Monitoring and Fault detection of the Stator short- circuit fault in induction motor based on the Fuzzy

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Proceedings of Engineering & Technology (PET)

Merabet. Hichem

Welding and NDT research center (CSC) BP 64 Cheraga, Algeria

h.merabet@csc.dz Drici. Djalel

J.drici@csc.dz

Abstract— the diagnostic of the induction machines becomes more and more important. This made necessary the monitoring function condition of these machines for improved an exploitation of the installation. The aim of this work is the proposal of a monitoring strategy based on the fuzzy logic, that informs us about the healthy and fault operating condition of short-circuit between turns of the stator windings. The principle adopted for the strategy suggested is based on monitoring of the average root mean square (RMS) value of the stator current, which will be useful as input data with the fuzzy logic block and considered to making decision on the machine state.

Keywords — Induction Machine, Monitoring, Detection, Fuzzy logic, RMS, Modeling, Simulation.

1. INTRODUCTION

he faults diagnosis of the induction machines (IM) is studied under various approaches by many research work because of its considerable interest for the continuity of the industrial processes service [1, 2].

An early detection of the faults and the diagnosis allow to minimize the downtime, the turn-around time of the process in question, to avoid the damaging consequences, and to reduce the financial losses [3-5].This is performed by measuring accessible sizes and easily measurable of the machine, to analyze them in a minimum of time and to conclude the state of the induction machine [6, 7].

In general, the electric machines can be external or internal fault [8, 9]. For the external faults, they are caused by the feeding source, the mechanical load, and environment of the machine use. The intern faults are caused in the magnetic circuits, stator and/or rotor windings, mechanical air-gap, and the cage rotor of the machine [10, 11]. Within this framework, the statistics reveal that the electrical faults on the level of the stator are the most recurrent [12, 13].

Aouabdi. Salim

h.aouabdi@csc.dz Berrahal. Khoukha

K.berrahal@csc.dz

However, through this work, we will be interested particularly in the short-circuit faults between stator turns of the induction machine (IM). As know that the principal consequence which causes this faults type is the increase in the stator currents amplitudes [14, 15].

Therefore, the approach that we propose is based on the artificial intelligence, in order to increase the efficiency and the reliability of the diagnosis in the supervision field and diagnosis of the IM [16-17]. The model of the approach as well as the global model are simulated by using software MatLab ^®SIMULINK and results of simulations obtained in a healthy function and short-circuit faults are presented and interpreted.

I. MODELING OF THE IM

The development of a diagnosis procedure containing analytical models of the induction machine must cover a certain number of problems of the synthesis methods describing the behavior of the machine, by integrating precisely certain parameters for describing the performance of the machine. The models must be adequate to describe clearly the detection method [18, 19].

The proper inductances and mutual inductances, issue respectively expressed in (1) and (2) are given by using the theory of winding function:

(1) (2) μ0 : air permeability;

g: thickness of the air-gap ; l: length of stator/rotor ; r: Means radius of stator/rotor;

Nt : number of windings turns;

θr : angular position between rotor windings;

P : poles number.

Monitoring and Fault detection of the Stator short- circuit fault in induction motor based on the Fuzzy

Logic approach

T

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Proceedings of Engineering & Technology (PET)

The voltage stator and rotor equations can be expressed in the form of matrix following:

_ _ _

0 0

⁽³⁾

Voltage rotor equations:

_ _ _

0 0

⁽⁴⁾

With;

_ (5)

_

(6)

The flow stator and rotor equations can be expressed in the form of matrix following:

(7)

Electromagnetic Torque equation:

. → → . . →

→

(8)

The inductances matrices are obtained to leave:

⁽⁹⁾

sin sin sin

(10)

sin sin sin

11

⁽¹²⁾

With;

The mutual inductances of the stator tow-phase winding:

⁽¹³⁾

The mutual inductance of the rotor tow-phase winding:

(14)

The self mutual inductance of the stator and rotor:

⁽¹⁵⁾

Where;

Lls, Llr : stator and rotor leakage inductances;

Ns , Nr : number of the stator and the rotor turns.

II. MODEL OF SHORT-CIRCUIT OF THE IM

The voltage and flows equations of the machine in the presence of the short-circuit faults are [20]:

0

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rcc: resistance of the short-circuit winding

.

