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Marot F y Velásquez S. Diagnosis of low insulation fault in the starting transient of squirrel cage rotor induction motors using wavelet analysis
https://doi.org/10.47460/athenea.v5i17.82
Tipo de artículo: artículo de investigación
Diagnosis of low insulation fault in the starting transient of
squirrel cage rotor induction motors using wavelet analysis
Correspondence author: aamarotgu@estudiante.unexpo.com
Received (12/07/2024), Accepted (15/09/2024)
Abstract. - The objective of this work was to diagnose faults in squirrel-cage induction motors during the
startup transient, by analyzing the stator current signal. To achieve this, low- and medium-voltage motors
were modeled in Simulink using MATLAB. Previously, the fault due to low insulation was diagnosed through
a static test. It was demonstrated that, during the startup transient, the low insulation fault manifests
through a Daubechies wavelet analysis at level 8 of the current signal. The fault was identified in the detail
levels 1, 2, 5, 6, 7, and 8, for both low-voltage and medium-voltage motors.
Keywords: wavelet, daubechies, isolation.
Diagnóstico de falla de bajo aislamiento en el transitorio de arranque de motores de
inducción con rotor jaula de ardilla mediante análisis de wavelet
Resumen: El objetivo de este trabajo fue diagnosticar fallas en motores de inducción con rotor de tipo jaula
de ardilla durante el transitorio de arranque, mediante el análisis de la señal de corriente del estator. Para
ello, se modelaron motores de baja y media tensión en Simulink, utilizando MATLAB. Previamente, la falla
por bajo aislamiento fue diagnosticada mediante prueba estática. Se demostró que, durante el transitorio
de arranque, la falla de bajo aislamiento se manifiesta a través de un análisis de wavelet Daubechies de nivel
8 aplicado a la señal de corriente. La falla se evidenció en los niveles de detalle 1, 2, 5, 6, 7 y 8, tanto en
motores de baja tensión como en motores de media tensión.
Palabras clave: wavelet, daubechies, aislamiento.
Alfredo Marot
https://orcid.org/0000-0002-8829-4124
aamarotgu@estudiante.unexpo.com
Universidad de Oriente núcleo Anzoátegui
Barcelona, Venezuela
Sergio Velásquez
https://orcid.org/0000-0002-3516-4430
velasquez@unexpo.edu.ve
UNEXPO Vicerrectorado Puerto Ordaz
Puerto Ordaz, Venezuela
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Marot F y Velásquez S. Diagnosis of low insulation fault in the starting transient of squirrel cage rotor induction motors using wavelet analysis
I. INTRODUCTION
Induction Motors (IMs), with capacities ranging from a few watts to megawatts, are employed as prime
movers and play a fundamental role in today's industries [1]. Due to their robustness, reliability, and low
maintenance costs, IMs have received increasing attention in the automotive industry, electric vehicle
traction, and power conversion systems [1]. Induction machines are gaining popularity in renewable energy
applications, which demands constant research on their performance. The lack of regulation of failures in
processes causes considerable economic losses and degrades process performance [2]. Induction motors
are put to the test in a variety of circumstances and environments. Motor failure implies unwanted
downtime, costly repairs, and in some cases, can even lead to casualties [3].
Motor current analysis is a valuable tool for the detection and diagnosis of faults in induction motors. This
technique allows to prevent breakdowns, reduce maintenance costs, and improve the safety of facilities.
Motor current signature analysis (MCSA) is considered the most common technique for fault analysis [4].
The phase current signal contains components that depend on the motor's operation, a product of the
rotating flux. The appearance of faults causes changes in the supply current with specific harmonic content
that depend on the type of fault. The MCSA technique uses stator current measurements to detect these
harmonics, and although they are not desired, they are used for fault analysis. MCSA provides current
spectra with information to detect electrical and mechanical faults. Current measurements in a three-phase
induction motor can only be performed at specific times. The usual approach is to measure the current
during motor operation, as it is the simplest way to do so and provides input data of sufficient quality. This
technique is used by most condition monitoring methods. On-line current measurements can be divided
into two types: with load and without load. Another convenient time for current signal monitoring is within
the startup window [5].
