Proposed Fault Diagnostics of a Broken Rotor Bar ...

Accepted Manuscript Title: Proposed Fault Diagnostics of a Broken Rotor Bar Induction Motor Fed From PWM Inverter Author: Faeka M.H. Khater Mohamed I. Abu El-Sebah Mohamed Osama Khaled S. Sakkoury PII: DOI: Reference:

S2314-7172(16)30051-4 http://dx.doi.org/doi:10.1016/j.jesit.2016.07.004 JESIT 106

To appear in: Received date: Revised date: Accepted date:

27-6-2016 10-7-2016 25-7-2016

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Proposed Fault Diagnostics of a Broken Rotor Bar Induction Motor Fed From PWM Inverter Faeka M.H. Khater*, Mohamed I. Abu EL- Sebah*†, Mohamed OSAMA**, and Khaled S. Sakkoury* * Electronics Research Institute - Dokki, Cairo, Egypt †Arab academy for science and technology and maritime transport, Faculty of Engineering ** High Institute of Engineering – Six October City, Egypt Abstract: This paper presents a fault diagnostics technique for a three-phase squirrel cage induction motor. The method is developed using a simplified model affected by bar resistance variation. Based on 3-phase time domain model, the rotor broken bar with different conditions has been simulated to investigate the resulting torque speed characteristic in each condition. The developed fault diagnostics system is capable of identifying the type of the broken- bar faults in the squirrel cage induction machines. Keywords: fault diagnostics, Squirrel Cage Induction Motor, induction motor model, rotor broken bar, rotor broken bar model. I. INTRODUCTION A great attention has been paid for induction motor fault diagnostics especially for the broken bar fault. This fault type constitutes between 5 to 10% of the total cage rotor - induction motor failures [1].Many methods to detect the faults related to the rotor broken bars have been adopted [2-10]. Motor current signature analysis (MCSA) based on the 50/60-Hz sidebands has become a common test in industry for monitoring the condition of the induction motor rotor cage. However, many cases of unnecessary motor inspection or outage due to false alarms produced by rotor axial duct interference have been reported [2]. Fault diagnostics of drive systems have to cover the converter and the motor. A previous work has Proposed a rule -based fuzzy Logic system for fault cases of inverter fed induction machine focusing on the power switches of the inverter [11] . The developed system is capable of identifying the type and location of the fault. The authors in [3,4] used the MCSA and mathematical morphology to detect broken bars on induction motors under different mechanical load condition. The proposed algorithm was tested then implemented in an FPGA to be used in real- time applications. Finite element method was used in [5] to study the influences of the broken bar fault on the electromagnetic characteristics of the cage rotor induction motor. To avoid eventual wrong diagnostics of the conventional MCSA in certain industrial situations, transient-based fault diagnosis in induction motors has been used by the authors in [6].Rotor broken bars diagnosis based on wavelet coefficients of stator current was studied in [7, 8]. Another modification to the MCSA method was introduced in [9] where modulation signal bispectrum (MSB) analysis is applied to motor currents from different broken bar cases and a new MSB based sideband estimator is introduced. The authors in [10] proposed a method based on Principal Component Analysis

(PCA) and was applied to the stator’s three phase start-up current. The fault detection is easier in the start-up transient because of the increased current in the rotor circuit, which amplifies the effects of the fault in the stator’s current independently of the motor’s load. However, most of these methods have suffered from some drawbacks such as it is difficult to determine the fault type at no load and the symmetrical fault will appear as no fault. Also, at light load conditions, it is quite difficult to distinguish between healthy and faulty rotors because the characteristics of broken rotor bar fault frequencies are very close to fundamental component and their amplitude are small in comparison. In order to overcome the above problems, the rotor resistance detection (RRD) method is proposed for the broken rotor bar fault detection purpose in the induction machines. The proposed technique applies the RRD to the torque- speed characteristics during the motor starting. The torque speed curve is used to detect resistance from the maximum torque point, which overshadows the characteristic differences between a healthy motor and a faulty motor with broken rotor bars. Induction motor model can be derived in two different concepts, the first model is derived in a 3-phase (abc) axis system, while the second model is derived in 2-phase (d-q) axis. The simulation utilized an inverter to drive the motor to study the broken bars effect with reduced stator currents. II. INDUCTION MOTOR MODEL IN ABC AXES The following equations represent the induction motor in the abc axis. The model covers both the electrical and mechanical parts of the motor. Starting with the voltage equation (1) Where (2) (3) (4) Where (5) Leads to derive the electrical side equations in the form ( ) While Mechanical Part driven from the torque equation

