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.

II. INTRODUCTION

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

that allows knowing the motor’s condition without intervening in the equipment’s operation.

A failure in a component is usually defined as a capacity

reduction condition, related to specification minimal requirements, and is the result of the normal waste, a bad design or poor specification, incorrect assembly, misuse or a combination of all. If a failure is not detected on time, or if it develops farther, it could lead to the machine’s collapse. Nowadays it is important to consider the implementation of a failure diagnosis strategy, to increase the machine useful life components, increasing the plant’s availability and productivity. To determine motor problems it has to be confident and secure and electrical motors analysis has to contain results in this failure zones: power circuit, isolation, stator, rotor, air-gap and energy quality.

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.

D. Diaz is with the Electrical and Electronic Engineering School,

Universidad del Valle, Cali, Colombia (e-mail: dariodiazs@gmail.com).

Fig. 1. Diagnosis methods

III. THE INVERSE SEQUENCE IMPEDANCE [3]

It has been shown that is possible to diagnose the presence of short circuit turns in the stator winding of an induction motor, using a parameter called inverse sequence effective impedance. This parameter is very useful as failure indicator in the functioning induction motor stator winding. In practice, the voltage system which feeds a motor never is well-equilibrate. There always are light differences between the efficient values of the voltage and phase angles. The good-condition induction motor behavior, fed by an imbalanced system, could be analyzed by the study of the inverse and direct sequence equivalent circuits.

Figure 2 (top) shows the equivalent direct sequence

circuit, where Rs and Rr represent the stator and rotor reactances respectively. The stator and rotor leakage reactances and the magnetization reactance correspond to Xs, Xr and Xm respectively.

Fig. 2. Direct sequence equivalent circuit and inverse sequence equivalent

circuit.

Interturn Short-circuit Analysis in an Induction Machine by Finite Elements Method and Field Tests

D. Díaz, M. C. Amaya

T

The variable component of the rotor RL1 resistance is the one that allow calculating the mechanical power of the motor, as a function of the rotor sliding (s):

��� = � � ∙���

� (1)

�(���)

��= � � ∙

��

�� (2)

This value is very sensitive to the sliding changes, as is

shown in the derived function (equation 2). As the inverse sequence field spins opposite to the direct

field, the equivalent circuit for the inverse sequence could be obtained substituting the sliding, s, in the direct sequence circuit by the quantity (2-s). In the figure 2 (lower) the resulting circuit is shown. Now, the impedance variable component is expressed as (equation 3):

��� = −� � ∙���

��� (3)

�(���)

��= � � ∙

��

(���)� (4)

This expression is not as sensitive to the sliding changes,

as is shown in the equation 4. Taking into account that most of the induction motors works with very low sliding, of 3% order, two main observations could be done. The first is that the inverse sequence impedance is lower than the direct 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 current inverse sequence component, as shown in the equation 5.

���� = ���/��� (5)

Where:

Vr2 e Ir2 are the voltages and currents inverse sequence

components respectively, calculated with the symmetrical

components theory, as shown in equations 6 and 7.

��� =�

�(�� + �

� ∙ �� + � ∙ ��) (6)

��� =�

�(�� + �

� ∙ �� + � ∙ ��) (7)

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 vectorj1 2 0e

.

When some deficiency in the isolation state of the stator is manifested, the symmetry is lost and the motor stops showing an inverse sequence current impedance constant 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 these effects, Z2ef is altered during an incipient fail, and could be used to monitoring purposes of the fails. Conducted experiments with this method conclude that the negative sequence impedance shows an evolution tendency determined by the presence of stator isolation failures; the module changes the value considerably, even when appears a short circuit affecting only a pair of turns. This method has not been implemented to an industrial level, because the development of equipments based on microcontrollers that allow making inverse sequence impedance calculus of industrial plant motors are just being performed.

