
Research Article


Broken Bars Detection in Squirrel Cage Induction Motors Using Wavelet Theory 

M.R. Askari



ABSTRACT

Induction motors, especially squirrel cage motors, have an important role in industry. Their rotor or stator may be failed under stresses depending on their application and sometimes an unexpected motor failure in a manufacture production process may result in unexpected and unforeseen tripping. So, if the failure can be detected during its operation, there are some methods to prevent failure spread and also manufacture trip. This study aimed to model and simulate the squirrel cage induction motor at any operation condition such as healthy condition and broken bars failures in side of rotor, in order to achieve an algorithm for failure detection. So, in this study a new method base on Wavelet theory is used for failure detection. Finally, simulation and experimental results are compared. The results show that using wavelet transform can effectively be used to diagnose the broken bars in the motor.







INTRODUCTION
Since, induction motors present numerous advantages due to their robustness
and their power to weight ratio, they are widely used in the industry. Therefore,
there is a considerable demand to reduce maintenance costs and prevent unscheduled
downtimes for electrical drive systems, especially ac induction machine. In
the past two decades, there have been many investigations on condition monitoring
and fault diagnostics in electric machines, especially squirrelcage induction
motors (Haji and Toliyat, 2001; Kliman
et al., 1996; Kohler et al., 1992;
Tallam et al., 2003).
Sudden machine failure is very damaging or catastrophic in applications such
as large industrial systems or central station power plant auxiliaries in which
the electric machine is the prime mover. These machine failures reduce productivity
in industrial and power systems. Maintenance schedules can proactively be implemented
to reduce or prevent these failures although the probability of a sudden machine
failure cannot be entirely ruled out. On the other hand, increasing the frequency
of scheduled maintenance increases the cost and decreases the productivity of
a system. Accordingly, an online fault diagnostic system becomes a valuable
tool to increase the system efficiency and reliability (Tallam
et al., 2003; Bellini et al., 2001;
Elkasabgy et al., 1992).
Numerous diagnostic techniques for induction motors have been reported in the
literature to diagnose electric machine faults, such as stator winding interturn
shorts, broken rotor bars, broken endring connectors and bearing faults. These
diagnostic techniques include computation of the negative sequence components
of motor terminal quantities (Kliman et al., 1996;
Kohler et al., 1992; Tallam
et al., 2003) detection of the frequency spectrum sideband components
(Bellini et al., 2001; Elkasabgy
et al., 1992), motor parameter estimation methods (Vas,
1993; Said et al., 2000) Artificial Intelligence
(AI) based statistical machine learning approach (Yeh et
al., 2004; Povinelli et al., 2002), artificial
neural networks (Filippetti et al., 1998; Murray
and Penman, 1997; Bernieri et al., 1996)
as well as the recently proposed motor magnetic field pendulous oscillation
phenomenon (Mirafzal and Demerdash, 2003,
2005, 2006).
Wavelet analysis was introduced to overcome the shortcomings of Fourier analysis.
In Fourier analysis the basis functions are complex exponentials producing the
same results for a particular waveform being analyzed. However in wavelet analysis
the basis function could be any permissible wavelet and the results produced
are unique to the selected wavelet. Some wavelets are more efficient at encoding,
denoising, compressing, decomposing and reconstructing signals than others.
It is therefore desirable to select a wavelet that produces the best results
for the signal being analyzed (Halbaoui et al., 2009;
Lasaad et al., 2007; Sarhan
and Issa, 2006).
In this study, discrete wavelet transform has been used for detecting the broken bars in the induction motors.
Wavelet theory application in signal analysis: The wavelet expression
is applied to a family of functions, produced from translation and dilation
of a function, called mother wavelet (Chik et al.,
2009; SanchezLopez et al., 2003). Like the
Fourier analysis, Wavelet analysis also extends the functions according to a
set of basic functions. Against the Fourier analysis, the Wavelet analysis doesn't
extend the functions as the trigonometric or polynomial functions, but according
to the wavelets that themselves have created by delaying and transmission of
a mother wavelet. Wavelets have the specific scaling properties. They convert
a signal to the arbitrary signals with different scales and different levels
of resolution using the scaling and transmission properties. They offer a presentation
of signal at both time and frequency domain, so the Wavelets analysis is preferable,