Starting currents can offer better options for motor condition analysis, as they are measured at higher
motor slip and with a higher signal-to-noise ratio. This facilitates the detection and evaluation of the spectral
components of the signal. The most frequent causes of induction motor failures are winding and insulation
problems, accounting for between 30% and 40% of total failures [6]. Insulation failures are responsible for
80 to 90% of this percentage. For medium voltage drives [7]. Stator inter-turn short circuit (ITSC), present
in approximately 40% of induction motor (IM) failures, is a common defect in these machines. While a few
shorted turns do not usually show any noticeable physical signs, they can cause considerable damage to
the insulation in a short period of time [8]. Early detection of this fault can minimize further damage to
adjacent turns and the stator core, which would reduce maintenance costs and motor downtime [9]. Most
insulation faults affecting induction motors occur between phase and ground. Common practices for
assessing insulation condition require the motor to be stopped and cannot provide information about the
degrading agent affecting the motor [10].
An ITSC fault creates harmonic frequency components in the motor current. The magnitude and frequency
of these harmonics change continuously with load variations. To accurately identify faults in induction
motors (IMs), cutting-edge techniques have been developed that extract telltale features from current
signals. Among the most notable tools are; Fast Fourier Transform (FFT): This technique decomposes the
current signal into its frequency components, revealing unique patterns associated with different types of
faults; Short Time Fourier Transform (STFT): Unlike FFT, STFT analyzes the current signal in shorter segments,
providing a more detailed view of how faults evolve over time; Power Spectral Density (PSD): This technique
quantifies the distribution of energy in the frequency spectrum, allowing the presence and severity of faults
to be identified with greater precision. Traditional fault diagnosis techniques in induction motors, based on
steady-state current, have limitations such as sensitivity to operating conditions and difficulty in detecting
incipient faults. One of the most important analysis tools in both the frequency and time domains is the
wavelet.
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Marot F y Velásquez S. Diagnosis of low insulation fault in the starting transient of squirrel cage rotor induction motors using wavelet analysis
Multiresolution analysis and good time localization make wavelets very attractive for fault diagnosis
research. Wavelets are localized in both the time and frequency domains because they have limited time
duration and frequency bandwidth [11].
II. DEVELOPMENT
A. Mathematical model of the induction motor in the reference frame fixed to the rotor.
The Simulink block used in this study. implements equations that are expressed in a stationary rotor (dq)
reference frame. The d axis is aligned with an axis. All quantities in the rotor reference frame are referred
to the stator [12].
Equations to calculate electrical speed (ω
em
) and sliding speed (ω
slip
).
(1)
(2)
To calculate the electrical speed of the rotor dq with respect to the rotor axis A (dA), the difference
between the speed of the shaft and the stator is used (da) and sliding speed:
(3)
o simplifies the equations for flux, voltage and current transformations, the block uses a stationary
reference frame:
(4)
(5)
Flow
(6)
Current
(7)
Inductance
(8)
Electromagnetic torque
(9)
Invariant power dq transformation to ensure dq and three-phase powers are equal
(10)
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Marot F y Velásquez S. Diagnosis of low insulation fault in the starting transient of squirrel cage rotor induction motors using wavelet analysis
The equations use these variables
ω
m
: Rotor angular speed (rad/s)
ω
em
: Electric rotor speed (rad/s)
ω
slip
: Electric rotor sliding speed (rad/s)
ω
syn
: Synchronous rotor speed (rad/s)
ω
da
: dq electrical speed of the stator with respect to the axis a of the rotor (rad/s)
ω
dA
: dq electrical speed of the stator with respect to the rotor axis A (rad/s)
Θ
da
: dq electrical angle of the stator with respect to the a axis of the rotor (rad)
Θ
dA
: dq electrical angle of the stator with respect to the A axis of the rotor (rad)
L
q
, L
d
: Inductances of the q and d axes (H)
L
s
: stator inductance (H)
L
r
: rotor inductance (H)
L
m
: Magnetizing inductance (H)
L
ls
: Stator leakage inductance (H)
L
lr
: Rotor leakage inductance (H)
v
sq
, v
sd
: Stator voltages on the q and d axes (V)
i
sq
, i
sd
: Stator currents in the q and d axes (A)
λ
sq
, λ
sd
: Stator flow in the q and d axes (Wb)
i
rq
, i
rd
: Rotor currents in the q and d axes (A)
λ
rq
, λ
rd
: Rotor q and d axis flow (Wb)
v
a
, v
b
, v
c
: Stator voltage phases a, b, c (V)
i
a
, i
b
, i
c
: Stator currents phases a, b, c (A)
R
s
: Resistance of stator windings (Ohm)
R
r
: Rotor winding resistance (Ohm)
P: Number of pole pairs
T
e
: electromagnetic torque (Nm)
A. Wavelet transforms
The wavelet transform (WT) is a signal analysis technique that solves the time-frequency resolution
problems of the Fourier transform. The WT is based on a function called the wavelet mother function, which
is used to decompose the signal into sub-bands. Wavelet functions can be classified into families, and the
choice of the appropriate family depends on the characteristics of the signal to be studied. The most used
wavelet functions are Daubechies, coiflet, simlet, biorthogonal and discrete Meyer. [13].