(6)

(7)

in the d-q frame which suits implementation of control equations Fig. 1.

Since Electric Quantities

(8)

Rotor Frame

 

Where Resistance matrix [Ω]:

 Rs 0  0 R 0 0   0

0 Rs 0 0 0 0

0 0 Rs 0 0 0

0 0 0 Rra 0 0

0 0 0 0 Rrb 0

0 0  0  0 0  Rrc 

Arbitrary Frame Stator Frame

Fig. 1 Stator and rotor frame. The stator voltage can be written in the following vector form: Where

d d (   )  r ,   a , dt dt

d   a  r dt

Referred to arbitrary reference frame

vsse j (  )  Rsisse j (  )  dtd [ Lmirse j (  )  Lsisse j (  ) ] vs  Rsis  js [ Lmir  Lsis ]  [ Lm

Inductance sub matrices[H]:   Ls  L Lss   m 2  Lm    2 



 Lm   Lr 2   L L  m  , Lrr   m  2 2   Lm  Ls    2  

Lm 2



Ls 

Lm 2



Lm 2 Lr



Lm 2

Lm  2  Lm   2   Lr   

Cos(   ) Cos(   )   Cos( )   Lsr  Lm .Cos(   ) Cos( ) Cos(   ) Cos(   ) Cos(   ) Cos( )  Sin(   ) Sin(   )   Sin( )   dLsr   Lm . Sin(   ) Sin( ) Sin(   )  Sin(   ) Sin(   ) Sin( ) 

Where  is the phase angle

Inductance matrix L:

dLsr  Zeros dLsr    ' d  dLsr Zeros 0 0 0 Sin( ) Sin(   ) Sin(   )     0 0 0 Sin (    ) Sin( ) Sin(   )   dLsr 0 0 0 Sin(   ) Sin(   ) Sin( )    Lm .  Sin(   ) Sin(   ) 0 0 0 d  Sin( )   Sin(   )  Sin( ) Sin(   ) 0 0 0   Sin( ) 0 0 0  Sin(   ) Sin(   ) 

III. INDUCTION MOTOR MODEL IN D-Q AXES The model of the induction motor in the arbitrary rotating reference frame will be presented to deduce the model in the - frame which is required to be used to simulate the induction motor

d dt s

i]

(10)

The above equation can be written in the following form:

vs  Rsis  ja s  dtd s

(11)

Where

ds  Ls ids  Lm idr qs  Lsiqs  Lmiqr

Decomposing the stator voltage into two components labeled as d,q

vsd  Rs isd  a sq  dtd sd

(12)

vsq  Rsisq  asd  dtd sq

(13)

The rotor voltage can be written in the following vector form as follows: 

 dLss dLsr  L  ' dLsr dLrr

i  Ls

d dt r

(9)



v r  Rr i r 

d  r dt

Referred to the arbitrary reference frame

vrr e J ( )  Rr irr e j ( )  dtd [ Lmisr e j ( )  Lr irr e j ( ) ]

(14)

vrs  Rr irs  j (a  r )[ Lmiss  Lr irs ]  [ Lm dtd iss  Lr dtd irs ] (15) The above equation can be written in the following form:

dr  Lr idr  Lmids qdr  Lr iqr  Lmiqs

(16)