from this aspect, compare with the Fourier analysis and efficiently is used
in many different fields such as: astronomy, Acoustic, nuclear engineering,
signal and image processing, neurophysiology, music, magnetic resonances, xerography,
speech distinction, earthquake predication, radar, Optic and the applications
of pure math.
Recently, this theory is appeared as an important mathematical model in electrical
engineering community. This theory has a special application in concentration
and time locating of transient phenomenon in power electrical engineering. The
next advantage of this conversion is having different resolutions in different
scales so that for high frequency phenomenon, the frequency resolution increases
and the time resolution decreases and vise versa for low frequency phenomenon.
So, the difference of this analysis with others from the resolution and accuracy
aspect (that its definition will be presented more obviously) is shown in Fig.
1ad.
Wavelet conversion is resulted from passing the signal through two low and
highpass filters. The lowpass filter output is called as signal approximation
that contains most of the main and low frequencies, also the highpass filter
output is called as signal details and contains the transient phenomenon and
sharp signals.
 Fig. 1:  Comparison
of the resolutions in different analysis. (a) Time domain (Shannon), (b)
Frequency domain (Fourier), (c) STFT (Gabor) and (d) Wavelet analysis 
Figure 2 shows the chart of signal dividing into these two
components.
The operation of down sampling, shown in Fig. 3, is used to limit the number of samples. This decomposition of signal can be continued to more levels as shown in the chart of Fig. 4. The application of Wavelets theory for broken bars detection: If the mother Wavelet and scaling functions are orthonormal basis, then the theorem of Parseval proves that the energy of disturbed signal depends on expansion coefficients and itself coefficients of the Wavelets. On the other hand, if the basis functions are orthonormal, then: where, the values of C in continues mode are as follow: where, the function Ψ(w) is the Fourier conversion of the function ψ(t), described at the previous part. Then the inequality Eq. 2 will be a logical relation. Thus, the coefficients of the wavelet conversion will be defined as inner production of the wavelet ψ_{a,b}(t) and the signal x(t) for the given values a and b is as follow:
According to the Eq. 1 and 2, the energy
of disturbed signal is divided depending on disturbance type in the various
levels or scales. Here, for a signal the standard deviation with average of
zero can represent its energy.
 Fig. 2:  Method
of dividing the signal into approximation and various components 
 Fig. 3:  Sampling
down operation 
 Fig. 4:  Diagram
of Wavelet conversion using multilevel decomposition 
So, in this method the standard deviation for the components of decomposed
signal in various levels is used as an index to classify various power quality
disturbances.
Since, the input signal is discrete in most applications, so the discrete from of previous relation is used as follow: where, N is the number of samples. The resultant coefficients from upper relation will be an imaginary number. Here for optimum using of this coefficients the absolute value of them is used as follow: These coefficients may be written as a matrix as follow:
where, the arrays of matrix A have the following properties:
• 
For a constant value of j = u, the value of C_{ui} represents
the frequency response of input signal at a given time 
• 
For a constant value of I = v the value of C_{jv} represents the
relative level of a special frequency during one period 
• 
Therefore, any column of matrix A, A_{i}(i = 1,Y,n) is a filtered
level of the main signal 
The proposed method in this study is based on using the energy of signals,
resulted from wavelet converting of stator current signal to various levels,
which corresponds with summation of square coefficients in the various levels
of filtered signal. 4th order Daubechies Wavelet is used to decompose the main
signal to the various levels. The signal is divided to 12 levels using this
wavelet and then the energy of these levels is applied as a criterion to detect
the fault. Figure 5al show the decomposition
of stator current signal to 12 levels for the condition of four broken bars.
Figure 5a shows the motor current signal for the condition
of four broken bars and the Fig. 5bl
are low and high frequency levels of under investigation signal, so that, the
summation of these signals is equal to the main signal.
The Fig. 5k contains the main component and adjacent components
such as f_{b} = (1"2s) f frequency, the latent energy in these levels
are used for detecting of motor broken bars.
Simulation and experimental results: First the healthy motor is simulated
using winding function as described in (Bellini et al.,
2001) in MATLAB. Then the motor is simulated by using this method and writing