Identification of the fault can be done in two ways: by analyzing the coefficients resulting from the
decomposition of the signal or by studying the high-level wavelet signals. High-level wavelet signals are
those that contain information about the nature of the failure. The integral wavelet transforms of a function
f(t) ϵ L^2 with respect to a wavelet analyzer is defined as [14]:
(11)
Where
(12)
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Marot F y Velásquez S. Diagnosis of low insulation fault in the starting transient of squirrel cage rotor induction motors using wavelet analysis
The parameters b and a are called translation and dilation parameters respectively. Normalization factor
is included
so that
The expression for the inverse wavelet transform is
(13)
Where
is a constant that depends on the choice of the wavelet and is given by:
(14)
The coefficients constitute the results of a regression of the original signal carried out on the wavelets. A
graph can be generated with the x-axis representing the position along the signal (time), the y-axis
representing the scale, and the color at the x-y point representing the magnitude of the wavelet coefficient
C. These coefficient plots are generated with graphic tools.
A. Discrete Wavelet Transform (DWT)
The discrete wavelet transform performs the decomposition of a signal
in an approximation
coefficient at a given level of decomposition
, and detail signs
con [15].
(15)
Where
y
They are the scaling function at level k and the wavelet function at level j respectively. On
the other hand, the coefficients
y
se calculan utilizando el algoritmo de codificación por sub-bandas
[16].
Discrete Wavelet Coiflet
(16)
Wavelet Cohen Daubechies
(17)
Wavelet Daubechies
(18)
Binomial-quadrature mirror
filter (QMF)
(19)
Wavelet Haar
(20)
Wavelet Mathieu
(21)
Wavelet Legendre
(22)
III. METHODOLOGY
In this work we start from the fact that we have proposed the following hypothesis:
Hypothesis: The hypothesis posits that Wavelet analysis using Daubechies wavelets applied to squirrel-
cage induction motors will effectively detect and diagnose insulation faults, considering the specific motor
properties that influence the dynamics of these faults. A significant relationship is expected between the
individual characteristics of the studied motors and the Wavelet analysis' ability to accurately and timely
identify existing insulation faults, which will contribute to improving predictive maintenance practices in
industrial machinery.
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Marot F y Velásquez S. Diagnosis of low insulation fault in the starting transient of squirrel cage rotor induction motors using wavelet analysis
Study Population and Sample: The study population consisted of 477 electric motors from a petrochemical
plant with a history of low insulation problems in some motors. A sample of 20 motors with data from
previous static insulation tests was available. The objective was to employ wavelet analysis to evaluate these
motors and demonstrate its ability to diagnose low insulation faults.
Motor Simulations: In this scenario, 20 squirrel-cage induction motors were simulated in Simulink. For this
study, one low-voltage and one medium-voltage motor were selected. The low-voltage motor belonged to
a process fluid pump in the Urea plant, and the medium-voltage motor belonged to a pump in the plant's
cooling water system. These motors were chosen because the low-voltage motor was the most recent one
subjected to a static insulation test, and the insulation resistance value obtained was less than 200 kΩ, which
is below the value established in IEEE Standard 43-2013 (5 MΩ between phases and ground and between
phases for low-voltage motors). The medium-voltage motor was selected because it was one of the highest-
power motors in the population, allowing the proposed methodology to be validated for medium-voltage
motors as well.