Decomposing the rotor voltage into two components labeled as d,q

vrd  Rr ird  (a  r )rq  dtd rd

(17)

vrq  Rr irq  (a  r )rd  dtd rq

(18)

The motor in the d-q axis can be represented in a matrix form equations as follows

 a Ls pLm  a Lm  isd  vsd   Rs  pLs v    L  i  Rs  pLs a Lm pLm a s  sq       sq  vrd   pLm  (a  r ) Lm Rrd  pLr  (a  r ) Lr  ird        pLm (a  r ) Lr Rrq  pLr  irq  vrq  (a  r ) Lm

(23)

⁄

Where Nb: total number of rotor bars rr: rotor resistance rb: single bar resistance

(19) By simplifying the above equation we obtain the motor model in the arbitrary rotating reference frame i sd  i sd  i  i  1 1 sq sq p.   .A     2 ird  Ls Lr  L m ird  Ls Lr  L2 m     irq  irq    R s Lr    L L  ( a   r ) L2 m A a s r  R s Lm   a Lm Ls  ( a   r ) Lm Ls

 Lr  0 .   Lm   0

0

 Lm

Lr

0

0

Ls

 Lm

0

0  v sd   Lm  v sq    0  0    Ls   0 

 a Lm Lr  ( a   r ) Lm Lr 

 a Ls Lr  ( a   r ) L2 m

R r Lm

 R s Lr

  a Lm Lr  ( a   r ) Lm Lr

  a Lm Ls  ( a   r ) Lm Ls

 Rr Ls

R s Lm

 a L2 m  ( a   r ) L2 r

 R r Lm    a L2 m  ( a   r ) L2 r    Rr Ls 

(20) 3P (21) T Lm (ird .isq  irq .isd ) 2 d (22) Te  J  B.  TL dt The rotor reference frame is obtained by putting  a   r The model was tested on a healthy motor with the parameters given in section VII. The simulation was run at a frequency of 40 Hz. Fig. 2 shows the torque-speed curve of the motor under study. The synchronous speed is 251.3 rad/sec and the maximum torque occurs at a speed of 230 rad/sec.

Fig.3 The induction motor torque speed characteristic under balanced rotor resistance variation

Broken bars means one or more of the parallel resistances will be removed which leads to the increase in the rotor resistance by Δr. The number of healthy bar becomes which leads to a new phase resistance

Torque speed at no load 60

50

for this phase,

(24)

⁄

Where Δr: Change of rotor Resistance nbb: number of broken bars

40 torque in Nm

⁄

30

This change of rotor resistance can be calculated as follows 20

⁄

10

⁄ ⁄

0

0

50

100

150 200 Speed in rad/sec

250

300

350

Fig. 2 Motor model test.

IV. PROPOSED ROTOR BROKEN BAR FAULT DETECTION METHOD

Figure 3 shows the effect of increasing the rotor resistance from R1(rated value) to R2up to R6 on the maximum torque peak position. It is clear that the maximum torque point is shifted to the left as the rotor resistance increases. Knowing that the broken bars increases the rotor resistance, as the number of parallel bars composing the rotor resistance per phase decreases. This leads to moving the speed of the maximum torque to the left or in other words, the slip increases. The variation of the resistance detected from the breakdown torque shift and hence the number of bars can be determined. By neglecting the end ring resistance, the rotor resistance per phase is the result of a number of parallel bars and is calculated as follows.

(

(25)

⁄ ⁄

(

⁄

(

)

⁄ ⁄

)

)

(26) (27) (28)

By adding this change to the rotor resistance, the stator current, torque and other machine variables with different number of broken bars are obtained. V. SIMULATION AND SIMULATION RESULTS The simulation results for induction motor with rotor broken bars are shown in figures 4 to 10 showing seven different cases for the fault under study. The figures show the torque- speed characteristic curves for one, two ….up to seven broken bars. The motor in each case runs at no load with 40 Hz driving frequency. It is clear that the disturbance in the curves increases as the number of broken bars increase when comparing it with the curve of Fig. 2 of a healthy motor. Also with more broken bars, the maximum torque - speed decreases and moves to the left of the graph indicating higher rotor resistance.



