1. Interturn Short-circuit Analysis in an Induction
Machine by Finite Elements Method and Field Tests
D. Díaz, M. C. Amaya

Abstract -- The torque and sequence negative impedance
analysis, with the evolution of short-circuit turns of the stator
phase winding in a 3HP induction machine was done in the
present paper.
Index Terms-- Electromagnetic torque, fast Fourier
transform, finite element method, induction machine, inter-
turn short-circuit, inverse sequence impedance, Park's Vector.
I. NOMENCLATURE
FFT: Fast Fourier Transform.
FEM: Finite Element Method.
EPVA: Extended Park’s Vector Approach.
Fig. 1. Diagnosis methods
II. INTRODUCTION
III. THE INVERSE SEQUENCE IMPEDANCE [3]
T he electrical induction motors are used in 90% more of
the industry applications, and is vital to guarantee their
correct functioning. So, it is necessary to have a tool
It has been shown that is possible to diagnose the
presence of short circuit turns in the stator winding of an
that allows knowing the motor’s condition without induction motor, using a parameter called inverse sequence
intervening in the equipment’s operation. effective impedance. This parameter is very useful as
failure indicator in the functioning induction motor stator
A failure in a component is usually defined as a capacity winding. In practice, the voltage system which feeds a
reduction condition, related to specification minimal motor never is well-equilibrate. There always are light
requirements, and is the result of the normal waste, a bad differences between the efficient values of the voltage and
design or poor specification, incorrect assembly, misuse or phase angles. The good-condition induction motor
a combination of all. If a failure is not detected on time, or behavior, fed by an imbalanced system, could be analyzed
if it develops farther, it could lead to the machine’s by the study of the inverse and direct sequence equivalent
collapse. Nowadays it is important to consider the circuits.
implementation of a failure diagnosis strategy, to increase
the machine useful life components, increasing the plant’s Figure 2 (top) shows the equivalent direct sequence
availability and productivity. To determine motor problems circuit, where Rs and Rr represent the stator and rotor
it has to be confident and secure and electrical motors reactances respectively. The stator and rotor leakage
analysis has to contain results in this failure zones: power reactances and the magnetization reactance correspond to
circuit, isolation, stator, rotor, air-gap and energy quality. Xs, Xr and Xm respectively.
The stator fails form the 37% of the electrical motor
failures, being the inter-turns short circuit the most
common, which reduces the ability of produce a balanced
electrical field, causing vibration increase on the machine,
and consequently, isolation degradation and motor bearings
failure.
Figure 1 shows the failure diagnosis methods in rotating
machines [1, 2]. This work resumes the use of the no
conventional electromagnetic torque and inverse sequence
impedance analysis methods, because the conventional ones
show the disadvantage that could damage the isolation
when applied.
Fig. 2. Direct sequence equivalent circuit and inverse sequence equivalent
circuit.
D. Diaz is with the Electrical and Electronic Engineering School,
Universidad del Valle, Cali, Colombia (e-mail: dariodiazs@gmail.com).

2. The variable component of the rotor RL1 resistance is the
one that allow calculating the mechanical power of the When some deficiency in the isolation state of the stator
motor, as a function of the rotor sliding (s): is manifested, the symmetry is lost and the motor stops
showing an inverse sequence current impedance constant
= ∙ (1) value. In this case, the components of different sequence
influence each other, and the voltage falls could be to the
( ) circulation of any sequence current components. Due to
= ∙ (2) these effects, Z2ef is altered during an incipient fail, and
could be used to monitoring purposes of the fails.
This value is very sensitive to the sliding changes, as is Conducted experiments with this method conclude that the
shown in the derived function (equation 2). negative sequence impedance shows an evolution tendency
determined by the presence of stator isolation failures; the
As the inverse sequence field spins opposite to the direct module changes the value considerably, even when appears
field, the equivalent circuit for the inverse sequence could a short circuit affecting only a pair of turns. This method
be obtained substituting the sliding, s, in the direct sequence has not been implemented to an industrial level, because the
circuit by the quantity (2-s). In the figure 2 (lower) the development of equipments based on microcontrollers that
resulting circuit is shown. Now, the impedance variable allow making inverse sequence impedance calculus of
component is expressed as (equation 3): industrial plant motors are just being performed.