Taking into consideration that if a ground fault is introduced in phase C of the motors, modeling the
insulation resistance of the winding. Starting from the fact that; You can emulate the insulation resistance
to ground by connecting a resistor to ground for each coil [17]. So to emulate insulation deterioration, a
capacitor is added, which increases the insulation capacitance.
Fig. 1. Equivalent circuit of electrical insulation system [18].
Modeling the circuit in figure 1
(23)
(24)
This approach was chosen because an aged insulating material would also cause a similar increase in
capacitance. The severity of insulation degradation can be varied depending on the capacitance of the
inserted capacitor. Phase to ground capacitances are between 1.5 nF and 21 nF [19]. The "3-phase induction
motor" block from the Simscape Electrical library in Simulink was used. To model each engine individually.
The parameters of each engine were configured according to the actual specifications or available reference
data. In which we can obtain the data required by the software, below we show the data of the low voltage
model motor.
Nominal Voltage (Vn) = 460;
Nominal frecuency (fn) = 60;
Rated Current (In) = 18.25;
Nominal Torque (Tn) = 49,8;
Maximum speed (Ns) = 1800;
Nominal speed (Nn) =1750;
Starting Current to Rated Current Ratio (Ist/In) = 6;
Starting Torque to Nominal Torque Ratio (Tst/Tn) = 2.5;
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Marot F y Velásquez S. Diagnosis of low insulation fault in the starting transient of squirrel cage rotor induction motors using wavelet analysis
Breaking Torque to Nominal Torque Ratio (Tbr/Tn) = 3;
power factor (pf)= 0.8;
With these data we introduce them into the parameter estimation block;
Fig. 2. Parameters of Low Voltage Motor 460 V, 11 KW; simulated in simulink.
The C phase current signal is extracted and brought into MATLAB to perform a wavelet analysis. Using the
"3-Phase Induction Motor" block from the Simscape Electrical library in Simulink to model each motor.
Fig. 3. Low and medium squirrel cage motor simulation; healthy state (a). Low and medium squirrel cage motor
simulation; Insulation failure (b)
The simulation of the start-up of the two induction machines in a healthy state was carried out.
Subsequently, the current signal of the start transient of phase C was extracted, with the Simulink Workspace
block into Matlab, for the healthy and failed cases. The signal was transferred from the Simulink workspace
to MATLAB for wavelet analysis using the level 8 Daubechies parent function.
IV. RESULTS
The results of the simulation of the start-up of the induction machines revealed a change in the signal at
all levels of detail; but more pronounced at the level of detail 1, 2, 5, 7 and 8; from Daubechies wavelet
analysis. In the spectrum, the modification of both signals can be observed for both the medium voltage
motor and the low voltage motor. Figure 5 shows the decomposition of the wavelet signal at level 8 in the
healthy state of the engine.
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Marot F y Velásquez S. Diagnosis of low insulation fault in the starting transient of squirrel cage rotor induction motors using wavelet analysis
Fig. 4. Wavelet Daubechies Level 8 Low Voltage Motor 460 V, 11 KW; shows the spectrum of the engine in healthy
state.
Fig. 5. Wavelet Daubechies Level 8 Low Voltage Motor 460 V, 11 KW; shows the spectrum of the motor in the fault
state with low insulation.
Figure 4 shows the decomposition of the wavelet signal at level 8 in the healthy state of the engine. When
viewing both spectra, we can observe the difference that exists with respect to figure 5 at the level of detail
Daubechies 1, 2, 3, 5, 7 and 8; how the signal changes when a 200kΩ low insulation fault is introduced.
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Marot F y Velásquez S. Diagnosis of low insulation fault in the starting transient of squirrel cage rotor induction motors using wavelet analysis
Fig. 6. Wavelet Daubechies Level 8 Medium Voltage Motor 13800 V, 3 MVA; shows the spectrum of the engine in healthy state.
Fig. 7. Wavelet Daubechies Level 8 Medium Voltage Motor 13800 V, 3 MVA; shows the spectrum of the motor with insulation
failure for 200kΩ.
