Modeling of Broken Rotor Bars in a Squirrel-Cage ...

Modeling of Broken Rotor Bars in a Squirrel-Cage Induction Motor Abdurrahman ÜNSAL

Özkan KARA

Dumlupinar University Department of Electrical and Electronics Engineering Kütahya, Turkey [email protected]

Sakarya University Department of Electrical and Electronics Engineering Sakarya, Turkey [email protected]

Abstract—The history of faults of induction motors is nearly the same age as the history of induction motors. In the past, induction motors were used in limited places and the faults were solved by taking various measures such as grounding, using overcurrent protectors, or using voltage-regulators. Nowadays the induction motors are used in a wide area of applications. Therefore the diagnosis and repair of faults are important to prevent costly damage and downtime in commercial and industrial facilities. The main faults of induction motors are broken rotor bars, winding faults, and mechanical faults. The rotor faults can be observed as harmonics in stator current. In this paper broken rotor bars are modeled by using MATLAB/Simulink tool. The results demonstrate that MATLAB/Simulink model can be used for educational purposes. Keywords-electric motor; rotor faults; simulation; MATLAB

I.

INTRODUCTION

Induction motors are commonly used in industrial and commercial applications. Any fault in an induction motor may cause large damage to the motor and thus cause down-time and costly damage to the facility that may be run by the induction motor. The main faults of induction motors can be classified as stator winding faults, rotor faults, and mechanical faults. The majority of stator winding faults are coil shortcircuit and insulations failures. These types of faults cause unbalanced magnetic field, vibration and excessive heating. The major rotor (squirrel cage rotors) faults are cracked or broken rotor, cracked or broken end rings. These types of faults can be observed as harmonics in the stator current. Mechanical faults can be classified as bearing faults, slip of axis, and misalignment faults. The total faults in an induction motor can be categorized as 38% stator faults, 40% bearing faults, 10% rotor faults and 12% other mechanical faults accordingly [1]. The detection faults of induction motors is possible by observing and analyzing the stator current, voltage, speed, torque, heat, and vibration signals. The methods that are frequently used to detect induction motor faults can be summarized as follow [2]- [10]: • Time and frequency domain analysis • Analysis of electromagnetic torque and flux • Analysis of heat and radio frequency emission

• • •

Analysis of motor current Analysis of noise and vibration Analysis of torque and speed harmonic

Among these methods, motor current signature analysis (MCSA) method is the most commonly used method for the detection of rotor faults. The MCSA method is mainly based on the frequency spectrum analysis of the stator current of an induction motor. The broken rotor bars, the most common type of rotor faults, are reflected in the stator current as sideband current harmonics. The frequency of the side-band harmonics in the stator current due to the broken rotor bars can be written as

f b = (1 ± 2ks ) f1 , k= 1, 2, 3

(1)

where “fb” denotes side-band harmonic frequency, ‘s’ denotes the slip of the motor, and ‘f1’ denotes the supply frequency (50 Hz) or the fundamental frequency component. Since the slip of the motor varies with the change in the load, the side-band harmonic frequencies also change accordingly. Under the light loading conditions, the magnitudes of the side-band harmonics is quite low, hence it may be difficult to detect. The frequencies of the side-band harmonic components will be very close to the fundamental frequency component (50 Hz). When the motor load increases, magnitude and the frequency of the side-band harmonic component also increases. Therefore it will be very easy to detect the rotor fault by observing the stator current based on the magnitude and sidefrequency of the band harmonic components. Since the induction motors are the most commonly used electrical machines and any fault developing/occurring in an induction motor may cause costly damage to the facility, it is important to have a good educational curriculum for the fault of the induction motors in electrical engineering programs. A MATLAB/Simulink based educational tool is developed in [11] for the no-load and blocked-rotor tests of induction motors. A similar tool to be used for induction motor tests in the undergraduate electrical machinery courses by using MATLAB/Simulink is given in [12]. An energy conservation and efficiency tool for induction machine mainly for electrical machine courses is described in [13]. Since the detection of

the faults and the remedial measures for the induction motors are very important to prevent the costly damage a MATLAB/Simulink based educational curriculum is developed in [14] for the teaching of the basics of induction motors and their maintenance. In this paper, broken rotor bars of a squirrel-cage induction motor are modeled by using MATLAB/Simulink based on the frequency spectrum of the stator current. It is aimed to use this model for the teaching of the rotor faults of induction motors. The results of the developed model are compared to the experimental results for the verification purposes. The presentation of the paper is as follows: The development of the MATLAB/Simulink model will be discussed first. Then the simulation results are presented. Finally, the experimental results are presented and compared with the simulations results. II.