(17)

The flows equations are written in the form:

(18)

Lscc: mutual inductance between a stator phase and the short- circuit winding;

Lrcc: mutual inductance between a rotor phase and the short- circuit winding;

In the fault, we can write various inductances of short circuit winding compared to the stator and rotor phases:

(19)

3

2 cos sin

3

2 cos sin

3

2 . cos sin

3

2 . cos sin

(20)

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Proceedings of Engineering & Technology (PET)

Where, the relationship between the turn’s number in short- circuits and the number of healthy phase turns (_cc) are defines by:

(21)

After the transformation of the three-phase system into two- phase (

, ) the

voltage and flow equations become:

0

(22)

. . .

(23) With ,

. cos sin

cos sin (24)

̃

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, : the respectively common magnetizing flow and stator leakage flows.

The winding equation at fault brought back to the primary is written:

̃ . .

⁽²⁵⁾

The line currents are then the sum of the short-circuit currents and the currents consumed by the traditional model of Concordia. Thus, it becomes possible to express the equation of winding at fault in the reference stator:

̃ . .

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III. MONITORING OF THE STATOR BY FUZZY LOGIC

1. Monitoring system

In this work, we use fuzzy logic for the detection and the diagnosis of short-circuit faults in the induction machine. The diagram block of the suggested approach is shown in figure 1.

In this case, linguistic variables, fuzzy subsets and the membership functions describe amplitudes of the stator current. An interface fuzzy system comprising the rules and

the data bases is established to support the fuzzy inference.

The state of the machine is diagnosed by using a compositionally rule of fuzzy execution [21, 22].

2. Input-output variables of fuzzy system

The amplitudes of the stator currents (Ias, Ibs and Ics) and the state of stator, (CM) are respectively selected as input and output variables of the fuzzy system. All these variables are defined by using the fuzzy set theory. Figure 2, shows that CM interprets the state of the stator as a linguistic variable, which could be T (CM) = {Healthy Stator, Short-circuit, Critical Short-circuit, Open phase}.Each limit in T (CM) is characterized by a fuzzy subset. The dialog system CM {Healthy Stator (HS)}: interprets that the stator is healthy, {Short-circuit (SC)}: the stator can by present a short-circuit faults, {Critical Short-circuit (CSC)}: that the critical short- circuit fault, and {Open phase (OP)}: interprets that the stator open phase fault. The variables of input Ias, Ibs and Ics are also interpreted as linguistic variables, with, T (Q) = {Zero (Z), Small (S), Medium (M), Big (B)} as it is showing in figure 3.

The fuzzy rules of the membership functions are built by the whole data observation. There is, however, 14 rules used

Fig.1 monitoring system of IM state

Fig.2. Membership functions for output variables OP

SC CSC

HS

CM

Q

Z M L

Fig. 3 Membership functions for input variables S

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Proceedings of Engineering & Technology (PET)

starting from the membership functions for the input and the output. These rules are then defined, as the following:

Rule (01): If Ias is Z Then CM is OP Rule (02): If I_bs is Z Then CM is OP Rule (03): If I_cs is Z Then CM is OP Rule (04): If Ias is B Then CM is CSC Rule (05): If I_bs is B Then CM is CSC Rule (06): If I_cs is B Then CM is CSC

Rule (07): If Ias is M and Ibs is M and Ics is M Then CM is HS Rule (08): If I_as is S and I_bs is S and I_cs is S Then CM is HS Rule (09): If I_as is S and I_bs is S and I_cs is M Then CM is SC Rule (10): If I_as is S and I_as is M and I_cs is M Then CM is SC Rule (11): If Ias is M and Ibs is S et Ics is M Then CM is SC Rule (12): If I_as is S and I_bs is M et I_cs is S Then CM is SC Rule (13): If I_as is M and I_bs is S et I_cs is S Then CM is SC Rule (14): If Ias is M and Ibs is M et Ics is S Then CM is SC

IV. SIMULATIONS AND INTERPRETATIONS The figures 4.a present the three phases currents of a, b and c as well as part on largamente (zoom) of where the regime is permanent, this latter shows clearly that the three currents are balanced, figure. 4 b present the RMS of the three currents phases, it is noticed that their magnitudes are the same one in this case, the figure 4.c presents the output of the fuzzy value (the decision). This value is included in the interval CM = {HS [0 25]}, which corresponds to the limits of the healthy stator case. In addition, in the figure 4.d present the fuzzy inference diagram of the currents phases and the decision.