50 50

40

torque in Nm

torque in Nm

40

30

30

20

20

10

10

0

0

50

100


250

300

0

350

Fig. 4:Torque speed characteristic under one broken bar

0

50

100

50

50

40

40

30

20

10

10

100


250

300

350

Fig. 5:Torque speed characteristic under two broken bar

0

0

50

100


250

300

350

Fig. 9:Torque speed characteristic under six broken bar

Torque speed at no load


60

60

50

50

40

40

torque in Nm

torque in Nm

350

30

20

50

300


torque in Nm

torque in Nm


0

250

Fig. 8:Torque speed characteristic under five broken bar

60

0


30

20

30

20

10

10 0

0

50

100


250

300

350

Fig. 6:Torque speed characteristic under three broken

0

0

50

100


250

300

350

Fig. 10:Torque speed characteristic under seven broken bar


50

torque in Nm

40

30

20

10

0

0

50

100


250

300

350

Fig. 7:Torque speed characteristic under four broken bar

VI. DETECTING THE FAULTY MOTOR The induction motor under investigation will be run at no load with sensors coupled to its rotor to measure torque and rotational speed (Rotary Torque Sensor). Because of high price of the torque sensor, torque can be estimated using current and voltage sensors. The resulting curve will show the point at which maximum torque occurs. The actual rotor resistance will be calculated according to the following equation. From speed torque curve by differentiating the torque equation with respect to slip results (29) √ The value of Δr is calculated from Δr = (30)

(31) According to the value of Δr, the number of broken bars is estimated according to table 1. The table is constructed with 40 Hz as the driving frequency. Then ωSyn. = 251.3274rad/sec ⁄ √

For a healthy motor, Rated Case

Speed (at maximum torque) rad/sec 230 – 228 227 – 226 225 - 221 220 – 218 217 – 212 211 – 200 199 – 175 174 - 155

Smax Approx.

Δr Ohm

No. of broken bars by estimation 0.0808 0.9069 1.7071 3.1225 3.6500 4.6993 5.7688 7.0075

Decision (No. of broken bars) Healthy 1 2 3 4 5 6 7

0.0849 0.0215 1 0.0948 0.2691 2 0.1048 0.5596 3 0.1286 1.2569 4 0.1406 1.6055 5 0.1724 2.5353 6 0.2241 4.0460 7 0.3435 7.5325 8 Table 1: The comparison between different number of broken rotor bars An Effective Model of the Induction Motor provides the eigen values loci of the machine at full range of rotor Speed (with inverter). The model enables to find the eigen values as a function the machine parameters at specific speed and indicated that the increase in machine resistance leads to reduction in the damping [12]. This study confirms that broken bar faults can leads to the same result as increasing the machine resistance.

VII. CONCLUSION A fault diagnostics system has been proposed for a three phase squirrel cage induction motor. The system has been developed in simplified manner load independent. Based on a time domain simulation model, the induction motor different fault conditions have been simulated.The resulting torque - speed characteristic is providing the guide for the proposed detection technique. The proposed fault diagnostics system has resulted in a logged data that provides the fault condition according to the data base status. The developed system is capable of identifying the number of rotor broken bars. In addition, it is adequate for use in an on-line fault diagnostics system in induction motor drive. VIII. MACHINE PARAMETERS Rsa=3.85 Ohm Rsb=3.85 Ohm Rsc=3.85 Ohm Rra=2.50 Ohm Rrb=2.50 Ohm Rrc=2.50 Ohm Lls=0.0576 H Llr=0.0576 H Lm=0.28779 H P=4 J=0.03 kg.m2 B=0.003 kg.m2Sec Number of rotor bars: 28 IX. REFERENCES 1. S. Nandi, H. Toliyat and X. Li, “Condition Monitoring and Fault Diagnosis of Electrical Motors-A Review,” IEEE Trans. Energy .Conversion, Vol. 20, No. 4, Dec 2005, pp. 719-729.