A. Simulations with the finite elements method

To make the study, the software FLUX2D® [4] was used; it has a magnetic transitory formulation included, which solves the problem in discrete time points. The geometry of the materials and the development of the winding were obtained by fragmenting a real motor, in which field test were performed. Figure 3 shows the machine geometry entirety, in which stator and rotor core regions, and squirrel’s cage bars are shown. [5]

Fig. 3. Geometry and mesh of NEMA B motor

Figure 4 (top) shows electrical circuit used in the non-failure motor simulations. This circuit is divided in three parts: external sources, stator circuit and the squirrel cage. To make the different simulations of the short-circuit turns motor, the winding was divided in two parts, one corresponding to the short-circuit turns and the other corresponding to the other turns; adding an interrupter to cause the short circuit to the required turns.

In the figure 4 (lower) is shown the circuit used for

making that failure simulation [6].

Fig. 4. Connection circuit of the NEMA B motor without (A) and with (B)

short-circuit turns.

B. Electromagnetic torque analysis

In the figures 5 details of the torque curves obtained in the MEF simulations, in the starting and maximum torque zone, is shown. The change in the torque curve is not considerable when the motor has short-circuited phase A turns.

In order to analyze the torque curves, it could be

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. 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 maximum torque [6].

IV. INVERSE SEQUENCE IMPEDANCE ANALYSIS.

Based in the previously displayed theory, it proceeds to show the results obtained through the calculated inverse sequence impedance in the motor MEF simulations. From the obtained data in the transitory simulations, it’s possible to find the magnitude and phase angle for both voltage and current ones in the three signals and calculate the respective inverse sequence impedance for the motor with several short-circuit turns.

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-

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 -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.7. Fault current for several short turns.

The following figures show current spectra results for

the slightest and severe failure:

Fig.8. FFT Fase A para 5 espiras en corto y R=0.14.

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:

������������������ = ��� + �� ��(10)

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)

Lissajou curve represents the function among axis d and

q components iq=f(id). In the equation above, Lissajou curve for no faulted motor is a perfect circle with its center located in the origin and its diameter equals to (√6⁄2)I, as it can be observed in figure 8(a). As diameter is proportional to current amplitude, the curve becomes thicker as the motor load varies. In addition, current modules for no-fault motor only have a DC component.

B. Faulty condition

In a faulty condition, due to the particular components influenced from faults on stator currents, the shape of Lissajou’s curve becomes distorted. In [8,9], detection of rotor asymmetry by monitoring the Lissajou’s curve has been presented. The rim of the Lissajou’s curve becomes thicker when the rotor is asymmetrical. For example, the Lissajou’s curve for 10-broken rotor bars shown in Figure 10(b). This is one of advantages, which allows the detection of faulty conditions by monitoring the deviations of the acquired patterns. The results have shown that the sideband components in the stator currents influenced from the rotor asymmetry could be transformed to place at the frequency 2sf1 ,4sf1 around DC in the current modulus [10]

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.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

sequence Lissajou curve may show some distortions like shape of an ellipse. For example, Figure 10(d) shows the curve for a short-circuit fault between 6 turns. Additionally, the negative sequence is manifested in the power modules for a component at twice the fundamental frequency [13,14]. Table I summarizes the EPVA fault indicators.

TABLE I

INDICADORES DE FALLA SEGÚN LA CURVA DE LISSAJOU Y EL ESPECTRO DE

LOS MÓDULOS DE PARK

Condition The Lissajou’s curve Spectrum of Park’s

modulus Healthy Circle DC

Broken rotor bar sor End

rings

Círcle, thicker DC, 2���, 4���

Mix eccentricity Circle (Thicker for high degree of eccentricities)

DC, ��, 2��

Stator winding faault

Ellipse DC, ��, 2��, 2��

VII. ASSEMBLY TEST BENCH

For the realization of different laboratory tests was performed the next assembly:

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.12. FFT Phase A for 1 turn short and R = 0.14 Ohms

Fig.13. FFT Phase A for 14 turns short and all values of R

Below is Lissajou curve for 1 turn short with a limiting

resistor of 0.14 Ohms. As expected, due to the asymmetry in the stator field caused by the failure, the curve takes the form of an ellipse instead of a circle, which is indicative of the presence of shorted turns.