The continuation of the tests consist in analyzing the same sizes but when the machine presents a short-circuit faults with 5% (fig. 5) and 10% (fig. 6) between the turns of the phase

"a". These tests are basically the object of showing the possibility of detecting such a fault and also of monitoring on the state of its severity. Indeed, it is noticed that the stator short-circuit fault cause an imbalance of the currents of the machine. We notice the increase in the amplitudes of the currents of the stator phases, but with different rates, and this although the fault lies only in the level of the phase "a".

The figures 5.a-b and 6.a-b corresponding to tests of short-circuit (Currents phases and RMS), present increases in magnitudes proportional to the numbers (proportion) of the short-circuit stator turns. In addition, the figures 5.c and 6.c indicate values which correspond to those that indicate the presence of the fault. Indeed, in the case of 5% shorted- circuit turns the decision indicates CM = {SC [20 50]}. On the other hand, for 10% of shorted-circuit stator turns the decision indicates CM = {CSC [45 75]}.Therefore, these tests validate that the approach is reliable and exploitable.

For proved that our approach of detection and monitoring of induction machine function state gives satisfactory results even in the cases where the short-circuit fault is caused within the other phases (B and c) of the machine. We tested our model in the case of a defect 10% of turn’s shorted- circuit with the phase "b" then the same rate for the phase

"c".

-a- Stator currents

0 0.5 1 1.5 2 2.5 3

-40 -30 -20 -10 0 10 20 30 40

Time (s)

Stator Currents (A)

Isa Isb Isc

1.45 1.5 1.55

-6 -4 -2 0 2 4 6

0 0.5 1 1.5 2 2.5 3

0 5 10 15 20 25

Time (s)

RMS of stator currents(A)

RMS__Ias RMS__Ibs RMS__Ics

0 0.5 1 1.5 2 2.5 3

0 20 40 60 80 100

Time (S)

Fuzzy Values

Fig.4 Characteristics of the IM (healthy case) -d- Fuzzy inference diagram

-c- Output fuzzy Values -b- RMS of the stator currents

HS

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Proceedings of Engineering & Technology (PET)

-b- RMS of the stator currents -a- Stator currents

-c- Output fuzzy Values

-d- Fuzzy inference diagram

Fig.5 Characteristics of the IM with 5% short-circuit of phase "a" (short-circuit case)

0 0.5 1 1.5 2 2.5 3

-40 -30 -20 -10 0 10 20 30 40

Time (s)

Stator Currents (A)

Isa Isb Isc

1.45 1.5 1.55

-30 -20 -10 0 10 20 30

0 0.5 1 1.5 2 2.5 3

0 5 10 15 20 25

Time (s)

RMS__Isa RMS__Isb RMS__Isc

0 0.5 1 1.5 2 2.5 3

0 20 40 60 80 100

Time (s)

Fuzzy Values

-b- RMS of the stator currents -a- Stator currents

0 0.5 1 1.5 2 2.5 3

-50 -25 0 25 50

Time (s)

Stator Currents (A)

Isa Isb Isc

1.45 1.5 1.55

-50 -25 0 25 50

Time (s)

Stator Currents (A)

0 0.5 1 1.5 2 2.5 3

0 5 10 15 20 25 30 35

Time (s)

RMS__Isa RMS__Isb RMS__Isc

0 0.5 1 1.5 2 2.5 3

0 20 40 60 80 100

Time (s)

Fuzzy Values

-c- Output fuzzy Values

-d- Fuzzy inference diagram

Fig.5 Characteristics of the IM with 10 % short-circuit of phase "a" (critical short-circuit case)

SC

CSC

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Proceedings of Engineering & Technology (PET)

For these tests, we are relieved to present only the corresponding fuzzy inference diagrams (figures 7 and 8) which show incontestably that the considered approach is valid and reliable.

V. CONCLUSION

In this paper, we presented the development of a fault model of the induction machine then the simulation of this type faults.

We initially presented in the first part the mathematical model then the simulation of healthy machine.

In the second part of this work we have assembled feasibility to detect and diagnosis the stator short-circuit fault between turns in an induction machine by supervising the magnitudes of the stator currents. In addition, this approach inform about the induction machine function condition and to predict the fault severity.

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Fig.7 Fuzzy inference diagram of the IM with 10%

short-circuit of phase "b"

Fig.8 Fuzzy inference diagram of the IM with 10%

short-circuit of phase "c"