induction motor condition can be deduced by observing the

amplitudes of stator current, negative sequence currents and speed of the machine under

corresponding fault condition. Interpretation of results, directly from the input variables is very

difficult because, the input amplitudes are vague. Therefore, fuzzy logic is used to represent

numerical data as linguistic information. In this work, two fuzzy logic algorithms have been used,

one for inter-turn short circuit and open circuit faults in stator windings and the other for earth fault

and external fault detection. For the first case, three variables such as each phase rms amplitude of

stator current Ia, Ib, and Ic are used as the input variables, and for the second case, five variables

such as each phase rms amplitude of stator current Ia, Ib, Ic , amplitude of negative sequence

current Ineg and amplitude of speed are used as the input variables. The motor condition, ‘MC’, is

chosen as the output variable. All the system inputs and outputs are defined using fuzzy set theory.

7. b. Linguistic Variables

It is known that basic tools of fuzzy logic are linguistic variables. Their values are words or

sentences in a natural or artificial language, providing a meaningful systematic manipulation of

vague and imprecise concepts. For inter-turn short circuit and open circuit fault analysis, the output

is the term set T(MC), interpreting motor condition, ‘MC’, as a linguistic variable, could be T(MC )

= Normal , Damaged, Seriously damaged, Open circuit_A, Open circuit_B, Open circuit_C and

the input variables Ia, Ib, and Ic are interpreted as linguistic variables, with T(Q) = Zero(Z),

Small(S), Medium(M), Big(B). Similarly for earth fault and external fault analysis the output

variable is the term set T(MC ) = NR, AEF, BEF, CEF, ABEF, BCEF, ACEF,ABCEF, MOL,

HOL, MUB, HUB, VHUB, MUVF, HUVF and the input variables of stator current amplitudes Ia,

Ib and Ic, negative sequence current amplitude Ineg and speed amplitude N are interpreted as

linguistic variables, with T(Q)= Normal (NR) Slightly high (SLH) medium (M), positive medium

(PM), High (H) Very high (VH), T(Ineg )= Very very small(VVS), very small(VS), small(S),

medium(M), large(L), very large(VL), and T(N )= Very very low(VVL), very low(VL), low(L),

medium(M), positive medium(PM, Normal(NR)

where Q = ia, ib, ic respectively.

8. c. Fuzzy membership functions

In order to handle the fuzzy data, it is necessary to convert the actual data into the fuzzy data

based on certain membership functions. Here two types of membership functions such as

trapezoidal and triangular functions are used.

Table 1. Fuzzy output membership function value ranges and corresponding motor condition for

inter-turn short circuit and open circuit faults

Output membership value range Motor condition

0.0 – 1.0 Healthy

1.5 – 2.5 Damaged

3.0 – 3.5 Open circuit A

4.0 – 4.5 Open circuit B

5.0 – 5.5 Open circuit C

6.0 – 10.0 Seriously damaged

Fuzzy rules and membership functions have been constructed by observing the data set. For

the measurements related to the stator currents, more insight into the data is needed, so membership

functions will be generated for all input and output variables. According to severity of the fault,

each fault condition is divided into a number of fuzzy sets. The output fuzzy linguistic variables

and their membership function value ranges of each fuzzy set for inter-turn short circuit and open

circuit fault detection algorithm are given in table1 and for earth fault and external fault detection

algorithm are given in table 2. For detection and diagnosis of faults, the amplitudes measured of

stator currents, negative sequence component of stator current and speed were converted into

corresponding fuzzy value as inputs. The outputs are then evaluated by fuzzy logic inference

engine using the knowledgebase.

Table 2. Fuzzy output membership function and motor condition for earth fault and external fault Output

membership value

Fault condition Output

membership value

Fault condition

-2.0 to 2.0 Normal 20.2 to 22.6 MOL (Medium Over Load)

2.2 to 4.6 AEF (Earth fault at A Phase) 22.8 to 25.2 HOL (Heavy Over Load)

4.8 to 7.2 BEF (Earth fault at B Phase) 25.4 to 27.8 MUB (Medium Unbalance)

7.4 to 9.8 CEF (Earth fault at C Phase) 27.9 to 29.1 HUB (Highly Unbalance)

10.0 to 12.4 ABEF (Earth fault at A &B Phases) 29.2 to 20.4 VHUB (Very High Unbalance)

12.6 to 15.0 BCEF (Earth fault at B&C Phases) 30.5 to 31.7 MUVF (Medium Under Voltage Fault)