the equations for the condition of 1, 2, 3 and 4 broken bars. The first set
of motors, used for simulation and experimentation, are 3 hp squirrel cage induction
motor with the specification of 380 volt, 50 Hz, four pole and three phases
with Yconnection, made in Tabriz Motozhen Company in Iran. The second set of
motors are 3 hp squirrel cage induction motor with the specification of 220
volt, 60 Hz, four pole and three phases with Yconnection, made in General Electric
Company. The electrical and mechanical specifications of these two set of motors
are available in appendix. The experimental results are obtained using a digital
4channel oscilloscope with the ability of connecting to the computer.
Figure 6ah show the frequency spectrum
for the current of stator phase a, for five different states (healthy, 1 to
3 broken bars). As shown in Fig. 6, the increase in number
of broken bars results in increase of the adjacent harmonics amplitude. Figure
6a shows the stator current spectrum for both the experimentation and simulation
of the healthy motor. The sensible difference between the simulation and experimental
results is significantly due to some nonsymmetrical properties in motor structure,
such as nonaxially property, imperfect injection of Aluminum to the rotor slots
and etc. As shown in Fig. 6, the rotor bars breaking will
change the magnitude of harmonics of stator current. It is also obvious that
in healthy motor, the adjacent components (1±2s)f are appeared in two
sides of the main component because the under investigation motor was a cast
aluminum motor, in this type of motors the injection of aluminum to the rotor
core is done at high pressure and temperature and therefore it is probable that
some bubbles of air or other gases create in rotor cage, which result in increment
of the local resistance of some bars or aluminum penetration in the rotor core.
Figure 6 shows the comparison of frequency spectrums, resulted
from the computer simulation and experimental measurements of motor, for the
conditions of 1, 2 and 3 broken bars and the healthy motor. It is obvious that,
the magnitude of the components (1±2s)f are increased by increment of
nonsymmetrical condition in rotor from the healthy state to the state of 3 broken
bars and also the other components which are near the main component, are changed.
 Fig. 5:  (al)
Stator current signal and its 11 levels of 12 resulted levels by filtering 
According to Fig. 6, since, the signal variations in side bands have a low sensitivity, so the fault detection is difficult using frequency spectrum analysis. Therefore the method of signal analysis is used in Wavelet conversion to detect rotor broken bars.
As already mentioned, using the latent energy in different frequency bands
is a suitable method to detect the disturbances in a signal. By using this method
at first, the latent energy of signal and then the summation of squared coefficients
in the levels 1 to 12 are calculated for the condition of 1, 2, 3 broken bars
and healthy motor. Figure 7ac show the
changes of this latent energy for different levels. Since breaking the bars
will affect more on adjacent harmonics of main parameter, it caused the increase
in these components as the figure shows. Also, the graphs illustrated that the
level 6 which indicates the latent energy of this frequency band, can be a suitable
criterion to detect the number of broken bars. The experimental results of 3
hp Motozhen and general electric motors are also shown in Fig.
7. As shown in Fig. 7, increase in the number of broken
bars in both experiments have the same result in increasing the energy of components
which are in adjacent of the main frequency and it is in accordance with simulation
results. Table 1 shows the values of stored energy at any
decomposed level in experiments and simulation results.
 Fig. 6:  The
changes of stator current spectrum for healthy and 1 to 3 broken bars
motor. (a) Healthy motor (experimentation), (b) healthy motor (simulation),
(c) one broken bar (experimentation), (d) one broken bar (simulation),
(e) two broken bars (simulation), (f) two broken bars (experimentation),
(g) three broken bars (simulation) and (h) three broken bars (experimentation) 
Table 1:  The
values of stored energy at any decomposed level (practical and simulation
results) 

 Fig. 7:  Latent
energy changes in various levels of decomposed signals. (a) Simulation,
(b) experimentation (Motozhen motor) and (c) general electric motor 
CONCLUSIONS In this study, a new method based on the use of wavelet theory for detection of broken bars in induction motors is presented. The results of computer simulation and laboratory measurements indicate that the wavelet analysis method is very effective and reliable diagnosis method for this aim. With this method the failure can be detected during motor operation and prevent failure spread and also manufacture trip.
APPENDIX

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