MATHEMATICAL MODEL OF THE INDUCTION MOTOR

A. Q-Axis Model Equations L2 dI qs L dϕ qr Rs I qs + ( Ls − m ) = Vqs − m Lr dt Lr dt

(16)

Lr dϕ qr L P + ϕ qr = I qs Lm + r (ω )ϕ dr Rr dt Rr 2

(17)

B. D-Axis Model Equations L dϕ dr L2 dI Rs I ds + ( Ls − m ) ds = Vds − m Lr dt Lr dt

(18)

Lr dϕ dr L P + ϕ dr = I ds Lm − r (ω )ϕ qr Rr dt Rr 2

(19)

C. Load Equation Te =

3 P Lm (ϕ dr I qs − ϕ qr I ds ) 2 2 Lr

D. Slip Equations

All rotor and stator equations of the modeled induction motor are calculated according to two-axis reference frame (dq frame). The “dq” model of an induction motor can be written as follows [3, 4]; dϕ qs dt

= Vqs − Rs I qs − ωϕ ds

dϕ qr dt

= − Rs I qr − (ω − ωr )ϕ dr

dϕ dr = − Rs I dr + (ω − ωr )ϕ qr dt

(3)

(7)

ϕ qr = Lr I qr + Lm I qs

(8)

ϕ dr = Lr I dr + Lm I ds

(9)

ϕ qs = Ls I qs + Lm I qr

(10)

ϕ ds = Ls I ds + Lm I dr

(11)

3 P Te = (ϕ ds I qs − ϕ qs I ds ) 2 2

a0 = Ls Lr − L2m ,

L a1 = r a0

,

P 2

(12) (13) (14) (15)

L a2 = m a0

ωe − ω ωe

(22)

120 f 0 P

(23)

628 rad , s = f1 = 50 Hz , ωe = s P

628 − ω P 628 P

(24)

(5)

I ds = ϕ ds a1 − ϕ dr a2

ωr = ω

s=

(4)

(6)

Lr = Llr + Lm

(21)

ns =

I qs = ϕ qs a1 − ϕ qr a 2

Ls = Lls + Lm

2πns 60

ωe =

(2)

dϕ ds = Vds − Rs I ds − ωϕ qs dt

(20)

Figure 1.

D-axis of the dq reference of the induction motor

Figure 2.

Q-axis of the dq reference of the induction motor

The definitions of the notations given in (2) - (24) are given in Table I. The "dq" model of the induction motor is developed by using equations (2)-(24). The d-axis model is shown in Fig. 1 while the q-axis model is shown in Fig. 2.

TABLE I.

THE PARAMETERS OF INDUCTION MOTOR

Notation

Definition

Rs , Rr

Stator and rotor resistances,

Ω

Lls

Stator leakage inductance, Henry

Llr

Rotor leakage inductance, Henry

Lm

Mutual inductance, Henry

Ls , Lr

Stator and rotor inductances, Henry

Vqs , Vqr

q axis stator and rotor voltages, volt

Iqs , Iqr

q axis stator and rotor currents, ampere

Vds , Vdr

d axis stator and rotor voltages, volt

Ids , Idr

d axis stator and rotor currents, ampere

ϕ qs , ϕ qr ϕ ds , ϕ dr

Stator and rotor q axis fluxes, Weber

ω

Rotor angular speed, radian/second

P

Pair pole number

ωr

Electrical angular speed, radian/second

T

Load, Newton-meter

Te

Electromagnetic load, Nm

J

Rotor and load inertia, kg-m2

f0

Main frequency (50 Hz), Hertz

ns

Nominal cycle per minute

ωe

Nominal angular speed, radian/second

s

Slip

b

Number of broken rotor bars

Stator and rotor d axis fluxes, Weber

III.

THE SIMULINK MODEL

The Simulink model is developed in such a way that the user can set parameters and the loading condition of the motor. The loading condition is set as a percentage of the full-load of the motor including 25%, 50%, 75%, and 100%. In addition, the number of broken rotor bars is also set by the user. The nameplate parameters of three-phase induction motor used in the model are given in Table II. TABLE II.

bars along with the loading conditions of the motor by using this block.

Figure 3.

Figure 4.

Function block parameter of induction motor

Input and output parameters of the induction motor

The Simulink block shown in Fig. 4 is the input-output parameter block of the model. Some of the details of this block are given Fig. 5 - Fig. 7. This block uses the parameters set by the user along with the nameplate parameters of the motor which are given in Table II. The shaft torque, speed, and stator current of the modeled motor is then calculated. The torque and speed of the motor is used for informational purposes while the stator current signal is used to perform MCSA for detecting broken rotor bars by using Fast Fourier Transform (FFT) analysis. The effect of the broken rotor bars is reflected into the stator current as side-band harmonics.