15.2 to 17.6 ACEF (Earth fault at A&C Phases) 31.8 to 34.0 VHUVF (Very High Under Voltage Fault)

17.8 to 20.2 ABCEF (Earth fault all Phases)

9. Simulation results under inter-turn short circuit fault and open circuit fault

A fuzzy logic algorithm is developed for the detection and diagnosis of the inter-turn short

circuit fault in the stator winding and open circuit fault of an induction motor. The mathematical

model of induction motor is developed and simulated by MATLAB® SIMULINK toolbox and the

simulation results are given below for a 2 hp motor with parameters given in Appendix A. The

results are taken during acceleration from standstill to full speed. Fig. 5a. and Fig 5b. show the

speed and torque responses of an asymmetrical machine under normal condition and with 5 turns

shorted condition respectively. In the normal condition, the starting torque is about 60 Nm and the

speed is about 159 rad/sec and the motor will maintain the constant speed within 0.4 sec and

because of stator asymmetry in the 5 turns shorted condition, the torque graph shows more

pulsation and will take more time (0.7 sec) to reach steady state as compared to the normal running

condition.

0 0.2 0.4 0.6 0.8 1 1.20

50

100

150

200

0 0.2 0.4 0.6 0.8 1 1.20

20

40

60

80

100

120

140

160

0 0.2 0.4 0.6 0.8 1 1.2-20

0

20

40

60

80

0 0.2 0.4 0.6 0.8 1 1.2

-50

0

50

100

150

Fig. 5a. Speed and Torque response under

normal condition

Fig. 5b. Speed and Torque response with 5 turns

shorted

0 0.2 0.4 0.6 0.8 1 1.20

5

10

15

20

25

30

iaibic

0 0.2 0.4 0.6 0.8 1 1.20

0.005

0.01

0.015

0.02

0.025

ineg

Fig. 6a. Stator current amplitude under normal

condition

Fig. 6b. Negative sequence current amplitude

under normal condition

0 0.2 0.4 0.6 0.8 1 1.2

-50

0

50

100

150

speedtorque

0 0.2 0.4 0.6 0.8 1 1.20

10

20

30

0 0.2 0.4 0.6 0.8 1 1.20

10

20

30

0 0.2 0.4 0.6 0.8 1 1.20

10

20

30

Fig. 7. Speed and Torque responses with five

turns shorted with 1.5 Ω resistance

Fig. 8. Three phase stator rms currents with five

turns shorted.

N (r

ad/s

ec),

T (N

m)

Time (sec)

I a rm

s (A

) I b

rms (

A)

I c rm

s (A

)

Time (sec)

N (r

ad/s

ec)

T (N

m)

N (r

ad/s

ec)

T (N

m)

Time (sec) Time (sec)

Time (sec) Time (sec)

Cur

rent

(A)

Cur

rent

(A)

Fig. 6a and fig. 6b show the amplitude of stator current and negative sequence current of the

asymmetrical induction motor under normal working condition. Fig. 7 shows the speed and torque

behavior of inter-turn short circuited asymmetrical machine with an external resistance of 1.5 Ω to

limit the short circuit current initially to protect the motor. The torque still has pulsation but smaller

in magnitude and is taking less time to reach steady state than without external resistance. Fig. 8

shows the result of rms stator currents during stand still to steady state with stator turns shorted.

The magnitudes of stator currents are very high at starting itself in the faulty phase. The currents in

the rest of the two phases will get unbalanced and also the amplitudes reduced. The effect of

unbalance will depend on the number of shorted turns. Fig. 9 shows the result of speed and torque

variation of motor and corresponding stator current amplitudes variation when phase-A is opened at

0.4 seconds during the running condition. The speed and torque are not reaching the steady state

positions after opening the phase. The stator current magnitude is zero in phase-A after opening.

0 0.2 0.4 0.6 0.8 1 1.2

-40

-20

0

20

40

60

80

100

120

140

160

Torquespeed

0.38 0.385 0.39 0.395 0.4 0.405 0.41 0.415 0.42 0.425 0.43

-30

-20

-10

0

10

20

30

IaIbIc

Fig. 9. Responses of Speed, Torque, and stator currents of motor with stator phase A opened

The stator current amplitudes are applied to the fuzzy logic detection algorithm and the

corresponding fuzzy rule viewer for healthy condition and damaged condition of the motor is

shown in fig. 10.