Figure 7. Wavelet Daubechies Level 8 Medium Voltage Motor 13800 V, 3 MVA; simulated in simulink;
shows the spectrum of the engine in healthy state. Figure 8; Wavelet Daubechies Level 8 Medium Voltage
Motor; We can observe the difference with respect to figure 7 in the level of detail Daubechies 8, 7 and 6 in
this case as the signal changes when a low insulation fault of 200kΩ is introduced.
Next we analyze wavelet histograms which can show how wavelet coefficients are distributed at different
scales. In this case, they are used to analyze the health status of low and medium voltage motors, both in
healthy conditions and with failure due to low insulation.
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Marot F y Velásquez S. Diagnosis of low insulation fault in the starting transient of squirrel cage rotor induction motors using wavelet analysis
Fig. 9. Histograms. Wavelet Daubechies Level 8 Medium and low voltage motor.
Figure 9 shows Histograms. Wavelet Daubechies Level 8 Medium and low voltage motor. The first top left
histogram (a) belongs to the low voltage motor in healthy state, the second top right side histogram (b)
belongs to the motor in failed state with low insulation. The lower left side histogram (c) belongs to the
medium voltage motor in healthy state. The lower right-side histogram (c) belongs to the failed medium
voltage motor with low insulation. The histograms of the low voltage motor represent a significant
difference in the distribution of energy levels, both have a unimodal distribution, but the one in the failed
state is more asymmetric than that of the motor in the healthy state, with a longer tail to the right. . This
may indicate a greater tendency towards higher wavelet coefficient values, which could be related to low
insulation failure. The histograms of the medium voltage motor present a bimodal distribution, and a
difference is made in terms of the peaks on the left side with two almost uniform bands in the case of the
healthy motor. The medium voltage healthy state histogram is slightly asymmetric to the right, similar to
that of the low voltage motor in healthy state.
In the case of the low voltage motor, we have then simulated 2 low insulation scenarios; in which it could
be detected that as the insulation degrades at 20 kΩ and 2 kΩ; You can continue to observe the changes
in the levels of detail of the wavelet spectrum, in addition to the energy distribution changing in the signal;
In Table 1 we can observe the changes in the statistics of the signal energy distribution for each scenario,
motor in healthy state, failed motor with 200 kΩ, 20 kΩ and 2 kΩ;
Table 1. the statistics of the signal energy distribution.
Statistical
Healthy
Isolation 200k
Isolation 20k
Isolation 2k
mean
-0,3463
-1,011
-0,7334
-0,7312
median
2,347
0,8336
1,93
1,966
miximum
131,2
131,5
131,4
131,4
minimum
-135,6
-135,3
-135,6
-135,6
range
266,9
266,9
267
167
standard dev
63,46
63,4
63,24
63,24
median abs dev
36,6
39,91
38,96
39,89
mean abs dev
49,62
49,47
49,41
49,42
l1 norm
1,83E+04
1,83E+04
1,82E+04
1,82E+04
L2 norm
1216
1220
1215
1215
max norm
135,6
135,3
135,6
135,6
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Marot F y Velásquez S. Diagnosis of low insulation fault in the starting transient of squirrel cage rotor induction motors using wavelet analysis
IEEE Standard 493 provides valuable information on expected failure rates for high-power electric motors.
According to this standard, a differentiation in failure rates is observed depending on the operating voltage
and the type of motor:Motores de inducción:
Less than 1000 Volts: The estimated failure rate is 0.0824. From 1000 to 5000 Volts: The estimated failure
rate is 0.0714 [20]. Taking this reference for our population at this failure rate, it is likely that in a year we
will have 32 low voltage motors and 7 medium voltage motors. Therefore, it would be estimated that of the
31 low voltage motors, taking the reference mentioned above, 40% of the failures will be due to winding
problems. We include in these problems generated by insulation failures; With this probability, 13 low
voltage motors and 7 medium voltage motors would fail, so to validate the tests we carried out simulations
taking these samples as a reference.