INDUCTION MOTOR NAMEPLATE VALUES

Input voltage and frequency

380 V, 50 Hz

Power and number of poles

5.5 kW, 4

The functional block which is used to set the parameters of the induction motor in the model is shown in Fig. 3. The user sets the motor parameters such as stator resistance, rotor resistance, inductance of stator and rotor, mutual inductance, inertia, the number of poles, and the number of broken rotor

Figure 5.

Details of the model

The magnitude and frequency of the side-band current harmonics appearing in the stator current are dependent on motor parameters including slip (s), number of broken rotor bars (b), and loading condition (T). Fig. 5 depicts the details of the induction motor block which is shown in Fig. 4

the side-band current harmonics also increases accordingly but, the frequency does not change. This can be seen by comparing Fig. 9 (a) and Fig. 9 (b).

Fig. 5 indicates the model-based calculation of side-band harmonics related to the broken rotor bars. The main block which calculates the speed, slip, and stator current of the motor is shown with details in Fig. 6.

Figure 7.

Figure 6.

Details of the parameter computation block

The detailed model-based calculation of the side-band harmonics including magnitude and frequency is given in Fig. 7. The developed induction motor model is tested for four different loading conditions: The loading conditions are set as 25%, 50%, 75%, and 100% of the full load of the modeled motor. The fault on the rotor is implemented as one broken rotor bar and four broken rotor bars. IV.

Harmonic calculation block

Figure 8.

Stator current under no-load condition

SIMULATION RESULTS

The developed model was tested under various conditions. The results are shown in Fig. 8 - Fig. 12. The first test was implemented under "no-load" condition. The rotor was initially tested without broken bars, then with one broken bar, and then with four broken bars. Since under no-load conditions the slip of the motor is too low and the current drawn from the supply is quite low, the spectrum of the current does not reflect the broken rotor bars and therefore the results of this test with and without broken bars is almost the same. The spectrum of the stator current with no-load is given in Fig. 8. It can be seen that the side-band frequencies are not apparent. Fig. 9 (a) shows the stator current with one broken rotor bar under 25% loading condition. Since the motor is lightly loaded, the slip is likely to be very small and therefore the frequency and magnitude of the side-band harmonics will also be very low. The stator current with four broken rotor bars under 25% loading condition is shown in Fig. 9 (b). The side-band frequencies appear in the stator current. When the number of broken rotor bars increases from one to four, the magnitude of

(a) Figure 9.

(b)

Stator current with one (a) and four (b) broken rotor bars under 25% loading condition

Fig. 10 (a) shows the simulation results with one broken rotor bar under 50% loading condition. The side-band frequencies can be clearly seen. Fig. 10 (b) shows the stator current with four broken rotor bars under the same loading condition. It can be seen that when the number of broken rotor bar increases from one to four the magnitude of the side-band frequencies increases.

(a) Figure 10.

(b)

Stator current with one (a) and four (b) broken rotor bars under 50% load condition

faults and loading conditions. The motor is loaded with a beltpulley system. The loading conditions were observed from the stator current. Rotor fault were created by drilling the bars of two identical rotors: One broken rotor bar was created by drilling one rotor bar and four broken rotor bars were created by drilling four rotor bars. Fig. 14 shows two identical rotors with one broken bar (a) and four broken bars (b). (a) Figure 11.

(b)


Fig. 11 (a) shows the simulation results with one broken rotor bar under 75% loading condition while Fig. 11 (b) shows the simulation results with four broken rotor bars under the same loading condition. The frequency and magnitude of the side-band harmonics can be clearly seen. The simulation results with four broken rotor bars reflect the broken rotor bars much clearer.

(a)

(b) Figure 14.

The broken rotor bars

Fig. 12 (a) and (b) show the simulation results with one broken rotor bar and with four broken rotor bars respectively, both under 100% loading conditions. The magnitude and frequency of the side-band harmonics became more apparent as the load of the modeled motor increases.

(a) Figure 15.

(a) Figure 12.

(b)


(b)


(a)

(b)

Figure 16. Stator current with one (a) and four (b) broken rotor bars under 50% load condition

Figure 13.

V.

Experimental set-up

EXPERIMENTAL VERIFICATION OF THE MODEL

Fig. 13 shows the experimental set-up used in this study. In order to verify the performance of the developed model an induction motor with the same nameplate parameters which was used in the simulation was tested under the same rotor

The stator currents of the motor under the previously mentioned loading conditions are transferred to a computer by a data acquisition card (DataQ). The spectrum (FFT) of the stator current is calculated by using the software tool provided by the data acquisition card. The results of the experimental tests under the same loading and fault conditions in simulation are given in Fig. 15 - Fig. 18. The experimental test results are in agreement with the simulation results except that the experimental currents contain noise which may be originated

from the current measurement system and electromagnetic noise which may come from test motor itself. The spectrum of the noise may be overlapped with the spectrum of the sideband harmonics related to the broken rotor bars and therefore lead to fault detection errors. But this situation is not a problem for this study. The best experimental and simulated matched results are gained under full-load condition. This can be seen by comparing Fig. 18 with Fig. 12.