=− ∙ (3) A. Simulations with the finite elements method
( ) To make the study, the software FLUX2D® [4] was
= ∙( )
(4)
used; it has a magnetic transitory formulation included,
which solves the problem in discrete time points. The
This expression is not as sensitive to the sliding changes, geometry of the materials and the development of the
as is shown in the equation 4. Taking into account that most winding were obtained by fragmenting a real motor, in
of the induction motors works with very low sliding, of 3% which field test were performed. Figure 3 shows the
order, two main observations could be done. The first is machine geometry entirety, in which stator and rotor core
that the inverse sequence impedance is lower than the direct regions, and squirrel’s cage bars are shown. [5]
sequence impedance of a motor; by the way, for inverse
sequence voltage low levels, high inverse sequence current
levels are circling. This is a problem when is time to
monitoring the line current, because this is affected by little
voltage unbalances, and hide any symptom of incipient fail.
Another interesting observation is that, unlike the direct
sequence impedance, the inverse sequence impedance of an
induction motor is less sensible to the sliding changes. In
consequence the inverse sequence impedance is practically
constant to the load variations and the inverse sequence
current flux.
This impedance value could be calculated as the quotient
between the voltages inverse sequence component and the Fig. 3. Geometry and mesh of NEMA B motor
current inverse sequence component, as shown in the
equation 5. Figure 4 (top) shows electrical circuit used in the non-
= / (5) failure motor simulations. This circuit is divided in three
parts: external sources, stator circuit and the squirrel cage.
Where:
To make the different simulations of the short-circuit turns
Vr2 e Ir2 are the voltages and currents inverse sequence motor, the winding was divided in two parts, one
components respectively, calculated with the symmetrical corresponding to the short-circuit turns and the other
components theory, as shown in equations 6 and 7. corresponding to the other turns; adding an interrupter to
cause the short circuit to the required turns.
= ( + ∙ + ∙ ) (6)
In the figure 4 (lower) is shown the circuit used for
= ( + ∙ + ∙ ) (7) making that failure simulation [6].
Where:
Vr, Vs, Vt are the voltages of the r, s y t phases,
respectively; Ir, Is, It are the currents of the r, s y t phases,
respectively and a is the unitary vector e
 j1 2 0
.

3. Fig. 5. Torque curves in the starting (A) and maximum (B) torque zones
obtained of MEF simulations.
Where it is a torque variation for a motor with short-
circuit turns, according to the figures, is at the beginning of
the machine work and in the maximum torque zone. In the
curves can be seen that the starting torque difference
between the good-condition motor and the one with 34
short-circuit turns is 1 N-m (7% of normal starting torque).
It could be concluded that the inter-turns short circuit
causes a decrease in the starting torque and an increase in
the maximum torque, because R2 decreases as the number
of short-circuit turns increases, and it is also directly
proportional to the starting torque. On the other hand, the
maximum torque is inversely proportional to Xcc and
therefore it decreases, which leads to the increase of the
Fig. 4. Connection circuit of the NEMA B motor without (A) and with (B) maximum torque [6].
short-circuit turns.
IV. INVERSE SEQUENCE IMPEDANCE ANALYSIS.
B. Electromagnetic torque analysis Based in the previously displayed theory, it proceeds to
In the figures 5 details of the torque curves obtained in show the results obtained through the calculated inverse
the MEF simulations, in the starting and maximum torque sequence impedance in the motor MEF simulations. From
zone, is shown. The change in the torque curve is not the obtained data in the transitory simulations, it’s possible
considerable when the motor has short-circuited phase A to find the magnitude and phase angle for both voltage and
turns. current ones in the three signals and calculate the respective
inverse sequence impedance for the motor with several
In order to analyze the torque curves, it could be short-circuit turns.
appreciated that the variations around the machine’s work
point (1740 rpm) are light. The curves between the values
0.001 and 0.04 for the sliding are overlapped.
Fig. 6. Inverse sequence impedance for the motor with several short-
circuit turns (1740 rpm).