2. C. Yang, T. Kang,S. Lee, J.Yoo, A. Bellini,L.Zarri, and F.Filippetti, "Screening of false induction motor fault alarms produced by axial air ducts based on the space-harmonic-induced current components." IEEE Trans. on Industrial Electronics, Vol. 62, N0. 3, Mar 2015, pp 1803-1813. 3. J. Rangel-Magdaleno, J. Ramirez-Cortes and H. Peregrina-Barreto “Broken Bars Detection on Induction Motor Using MCSA and Mathematical Morphology: An Experimental Study”, 2013 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), Minneapolis, USA, 6-9 May 2013, pp. 825 829 4. J. Rangel-Magdaleno, H.Peregrina-Barreto, J. Ramirez-Cortes, P. Gomez-Gil, and R. Morales-Caporal, “FPGA-Based Broken Bars Detection on Induction Motors Under Different Load Using Motor Current Signature Analysis and Mathematical Morphology”, IEEE Trans.on Instrumentationand Measurement, Vol. 63, No. 5, May 2014, pp 1032 – 1040. 5. K.N. Gyftakis, D.V. Spyropoulos, J.C. Kappatou, and E.D. Mitronikas, “A Novel Approach for Broken Bar Fault Diagnosis in Induction Motors Through Torque Monitoring”, IEEE Trans.on Energy Conversion, VOL. 28, NO. 2, JUNE 2013, pp 267- 277. 6. J. Pons-Llinares, J.Antonino-Daviu, M. Riera-Guasp, S. Lee, T. Kang, C. Yang,“Advanced induction motor rotor fault diagnosis via continuous and discrete time–frequency tools”, IEEE Trans. on Industrial Electronics, Vol. 62, N0. 3, Mar 2015, pp 1791-1802. 7. B.M. Ebrahimi, J. Faiz, S. Lotfi-Fard, P. Pillay,” Novel indices for broken rotor bars fault diagnosis in induction motors using wavelet transform”, Mechanical Systems and Signal Processing. Vol. 30, Jul. 2012, pp 131-145. 8. Keskes H, Braham A, Lachiri Z. Broken rotor bar diagnosis in induction machines through stationary wavelet packet transform and multiclass wavelet SVM. Electric Power Systems Research. 2013 Apr 30;97:151-7. 9. F. Gu, T. Wang, A. Alwodai, X. Tian, Y. Shao and A.D. Ball,” A new method of accurate broken rotor bar diagnosis based on modulation signal bispectrum analysis of motor current signals”, Mechanical Systems and Signal Processing, Vol. 50, Jan. 2015, pp 400-413. 10. G. Georgoulas, M.O. Mustafa, I.P. Tsoumas, J.A. Antonino-Daviu, V. Climente-Alarcon, C.D. Stylios, G. Nikolakopoulos,“Principal Component Analysis of the start-up transient and Hidden Markov Modeling for broken rotor bar fault diagnosis in asynchronous machines. Expert Systems with Applications. Vol. 40, N0. 17, Dec. 1, 2013; pp 7024-7033.

11. A. Faeka Khater.”Modelling of Induction Motor at Constant Speed “, Journal of Engineering and Applied Science, Vo1.39 no.2 1992, pp .381-390. 12. Faeka Khater, Mohamed Abd El-Sebah and Mohamed Osama, “Fault Diagnostics in an Inverter Feeding an Induction Motor” , Proc of the International Conference on Electrical Engineering , July 6-10,2008,okinawa, Japan.