(a) Figure 17.

(b)


REFERENCES [1]

M.L.Sin, W.L.Soong & N.Ertugrul, "Induction machine on-line condition monitoring and fault diagnosis – a survey", AUPEC2003 Australasian Universities Power Engineering Conference, New Zealand, 2003. [2] M.Neelam & D.Ratna, "Motor Current Signature Analysis and its Applications in Induction Motor Fault Diagnosis", International Journal of Systems Applications, Engineering & Development, vol. 2, issue 1, 2007. [3] S. Nandi, H.A. Toliyat, & X. Li, "Condition Monitoring and Fault Diagnosis of Electrical Motors - A Review", IEEE Transactions On Energy Conversion, Vol. 20, No. 4, December 2005. [4] D. Basak, A. Tiwari, & S. P. Das, "Fault diagnosis and condition monitoring of electrical machines" - A Review, ICIT 2006, IEEE International Conference on Industrial Technology, 2006. [5] P.J. Tavner, "Review of Condition Monitoring of Rotating Electrical Machines", IEEE Electr. Power Appl., 2008, Vol. 2, No. 4, pp. 215–247. [6] N. Mehala & R. Dahiya, "Condition Monitoring Methods, Failure Identification and Analysis for Induction Machines", International Journal of Circuits Systems and Signal Processing, Issue 1, Volume 3, 2009. [7] S. H. Kia, H. Henao, & G. A. Capolino, "Digital Signal Processing for Induction Machines Diagnosis -A Review", The 33rd Annual Conference of the IEEE Industrial Electronics Society (IECON), Nov. 58, 2007, Taipei, Taiwan. [8] A.Bellini, F. Filippetti, C.Tassoni, & G. Capolino, "Advances in Diagnostic Techniques for Induction Machines", IEEE Transactions on Industrial Electronics, Vol. 55, No.12, December 2008. [9] M. H. Benbouzid, "A Review of Induction Motors Signature Analysis as a Medium for Faults Detection", IEEE Transactions on Industrial Electronics, Vol. 47, No. 5, October 2000. [10] D. Basak, A. Tiwari, & S. P. Das, "Fault diagnosis and condition monitoring of electrical machines" - A Review, ICIT 2006, IEEE International Conference on Industrial Technology, 2006. [11] A.Bentounsi, H.Djeghloud, H.Benalla, T.Birem, Computer-Aided Teaching Using MATLAB/Simulink for Enhancing an IM Course With Laboratory Tests, IEEE TRANSACTIONS ON EDUCATION, VOL. 54, NO. 3, AUGUST 2011.

(a) Figure 18.

(b)


VI.

CONCLUSIONS

In this paper, the effects of the broken rotor bars of a squirrel-cage induction motor on the stator current as sideband harmonics are modeled in MATLAB/Simulink. The goal of this study was to use this model for educational purposes in the electrical machinery courses. The model was tested under different loading conditions (25%, 50%, 75%, 100%) with one and four broken rotor bars. An induction motor induction motor with the same nameplate values which were used in the model was tested under the same loading conditions and the same rotor faults (one broken rotor bar and four broken rotor bars). The experimental results are in agreement with those in the literature. The experimental results are also in agreement with the simulation results. Therefore this developed model of broken rotor bars of is squirrel-cage induction motor can be used for educational purposes at undergraduate and graduate level electrical machinery courses.

[12] S.Ayasun, & C.O. Nwankpa, Induction Motor Tests Using MATLAB/Simulink and Their Integration Into Undergraduate Electric Machinery Courses, IEEE TRANSACTIONS ON EDUCATION, VOL. 48, NO. 1, FEBRUARY 2005. [13] N.Kumar, T.R.Chelliah, S. P. Srivastava, Energy Conservation Study on Induction Motors Using MATLAB/Simulink for Enhancing Electric Machinery Courses, IEEE International Conference on Teaching, Assessment, and Learning for Engineering (TALE) 2012, Hong Kong. [14] M.P.Sanches, V.C.Alarcon, M.R.Guasp R.P. Panadero & J.P.Llinares, Enhanced Simulink Induction Motor Model for Education and Maintenance Training, The 2nd International Conference on Education, Training and Informatics: ICETI 2011, Orlando, Florida USA.