artículoFault Diagnostic Based on Parity Equations Applied to Induction Motor

7/17/2019 artículoFault Diagnostic Based on Parity Equations Applied to Induction Motor

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Fault Diagnostic Based on Parity Equations Applied to Induction Motor

Marco A. Rodríguez, Manuel Hernandez, Victor Golikov, Gilberto Martínez

Universidad Autónoma del Carmen UNACAR, Departamento de Ingeniería Electrónica, Ciudaddel Carmen Campeche México.

E-Mail: [email protected] , [email protected]

Resumen: En este trabajo se presenta una técnica de detección de fallas basada en el análisis con ecuaciones de paridad y aplicadas al motor de inducción. La idea principal es aproximar, durante el marco de referencia

sincrónico, el modelo no lineal del motor de inducción al modelo lineal del motor de CD, con la intención degenerar un cambio significativo en los residuos obtenidos mediante ecuaciones de paridad en presencia de falla,

lo cual permite la simplificación y confiabilidad de la detección de la falla. Para validar la técnica propuesta se presenta una simulación y resultados experimentales utilizando PSIM y Labview respectivamente.

Abstract: In this paper, a fault detection technique by using parity equations applied to an induction motor is

presented. The nonlinear model of A.C. motor is matched with the lineal model of D.C. motor in synchronousreference frame in order to generate a relative large change in the residual obtained with parity equations in

presence of fault, which allows the simplicity and reliability of the fault detection. The good performance of thefault detection system is validated by using a simulator software of power electronics and motor control

applications (PSIM) and experimental tests using Labview.

Keywords: Fault diagnosis, induction motors, D.C. motor, parity equation, modeling.

NOMENCLATURE

B Friction coefficient

idr d axis rotor current in the synchronous frameids d axis stator current in the synchronous frames

i f Flux-producing component of the stator current

iqr q axis rotor current in the synchronous frame

iqs q axis stator current in the synchronous frame

iT Torque producing component of the stator current

J Moment of inertia

Lm Magnetizing inductance

Lr Rotor inductance

L s Stator inductance

R s Stator resistance

V qs q axis stator voltage in the synchronous frame

V ds d axis stator voltage in the synchronous frame

λr Rotor flux linkage phasor

σ Leakage coefficientωr Rotor electrical speed

ω s Slip speed

I. INTRODUCTION

Induction motor is the “workhorse” of industry and is

extensively used in a wide variety of industrial processes and

is often integrated in many critical processes. 1 Then, to

maintain the right working of the motors must to be very

reliable in order to insure a high degree of reliability by means

of maintenance programs and specific attention by using a

permanent monitoring of motor in order to detect incipient

faults and to avoid failures. Generally, the most frequent faults

in induction motor are mechanical [1], and these are related to

the electrical operation of the motor such as local overheating

and inter-turn short-circuit stator winding. These latter faults

result in changes of basic electric parameter values of motor

such as resistances and inductances. Thus, this fault must be

diagnosed opportunely by means of determining the type, size

and location of the fault as well as its time of detection.

The mechanical vibration analysis is the most studied

technique to detect faults in the induction motor [2]. This is

due to the significant magnitudes and the immunity to external

phenomena like the electromagnetic interference over sensorswhich are commonly accelerometers through the

accelerometers´ disadvantages are that they have very limited

operation ranges. The diagnosis technique most utilized, for

the mechanical and electrical faults in the induction motor is

the spectral analysis of the phase current [3-4]. Other

techniques are based on the motor current transformations [5].

Others evaluate the neutral terminal voltage of induction motor

[6] and finally by means of the system impedance calculation

XXI Congreso de la Asociación Chilena de Control Automático ACCA 2014ISSN (en trámite), Pág. 65-72. Santiago de Chile, 5 al 7 de Noviembre 2014

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[7]. The main problem of these techniques is that the time

delay of detection and localization of the fault is very long and

expensive. The stator winding fault is one of the electrical

faults in the literature that has reported short time delay of fault

detection by means of the model based methods like the

Winding Function Approach (WFA) [8]. Another model based

method is by using parity equations which can be suitable to

detect several faults [9] but to compute the residuals from thegeneral parity equation, it is necessary to obtain first an

accurate mathematic model of system. For this reason, it has

mainly been applied to linear systems, where accurate models

are more readily available. However, as accurate models for

nonlinear systems are more difficult to obtained in practice,

and besides the parity equation is sensitive to noise and model

uncertainties, the parity equation derived using existing

approaches cannot be readily applied to nonlinear and

uncertainty systems [9].