We wish to evaluate whether the diagnosis of failure due to low insulation of electric motors using
Daubuchies 8 wavelet transform signal analysis at level 8 is effective to identify failures in low voltage
motors. There is data from a sample of 13 low voltage motors, where 12 motors were correctly diagnosed
as failed. The failure rate of low voltage motors provided by the IEEE (0.0824) and the EPRI estimate of the
proportion of failures due to insulation problems (40%) are taken as a reference. Hipótesis:
Null hypothesis (H0): Diagnosis by wavelet transform has no effect on the identification of faults due to
low isolation, that is, the probability of a correct diagnosis is not different from the random probability.
Alternative hypothesis (H1): Diagnosis by wavelet transform does have an effect on the identification of
faults due to low isolation, that is, the probability of a correct diagnosis is greater than the random
probability. (We work under the assumption that this hypothesis is correct).
Statistical test selection:
Since we are trying to evaluate the proportion of correct diagnoses in a small sample (n < 30), the student’s
t test for a single sample can be used.
Calculation of the test statistic:
Number of successes (X): 12 engines diagnosed as failed (of 13 engines in the sample).
Population means under the null hypothesis (μ0): 0.4, since it is estimated that 40% of the motors are failed
due to low insulation.
Sample standard deviation (s): It is calculated using the formula:
(25)
In this case, s = 0.241.
test statistic t:
(26)
Degrees of freedom:
(27)
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Marot F y Velásquez S. Diagnosis of low insulation fault in the starting transient of squirrel cage rotor induction motors using wavelet analysis
Significance level:
A significance level (α) of 0.05 is established.
Calculation of p value:
Since this is a right-sided test, the p-value is calculated using Student's t-table with 12 degrees of freedom
and finding the area in the tail of the test statistic t = 2.49. In this case, the p value is 1.782 in table.
The null hypothesis is rejected and the alternative hypothesis is accepted. This means that there is sufficient
evidence to conclude that the Daubechies wavelet diagnostic method does have a significant effect on the
identification of low insulation faults in low voltage electric motors.
CONCLUSIONS
Daubechies Level 8 Wavelet analysis is presented as a novel and effective tool for diagnosing low insulation
faults in the stator coils of squirrel cage rotor induction motors, both at low and medium voltage. This
technique, based on the analysis of the stator current signal during the start-up transient, allows low
insulation faults to be accurately identified through characteristic changes in the wave spectrum and energy
distribution of the current signals. Levels of detail 8, 7, 6 and 5 are particularly relevant for the detection of
these faults. The detail curve patterns vary significantly in the failed engine with respect to the healthy
engine. The wavelet histograms show a difference in the distribution of energy levels between the healthy
and the failed motor, indicating a greater tendency towards higher wavelet coefficient values in the failed
motor. The student’s t test for a single sample demonstrates that wavelet transform diagnosis does have a
significant effect on the identification of faults due to low insulation in low voltage electric motors. Unlike
traditional static-state insulation testing, Daubechies Level 8 Wavelet Analysis offers early and accurate fault
detection, even in the presence of low insulation values. This capability opens a promising path for the
implementation of the method in condition monitoring systems, improving predictive maintenance
practices and reducing the incidence of catastrophic failures in electric motors. This study provides strong
evidence supporting Daubechies Level 8 wavelet analysis as a valuable tool for the diagnosis and prevention
of low insulation faults in induction motors.
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THE AUTHORS
Alfredo Alejandro Marot Guevara; Electrical/Electronic Engineer, specialist
in Industrial Automation and Computing; University professor for 18 years.
Currently professor of Dynamic Systems at the Universidad de Oriente, advisor
at MDJ Technology. c.a; and SJT Industrial Equipment and Services, residing
in the city of Barcelona, Anzoátegui. Venezuela.
Sergio Rafael Velásquez Guzmán - Coauthor, received the B.S. degree in
Electronic Engineering, from the UNEXPO, in 2008. M.S. degree in Education
from UPEL in 2011, an M.S. degree in Electronic Engineering from UNEXPO, in
2012, an MBA degree from UNY in 2014, a Doctor of Education degree in 2015
from UPEL, and a Doctor of Engineering Sciences from UNEXPO in 2019. He
is a type B Research Professor accredited by the MINCYT in Venezuela.
Currently, he is in charge of the Research and Postgraduate Department of
the UNEXPO Vice-Rectorate, Puerto Ordaz, Venezuela.