Fig.14. Lissajou curve for 1 turn short – Laboratory test.

A summary on a single graph the curves for short and 14

turns in all limiting resistor values:

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 may be due to harmonics inherent in the operation of the machine, like slot harmonics.

Analyzing the results achieved by the MEF was

observed that in the current spectrum there are harmonics at frequencies 180, 300, 400, 520, 760, 880 Hz. It is seen that 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

IX. REFERENCES

[1] D. F. Percy, J. L. Oslinger, “Pruebas de impulso y de alto voltaje de CD para la evaluación de devanados de maquinas rotativas.” Energy

Conversion Chair, Engineering Faculty, Universidad del Valle. Cali, Colombia 1998.

[2] D. F. Parra, G. O. Ocampo, “Estudio del comportamiento de motores de inducción ante fallas estatóricas”. Degree thesis. Universidad de Antioquia. Medellín, Colombia 2004.

[3] M. F. Cabañas, M. García Melero, G. A. Orcajo, J. M. Cano Rodríguez, J. S. Sariego. “Técnicas para el mantenimiento y diagnóstico de máquinas eléctricas rotativas”. Marcombo S.A. Barcelona, Spain 1998.

[4] FLUX2D®. Application software based on finite elements method, trade mark from CEDRAT group, information available on http://www.cedrat.com/.

[5] J. C. Urresty, “Diagnóstico de rotura de barras en un motor de inducción de Jaula de ardilla mediante la aplicación del método de Elementos finitos”. Degree thesis. Universidad del Valle. Engineering Faculty. Electronic and Electrical Engineering School. Cali, Colombia 2006.

[6] D. Díaz, R. Díaz, “Diagnóstico de fallas estatóricas en un motor de inducción de jaula de ardilla mediante la aplicación del método de elementos finitos”. Degree thesis. Universidad del Valle. Engineering Faculty. Electronic and Electrical Engineering School. Cali, Colombia 2007.

[7] FLUX users guide, www.cedrat.com [8] N. Benouzza, A. Benyettou, A. Bendiabdellah, “An Advance Park’s

Vectors Approach for Rotor Cage Diagnosis”, First International Symposium on Control, Communications and Signal Processing, 2004, page(s):461 – 464.

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[13] S. M. A. Cruz, A. J. M. Cardoso, “Stator Winding Fault Diagnosis in Three-Phase Synchronous and Asynchronous Motors, by the Extended Park’s Vector Approach”, IEEE Transactions on Industry Applications, Volume 37, Issue 5, Sept.-Oct. 2001 page(s):1227 – 1233.

[14] A. J. M. Cardoso, S. M. A. Cruz, D. S. B. Fonseca, “Inter-Turn Stator Winding Fault Diagnosis in Three-Phase Induction motors, by Park’s Vector Approach”, IEEE Transactions on Energy Conversion, Volume 14, Issue 3, Sept. 1999 page (s):595-598.

X. BIOGRAPHIES

Martha Cecilia Amaya Enciso: Electrical Engineer from the Universidad del Valle-Colombia. Master of Power Generation Systems from the same institution. Diplôme d’Études Approfondiees DEA of the Institut National Polytechnique, Grenoble-France. PH.D in Engineering of the Universidad del Valle. Professor of Energy Conversion Area at the Electrical and Electronic Engineering School of the Universidad del Valle, Cali, Colombia. His research field is the modeling, analyze and diagnosis of electrical machines in Energy Conversion Research Group. E-mail : martha.amaya@univalle.edu.co

Darío Díaz Sánchez was born in Santiago de Cali, Colombia, on April 2, 1981. He is electrical engineer graduated from the Universidad del Valle, Cali - Colombia in 2007 and currently studying last semester of master's degree in engineering at the same university. E-mail: dariodiazs@gmail.com

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