More generally, the diagnostic procedure is based on the

heuristic knowledge on the process and observed analytical

heuristic symptom commonly represented in a signal called

residual. In these last two cases, a priori knowledge of fault

symptom causalities, as well as, a large data bank is

necessary[10]. However, in the diagnosis by using analytical

symptoms with limit values of measurement signals and

change detection have a minimal mathematical effort and

without data bank, which allows the simplicity and reliability

when a relative large change of their feature is obtained [11].

In this paper, a new approach is presented not only to detect

faults, but also to isolate faults for the nonlinear model of

induction motor matching it with the linear model of D.C.

motor taking into account the performance during the steady

state.

II. MODELING OF INDUCTION MOTOR IN DQ REFERENCE

FRAME

The key assumption of motor model in synchronous referenceframe is that the rotor flux linkages are constant so that their

derivatives are zero, then the following equations are deduced

in the d-q reference frame.

= ( + ) + + + (1)

= + − + − (2)

Where , , , are the stator and rotor d -q axes currents

in the synchronous reference frame that are obtained by

projecting the stator and rotor current phasor on the d-qaxes

respectively. Likewise, and are the stator d -q axes

voltages in the synchronous reference frame.

A simplification can be obtained by using the followingrelations [12]. = − (3)

= − (4)

Substituting the above expressions in (1) and (2) result that.

= ( + ) + + (5)

= ( + ) − + (6)

Where is the leakage coefficient. On the other hand, it is well

know that the flux-producing component of the stator current

(i f ) is constant in the steady state, and that is the d axis statorcurrent in the synchronous frames (ids). Therefore, its derivate

is zero in the steady state. Also, it is know that the torque

producing component of the stator current (iT ) is the q axis

stator current in the synchronous frames (iqs),additionally, it is

know that the rotor flux linkages phasor = then.

= ( + ) + + = ( + ) +

(7)

Where

= = −

(8)

= + = + (9)

Then = ( + ) + + = + + + (10)

From which the torque producing component of the stator

current is derived as.

= − + + = 1 + − (11)

Where = + , = 1 , = (12)

One the torque producing component of stator current iT is

deduced is possible to obtain the electromagnetic torque with

the following expression.

= (13)

Where

= 32 2

(14)

Now, the load dynamics can be expressed by the

electromagnetic torque T e and the friction as.

+ = − = − (15)

In term of the electric rotor speed, is derived by multiplying

both sides by the pair of poles:


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+ = 2 − (16)

Hence, the transfer function between the speed and the torque

producing current is deduced as.

()() = 1 + (17)

Where = 2 , = + , = (18)

The block diagram of induction motor with constant rotor

flux linkages is shown in Fig. 1.

+

K a

1+sTaK f

P

2 +

- 1

B+sJ

B1

Ls.if

Electrical Mechanical

ωr

V qs I qs

T e- iT

Fig. 1 Block diagram of induction motor model with

constant rotor flux linkages

This model is so similar to CD motor model obtained in [13]

and [14]. Although the main difference is that the input

parameter is instead of the armature current I A.

III. R ESIDUAL GENERATION BY USING PARITY EQUATIONS

A simple model of induction motor in steady state which islittle similar to CD motor model[12] is used in this work,

because the fault detection based on parity equations for this

model types is availability to detect several parameters[13].

Based on known ways of theoretically modelling the structure

of a linear mathematical model in the continuous time without

considering disturbances (19) and (20), the state space

representation obtained for the induction motor is displayed in

(21) and (22).

() = () + () (19)

() = () (20)

= ⎣− − −( + ) ⎦ + 1 00 0 0 (21)

() = 1 00 1

(22)

Where = , = (23)

Note that, the structure obtained in (21) is similar to DC motor

model shown in [13] and [14] but no equal. An important

difference is that the second term of in (21) the magnetic

flow

is defined as the relation between the stator inductance

and the d axis stator current in the synchronous frames I ds.