The figure 6 shows the inverse sequence impedance
variation as the failure degree increases to 1740 rpm with 7,
14, 19, 24, 29 and 34 Phase A short-circuit turns. The
previous figure shows the inverse sequence impedance
decrease, due to the fact that when the number of short-

4. circuit turns increases; it increases the inverse sequence
flow in one of the phases. Thereby when the inverse
sequence impedance is inversely proportional to the
sequence current, it decreases (Z= V/I).
V. MOTOR CURRENT SIGNATURE
Given below are the results of inter-turn short-circuit
from a statoric phase winding by means of the
implementation of spectral current analysis applied to the
gotten results by running simulations through MEF. The
simulation was implemented on magneto-transient mode
from 0 to 0.4 seconds, time steps of 0.0005 seconds,
everything was carried out looking for enough data to apply
FFT. 5 failure states were simulated, each one with 5
different values of resistance to limit the fault current:
-5 short-circuited turns Fig.8. FFT Fase A para 5 espiras en corto y R=0.14.
-7 short-circuited turns
-10 short-circuited turns
-14 short-circuited turns
Although in reality the short-circuit fault occurs without
the limiting resistance, it means a direct short-circuit. In the
laboratory the resistance had to be implemented to limit the
current caused by the fault due such a high risk represented
for personnel that perform the test and for the machine as
well. Therefore, to validate the results(facing simulated
results with field tests) a resistance was introduced in the
circuit model corresponding to the motor under study by
means of MEF..
Due to the amount of data, only the results for the
slightest and severe failure will be shown (5 and 14 short-
circuited turns). The progress for the fault current can be
observed in the figure 7: Fig.9. FFT Phase A for 14 turns short and R = 0.14.
VI. APPROACH BY THE PARK VECTOR
Park Transformation is used to transform a three-phased
system of statoric currents (A-B-C) into a biphasic system
(D-Q). The expression for the transformation is presented
in [11,12,16,26,43,44];;
= − − (8)
√ √
= − (9)
√ √
Additionally, the expression for current modules:
Fig.7. Fault current for several short turns. = + (10)
The following figures show current spectra results for
the slightest and severe failure: A. No fault condition
When the motor operates in a normal condition, the three
currents can be expressed as shown as in equation 2. Hence,
axes d and q currents can be expressed as::
√
= sin( ) (11)
√
= sin − (12)

5. sequence Lissajou curve may show some distortions like
Lissajou curve represents the function among axis d and shape of an ellipse. For example, Figure 10(d) shows the
q components iq=f(id). In the equation above, Lissajou curve for a short-circuit fault between 6 turns. Additionally,
curve for no faulted motor is a perfect circle with its center the negative sequence is manifested in the power modules
located in the origin and its diameter equals to (√6⁄2)I, as it for a component at twice the fundamental frequency
can be observed in figure 8(a). As diameter is proportional [13,14]. Table I summarizes the EPVA fault indicators.
to current amplitude, the curve becomes thicker as the
motor load varies. In addition, current modules for no-fault TABLE I
INDICADORES DE FALLA SEGÚN LA CURVA DE LISSAJOU Y EL ESPECTRO DE
motor only have a DC component. LOS MÓDULOS DE PARK
Condition The Lissajou’s curve Spectrum of
B. Faulty condition Park’s
In a faulty condition, due to the particular components modulus
influenced from faults on stator currents, the shape of Healthy Circle DC
Broken rotor Círcle, thicker DC, 2 , 4
Lissajou’s curve becomes distorted. In [8,9], detection of
bar sor End
rotor asymmetry by monitoring the Lissajou’s curve has
rings
been presented. The rim of the Lissajou’s curve becomes Mix eccentricity Circle (Thicker for DC, ,2
thicker when the rotor is asymmetrical. For example, the high degree of
Lissajou’s curve for 10-broken rotor bars shown in Figure eccentricities)
10(b). This is one of advantages, which allows the detection Stator winding Ellipse DC, ,2 ,
of faulty conditions by monitoring the deviations of the faault 2
acquired patterns. The results have shown that the sideband
components in the stator currents influenced from the rotor VII. ASSEMBLY TEST BENCH
asymmetry could be transformed to place at the frequency
2sf1 ,4sf1 around DC in the current modulus [10] For the realization of different laboratory tests was
performed the next assembly:
It has also been shown that Lissajou curve is not very
useful for the detection of eccentricity [11,12] because the
curve does not vary much for these types of failures.