Fig. 10. Fuzzy inference diagram for an induction motor in healthy and damaged condition

Time (sec) Time (sec)

N (r

ad/s

ec),

T (N

m)

Cur

rent

(A)

In fig. 10, values of input current are Ia = Ib= Ic = 2.71A and its output membership function

value is 0.45 for healthy condition and the magnitudes of each phase current in damaged condition

are Ia = 5.32 A, Ib = 3.32 A and Ic= 1.96 A and its output membership function value is 1.96. As per

the fuzzy output membership function value ranges and motor condition for inter-turn short circuit

faults and open circuit faults given in table 1. These output membership function values indicate

healthy condition and damaged condition respectively.

The input current magnitudes and output fuzzy membership values for all fault conditions

such as healthy condition, damaged, seriously damaged, open circuit at ‘a’ phase, ‘b’ phase and ‘c’

phases respectively are given in table 3. The motor condition will be decided, according to the

output membership function value considered in the design of fuzzy logic detection algorithm. The

output membership function value ranges are given in table 1 for different types of motor condition.

Table 3. Simulated results of Fuzzy detection algorithm for inter-turn short circuit fault and

open circuit fault

Input Output Ia(A) Ib(A) Ic(A) MC Condition

2.71 2.71 2.71 0.45 Healthy 5.32 3.32 3.82 1.96 Damaged 38.80 21.27 18.00 8.25 Seriously damaged 0.00 22.00 19.00 3.30 Open at 'a' phase 26.80 0.00 28.00 4.40 Open at 'b' phase 17.80 25.80 0.00 5.20 Open at 'c' phase

10. Simulation results under Earth faults and External faults Another fuzzy logic algorithm is developed for the detection and diagnosis of incipient fault

such as unbalanced fault, under voltage fault, earth fault and over load fault in a symmetrical

induction motor and the corresponding simulation results are given below for the same machine.

The results are taken during acceleration from standstill to full speed. Fig. 11 shows the responses

of torque, speed and the stator phase currents ia, ib and ic of the machine under unbalanced fault

condition (Va = 230V, Vb= 190V and Vc = 160V). Due to unbalance in supply voltage, the currents

are in an unbalanced condition, so the motor will take more time (about 3.5 sec) to attain the steady

state speed. The starting torque gets reduced and the torque response consists of ripples and also the

premature failure of motor winding and nuisance of over load tripping will occur. The torque speed

characteristics and stator current waveforms of the induction motor in under voltage fault condition

is shown in fig. 12. The supply voltage is reduced to 60% of rated voltage on all the three phases

for simulating the under voltage fault. During under voltage fault, the stator current becomes very

high. Due to these high current, more heat is produced and it will take very large time to attain the

steady state speed.

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)

Torq

ue(N

m),S

peed

(rad/

sec)

SpeedTorque

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)

Cur

rent

(A)

IaIbIc

Fig. 11. Responses of Speed, Torque and Stator currents ia , ib and ic under unbalanced fault

condition

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)

Torq

ue(N

m),S

peed

(rad/

sec)

SpeedTorque

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)

Cur

rent

(A)

iaibic

Fig. 12. Responses of speed, torque and stator currents ia , ib and ic for under voltage fault condition

The speed and torque responses and corresponding currents in three phases such as a, b and c

of three phase induction motor under single phase to ground fault is shown fig. 13.

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)

Torq

ue(N

m),

Spee

d (ra

d/se

c)

SpeedTorque

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

5

10

15

20

25

30

Time(Sec)

Cur

rent

(A)

iaibic

Fig. 13. Responses of speed, torque and stator currents ia , ib and ic on single phase to ground fault

During normal running condition, at 1 sec, phase A is earthed and cleared at 2 sec for

simulating the single phase to ground fault. Due to this, more pulsation is occurred in speed and

torque responses, which will reduce the life time of the motor. Due to single phase to ground fault,

the unbalance is occurred in the stator currents and because of this, turn to turn insulation failure

and finally, the motor insulation failure will occur.