Another important difference is that the first term of ,themagnetic flow of D.C. motor model is defined as the

relationship among poles number P , magnetic inductance Lm,

rotor inductance Lr and flux-producing component of the stator

current I f . A way to add redundancy in the equations at the

same instant t is by introducing (19) in (20) with its respective

derivatives like:() = () + () (24)

Where

⎣

()()()⋮()⎦ = ⎣

⋮⎦ ()

+ 0 0 0 … 0 0 0 … 0⋮ ⋮

… 0⋮ ⋱ ⋮… ⎢()()()⋮()⎥ () (25)

Now, the residual vector based on state-space model for

continuous time is given in (26) which is deduced in [14] from

the residual generation with parity equation for MIMO process

with transfer functions and polynomial errors.

() = () − () (26)

An important condition to satisfy that both of the first and

second term of (26) are zeros is that W T=0 [14] where W is

called the null space of T and can be obtained by proposing the

greater number of zeros possible at the rows, taking into

account that the lines are linearly independent. In our case of

study, the W matrix obtained by the induction motor is (27):

= − 00 0 00 0 00 00 00 (27)

Where

=

, = +

, = + , = +

(28)

By the assumption that in the healthy operation the parameter

do not change, () = 0, then, a fault is detected when () ≠0. The residuals obtained by the induction motor are

() = () + () + () −

() = −() + () + () (29)

Fault Diagnostic Based on Parity Equations Applied to Induction Moto

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() = () + ( + ) () + ()− − ()

() = () + [ + ]() + () −

Note that during the steady state, the derived of

() is zero,

and

= , thus, the residual can be simplified, this is so

suitable when the fault type is incipient; considering that is themost common in the electrical machines, then, the residuals

can be reduced as.

() = () + () −

() = −() + ()

() = () −

() = () −

(30)

Likewise, as in the D.C. motor [14], if an additive fault occurs,

all residuals except the decouple one are deflected as shown inTable 1. This supports strongly to locate the sensor faults, and

thus this fault types are easy detectable. When a parametric

fault occurs on R s or Rr there is no a considerable increase in

r 3, thus, a null value can be considered to simplify the fault

detection matrix. Finally, a simple way to distinguish the fault

is by using classical limit-values detectors with a suitable

tuning, taking into account the behaviour of residual obtained

in Fig. 2.

Table 1. Fault detection matrix

faults r 1 r 2 r 3 r 4

p a r a m e t r

i c

R s I 0 0 I

Rr I 0 0 I

L s I 0 I I

Lr I I I I

B 0 I I I

Bl 0 I I I

a d d i t i v e I qs

e I I I 0

ωr I I 0 I

V qse I 0 I I

Where “I” represents a significant change which can be

positive or negative. Then with the above matrix can be seen

that the fault detection probability for R s, Rr , L s, B, Bl and V qse

are 50% and only for Lr , I qse and ωr are 100%.

IV. EXPERIMENTAL AND SIMULATION RESULTS.

In this case study, the change detection is used to locate the

parametric fault. Fig. 2 shows the simulation results in Matlab

obtained for induction motor when a parametric fault has

occurred. In all simulation cases, the transient appears from 0

to 3 seconds, the steady state begins to 3 seconds and the under

fault condition begins to 5 seconds with ±½%of its nominal

parametric value.

0 2 4 610

5

0

5

10

r1

r4

r1

r4

0 2 4 610

5

0

5

10

(a1) r 1, r 4 R= nominal value -50%

(a2) r 1, r 4 R = nominal value +50%

0 2 4 610

5

0

5

10

r1

r4

0 2 4 610

5

0

5

10

r1

r4

(b1) r 1, r 4 R = nominal value -50% (b2) r 1, r 4 R = nominal value +50%

0 2 4 610

5

0

5

10

r1

r2

r3

r4

r1

r2

r3

r4

0 2 4 610

5

0

5

10

(c1) r 1, r 2, r 3, r 4 L = nominal value -50%

(c2) r 1, r 2, r 3, r 4 L = nominal value +50%

r1

r3

0 2 4 610

5

0

5

10

r4

r1

r3

r4

0 2 4 610

5

0

5

10

(d1) r 1, r 3, r 4 L = nominal value -50%

(d2) r 1, r 3, r 4 L = nominal value +50%

r2

r3

r4

0 2 4 610

5

0

5

10

0 2 4 610

5

0

5

10

r2

r3

r4

(e1) r 2, r 3, r 4 B = nominal value -50%

(e2) r 2, r 3, r 4 B = nominal value +50%


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Fig. 2 Simulation results in Matlab of residuals by using the

induction motor model with constant rotor flux linkages

The parameters of induction motor used are:

Power 0.75 hp

RMS line to line voltage (V LL) 220 V

Number of poles ( P ) 4 polesStator supply frequency ( f ) 60 Hz

Rotor speed (ωr ) 1800 rpm

Stator resistance ( R s) 2.9 Ω

Rotor resistance ( Rr ) 3.54 Ω

Stator inductance ( L s) 0.105 H

Rotor inductance ( Lr ) 0.156 H

Magnetizing inductance ( Lm) 0.173 H

Moment of inertia ( J ) 0.001 kg.m2

Friction coefficient ( B) 0.025 N.m

The low performance of all residuals during the transient

period (0 to 3 seconds) in Fig. 2 appears by the incorrect

modeling of induction motor used for the residual generation,

provided that the rotor flux linkage phasor be constant.

However, the performance during the steady state is good. An

easy way to validate both of the good performance of the fault

detection technique proposed and the induction motor model

simplified during the steady state is by the simulation software

of power electronics and motor control applications (PSIM),

which contains an induction motor with available parameter

variation. The simulation diagram on PSIM of the induction

motor in healthy operation (output1) and under fault condition

(output2)are shown in Fig.3(a) and the sub diagram of r1 is

shown in Fig. 3(b)with the detection block which implements

the residual equations of (30).

(a) Main diagram on PSIM

(b) Sub diagram of r1

Fig. 3 Diagram on PSIM of residual switch a detection block

by using the internal induction motor model

r1 (Healthy operation) r1 (Under fault condition)

Isa (Healtly operation)Isa (Under fault condition)

Iqs (Healtly operation)Iqs (Under fault condition)

(a) FaultyR= + 50% of its nominal value

r1 (Healthy operation) r1 (Under fault condition)

Isa (Healtly operation)Isa (Under fault condition)

Iqs (Healtly operation)Iqs (Under fault condition)

(b) Faulty R= + 50% of its nominal value

Fig. 4 Simulation results in PSIM of detection circuit for the

residual r1

Fig.4 shows the simulation results on PSIM of residual r 1 when

R s and Rr are under fault with +50% of its nominal values, as

well as, when R s and R r are fault-free. It is evident to notice

that r 1 is affected in (30) when R s and R r are modified by two

reasons: first, because are involved in the first term of r 1; and

second, because the amplitude and phase of motor currents are

affected which are reflected in I qs, affecting the r 1 value too.

On the other hand, ωr and V qs are not affected significantly,

first because the rotor speed is not involved directly with this

parameter and second, because V qs only is based on the power

input supply voltage changes.

A practical way, to increase R s is easy placing resistance in

series with the stator winding. On the other hand, to increase

R r is not far from easy. A way to increase the R r is to break

some rotor bars although the increase of L r is associated too

which does not affect the result significantly because R r and Lr

are associate to the same residual

Fig.5 shows the experimental results of residual r 1 when R s and

Rr are under fault approximately at +50% of its nominal values

and when they are in healthy operation. The residual will be

obtained mathematical by using a data vector obtained with

experimental test.


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0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5(s)3

1

1

3

5 A

Iqs (Healthy operation)

Iqs (faulty R S) Iqs (faulty R r )

(a) q axis stator current in the synchronous frames for the

healthy and under fault condition with the motor stator

current like comparison point

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5(s)

5

0

2.5

5

7.5

10V

Healthy operation

7.5

Faulty R S Faulty R r

2.5

(b) Residual r1 for healthy condition and faulty condition of

R s and R r

Fig. 5 Experimental results for the residual r1

As expected, the experimental and simulation results have

similar behavior when a fault is carried out. However, the

magnitudes of the residuals are tiny different. In accordance

with simulation results between Matlab and PSIM, the

difference can be attributed to the model of Matlab. In

accordance with experimental results the difference between

PSIM and experimental tests, the difference can be attributed

to many factors as bad symmetrical component reflected in the

zero phase sequence, unbalance in the motor, measurement

errors and poor parameter extraction. However, these errors

can be considered in the definition of suitable thresholds on a

simple platform as Labview with a modest DAQ Target. In Fig.

6 shown the windows of fault detection implemented for this proposed.

Fig. 6 Panel front of Labview for Fault detection

V. CONCLUSIONS

Since a relative large change in the residual set obtained when

an incipient additive fault occurs it is not necessary to use

diagnosis methods to locate the fault, which simplifies the

supervision of the induction motor. Since that the induction

motor model is similar to the C.D. motor model the analysis

allows to assure the existence of parity space and therefore to

obtain the advantages of the fault detection for this system type.