Fig.11. Test Bench mounting in the laboratory.
The following figures shows the current spectrums of
phase A in the frequency domain using fast Fourier
transform and the help of Matlab software.
Fig.10. Lissajou curve for various fault conditions.
To detect shorted turns is necessary to determine the
power modules and Lissajou curve. In normal conditions
(without fail), the stator currents contain only the positive
sequence component, so that the circular form Lissajou
curve is still valid. However, under abnormal condition, the
impedance of the phases are unbalancing by the defect in
windings, causing unbalanced currents and introduces
negative sequence component. Due to this negative

6. turns in all limiting resistor values:
Fig.12. FFT Phase A for 1 turn short and R = 0.14 Ohms
Fig.15. Lissajou curve for 14 shorted turns – Laboratory test.
We see that the limiting resistor value does not
significantly influence the shape of the curve only at
distances of major and minor axes of the ellipse (current in
direct axis and quadrature). Therefore we can say that for
purposes of diagnosis, the resistance value is irrelevant,
what is important to consider is the shape of the curve
(vector geometric locus Park).
By determining the frequencies induced anomalies and
monitoring the harmonics of these frequencies is possible to
estimate the state of the machine, as well as the presence of
a fault and what type is.
Was observed in the results of the FEM simulations that
some frequencies are induced even without failure, which
Fig.13. FFT Phase A for 14 turns short and all values of R may be due to harmonics inherent in the operation of the
machine, like slot harmonics.
Below is Lissajou curve for 1 turn short with a limiting
resistor of 0.14 Ohms. As expected, due to the asymmetry Analyzing the results achieved by the MEF was
in the stator field caused by the failure, the curve takes the observed that in the current spectrum there are harmonics at
form of an ellipse instead of a circle, which is indicative of frequencies 180, 300, 400, 520, 760, 880 Hz. It is seen that
the presence of shorted turns. there is a 120Hz between a harmonic and the other. Such
behavior may be a useful indicator to diagnose shorted
turns in one phase.
By analyzing the shape of the Lissajou curve for
laboratory results it is concluded that the number of turns in
short clearly affects the form of it. If we analyze the current
module for the same results we see that the magnitude of
the module depends on the fault and the value of limiting
resistor.
VIII. ACKNOWLEDGMENT
The authors gratefully acknowledge the contributions of
the administrative department of science, technology and
innovation in Colombia - Colciencias, for the development
of this research project
Fig.14. Lissajou curve for 1 turn short – Laboratory test. IX. REFERENCES
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X. BIOGRAPHIES
Cali, Colombia 2007. Martha Cecilia Amaya Enciso: Electrical Engineer from the Universidad
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Vectors Approach for Rotor Cage Diagnosis”, First International Polytechnique, Grenoble-France. PH.D in Engineering of the Universidad
Symposium on Control, Communications and Signal Processing, del Valle. Professor of Energy Conversion Area at the Electrical and
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[9] A.J.M. Cardoso, S.M.A. Cruz, J.F.S. Carvalho, E.S. Saraiva, “Rotor Colombia. His research field is the modeling, analyze and diagnosis of
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[10] A. Aboubou, M. Sahraoui, S.E. Zouzou, H. Razik, A. Rezzoug, Darío Díaz Sánchez was born in Santiago de Cali, Colombia, on April 2,
“Broken Bar and/or End Rings Detection in Three-Phase Induction 1981. He is electrical engineer graduated from the Universidad del Valle,
Motors by the Extended Park’s Vector Approach”, Power Electronics Cali - Colombia in 2007 and currently studying last semester of master's
Congress, 2004, CIEP 2004, 9th IEEE International, 17-22 Oct. 2004 degree in engineering at the same university. E-mail:
page(s):128 – 133. dariodiazs@gmail.com
.