Table 4. Simulated results of Fuzzy detection algorithm for external and earth faults

Input Output Ia (A) Ib (A) Ic (A) Ineg (A) N (rad/sec) MC Condition 2.45 1.94 4.09 0.00811 157.0 27.3 Unbalance fault

12.80 11.90 1.90 0.0406 112.0 16.4 Earth fault 13.40 13.60 13.40 0.0043 77.9 32.9 Under voltage fault 15.30 24.70 24.30 0.0062 82.5 24 Over load fault

Fig. 14. Fuzzy inference diagram for unbalance 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. Due to this, the phase current is increased by

more than 7 times of the rated current and the motor will over heat. The stator current rms

amplitudes, speed and leakage current amplitudes are applied as input to the fuzzy logic fault

detection algorithm for incipient fault detection and the corresponding fuzzy rule viewer for

unbalance fault of the motor are shown in fig. 14. The input magnitudes of phase currents, negative

sequence current and speed and output membership values for all fault conditions such as

unbalance fault, earth fault, under voltage fault and over load faults are given in table 4. Here also

the motor condition can be assessed, according to the output membership function value obtained

in the design of fuzzy logic detection algorithm. The output membership function value ranges for

different types of motor fault conditions are given in table 2. Depending on the severity of the

fault, each fault condition of the motor is divided into different fuzzy sets. For example according

to severity of the unbalance, the unbalance fault condition is again divided into three fuzzy sets

named as ‘medium unbalance (MUB)’, ‘highly unbalance (HUB)’ and ‘very high unbalance

(VHUB)’.

11. Discussion

The work done in paper on electric fault detection and diagnosis of three phase induction

motor using fuzzy logic algorithm is accessible to any industry who can install the detection

algorithm module in concerned three phase induction motors. The extracted current and speed

signals from the working machine are applied to the fuzzy inference algorithm after processing.

This algorithm will indicate the motor condition whether it is healthy or damaged. Two algorithms

are developed in this work. First one is used for detection and diagnosis of stator inter-turn short

circuit fault and open circuit fault. The second algorithm is used to detect unbalance fault, under

voltage fault, over load fault and earth fault of three phase induction motor. Additional features are

also added to the algorithm for analyzing the severity of the fault. This fuzzy inference algorithm

facilitates the early detection of the motor fault, thereby reducing the maintenance cost and protects

the machine from the catastrophic faults.

12. Conclusion and future scope

The asymmetrical induction motor model is proposed for analyzing inter-turn short circuit

faults and the symmetrical induction motor model is proposed for analyzing different types of

incipient faults such as earth fault, unbalanced fault, under voltage faults and overloads faults and

open circuit faults. No such attempts are reported in the literature, in the context of induction

machine protection. The proposed models are based on general machine parameters so that it is not

necessary to know detailed geometry or physical layout of the windings. Inter-turn short circuit

fault of the stator winding of an induction motor is simulated by using the developed model of

asymmetrical induction motor and the fault severity is analyzed by varying the number of shorted

turns and an optional current limiting resistance across the short circuit windings. For analyzing the

external faults, the developed model of symmetrical induction motor is used. Simulation results

such as the stator current, negative sequence leakage current and speed are used as inputs to the

fault detection algorithms to detect the condition of the motor. A method using fuzzy logic to

interpret stator current signals and speed of induction motor for its condition monitoring is also

presented. The fuzzy decision system is achieved with high diagnosis accuracy. The proposed

method can be extended to identify and analyze the rotor fault of an induction motor by using fuzzy

inference or a rigorous modeling technique.

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Appendix A: Motor Parameters Horse Power: 2 hp, Line Voltage: 415 V, No. of Poles: 4, Rated speed: 1500 rpm / 50Hz,

Turns / phase: 252, Stator winding resistance: 4.05 Ω, Stator leakage inductance: 13.97 mH,

Rotor leakage inductance: 13.97 mH, Rotor resistance: 2.6 Ω, Magnetic inductance: 538.68 mH

Nomenclature

sabcv : stator voltage matrix in abc frame s

abcr : stator resistance matrix in abc frame sabci : stator current matrix in abc s

abc : stator flux linkage matrix in abc frame r

abcr : rotor resistance matrix in abc frame 0s

qdr : stator resistance matrix in qd0 frame

rqdor : rotor resistance matrix in qd0 frame

ssabcL : stator to stator inductance in abc frame

srabcL : stator to rotor inductance in abc frame

ssqdoL

: stator to stator inductance in qd0

srqdoL

: stator to rotor inductance in qd0 frame shqL : short circuit winding inductance in q-axis

sd ,

sq : d-axis and q- axis stator flux r

d ,rq : d-axis and q-axis rotor flux linkages

sdi , s

qi : d-axis and q- axis stator current rdi , r

qi : d-axis and q-axis rotor current shqi : q-axis short circuit current sshqL : mutual inductance between stator and short circuit in q- axis shrqL : mutual inductance between rotor and short circuit in q- axis