The Park transformed in order to interpret I qs and a simple

algebraic equation is sufficient to develop the mathematical

algorithm of detection system. In particular, the propose

technique, considering V qs equal to RMS value of stator

voltage V s, only uses fourth sensors; three of current and one

of speed. The main disadvantage of this technique applied to

induction motor is that the rotor flux linkages are constant, thus,

it is not possible to locate the particular fault related to each

phase and the synchronous speed is needed for fault detection.

VI. R EFERENCES

[1] M. Pineda-Sanchez, M. Riera-Guasp, J. Roger-

Folch, J.A. Antonino-Daviu, J. Perez-Cruz, R

Puche-Panadero, “Diagnosis of Induction Motor

Faults in Time-Varying Conditions Using the

Polynomial-Phase Transform of the Current,” IEEE

Trans. on Ind. Electron., vol. 58, no. 4, April2011,

pp. 1428- 1439.

[2] C. Bianchini, F. Immovilli, M. Cocconcelli, R.

Rubini, A. Bellini,“Fault Detection of Linear

Bearings in Brushless AC Linear Motors byVibration Analysis,” IEEE Trans. on Ind. Electron.,

vol. 58, no. 5, May 2011, pp. 1684- 1694.

[3] E. G. Strangas, S. Aviyente, S.S.H: Zaidi, “Time –

Frequency Analysis for Efficient Fault Diagnosis

and Failure Prognosis for Interior Permanent-

Magnet AC Motors,”IEEE Trans. on Ind. Electron.,

vol. 55, no. 12, Dec 2008, pp. 4191- 4199.

[4] K. A. Loparo, M. L. Adams, W. Lin, M.F. Abdel-

Magied, N. Afshari, “Fault Detection and Diagnosis


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of Rotating Machinery,” IEEE Trans. on Ind. Appl.,

vol. 47, no. 5, pp. 1005-1014, October 2000.

[5] A.M.S. Mendes and A.J. Cardoso, “Fault-Tolerant

Operating Strategies Applied to Three-Phase

Induction-Motor Drives,” IEEE Trans. on Ind.

Electron., vol. 53, no. 6, Dec 2006, pp. 1807- 1817.

[6] M. A. Cash, T G. Habetler and G. B. Kliman.,

“Insulation Failure Prediction in AC MachinesUsing Line- Neutral Voltages,” IEEE Trans. on Ind.

Appl., vol. 34, no. 6, pp. 1234-1238.

November/December 1998.

[7] J. Klima, “Analytical Investigation of an Induction

Motor Drive Under Inverter Fault Mode

Operations,” IEE Proc. Electr. Power Appl., vol.

150, no. 13, pp. 255-262, May 2003.

[8] Guillermo R. Bossio, Cristian H. De Angelo, Jorge

A. Solsona, Guillermo O. García, “Diagnostico de

Fallas en MI Mediante una Estrategia de Estimación

de Posición,” XIV Congresso Brasileiro de

Automática 2002.

[9] C. W. Chan, Song Hua, and Zhang Hong-Yue,

“Application of Fully Decouple Parity Equation in

Fault Detection and Identification of DC Motos,”

IEEE Trans. on Ind. Electron., vol. 53, no. 4, August

2006, pp. 1277- 1283.

[10] R. Iserman, “Model Based Fault Detection and

Diagnosis Methods,” Annual Reviews in Control of

Elsevier, vol. 29, Issue 1, 2005, Pages 71-85.

[11] R. Iserman, “Supervision, Fault-Detection and

Fault-Diagnosis Methods- an Introduction,” Elsevier

Science, Control Eng. Practice, vol. 5, no. 5, 1977,

pp 639-652, 1977.

[12] R. Krishnan, Electric Motor Drives Modeling,

Analysis and Control. Prentice Hall, 2001.

[13] C.W. Chan,Hua Song, Zhang Hong-Yue,

“Application of Fully Decoupled Parity Equation in

Fault Detection and Identification of DC Motors,”IEEE Trans. on Ind. Electron., vol. 53, no. 4, June

2006, pp. 1277- 1284.

[14] Hofing, T. and Isermann, R., “Fault Detection Based

on Adaptive Parity Equations and Single-Parameter

Tracking,” Elsevier Science, Control Eng Practice,

pp 1361-1369, 1996.


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artículoFault Diagnostic Based on Parity Equations Applied to Induction Motor

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