Interturn short circuit analysis in an induction machine by fem
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Interturn Short-circuit Analysis in an InductionMachine by Finite Elements Method and Field Tests D. Díaz, M. C. Amaya Abstract -- The torque and sequence negative impedanceanalysis, with the evolution of short-circuit turns of the statorphase winding in a 3HP induction machine was done in thepresent paper. Index Terms-- Electromagnetic torque, fast Fouriertransform, finite element method, induction machine, inter-turn short-circuit, inverse sequence impedance, Parks Vector. I. NOMENCLATUREFFT: 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 anthat allows knowing the motor’s condition without induction motor, using a parameter called inverse sequenceintervening 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 areduction condition, related to specification minimal motor never is well-equilibrate. There always are lightrequirements, and is the result of the normal waste, a bad differences between the efficient values of the voltage anddesign or poor specification, incorrect assembly, misuse or phase angles. The good-condition induction motora combination of all. If a failure is not detected on time, or behavior, fed by an imbalanced system, could be analyzedif it develops farther, it could lead to the machine’s by the study of the inverse and direct sequence equivalentcollapse. Nowadays it is important to consider the circuits.implementation of a failure diagnosis strategy, to increasethe machine useful life components, increasing the plant’s Figure 2 (top) shows the equivalent direct sequenceavailability and productivity. To determine motor problems circuit, where Rs and Rr represent the stator and rotorit has to be confident and secure and electrical motors reactances respectively. The stator and rotor leakageanalysis has to contain results in this failure zones: power reactances and the magnetization reactance correspond tocircuit, isolation, stator, rotor, air-gap and energy quality. Xs, Xr and Xm respectively.The stator fails form the 37% of the electrical motorfailures, being the inter-turns short circuit the mostcommon, which reduces the ability of produce a balancedelectrical field, causing vibration increase on the machine,and consequently, isolation degradation and motor bearingsfailure.Figure 1 shows the failure diagnosis methods in rotatingmachines [1, 2]. This work resumes the use of the noconventional electromagnetic torque and inverse sequenceimpedance analysis methods, because the conventional onesshow the disadvantage that could damage the isolationwhen 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).
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The variable component of the rotor RL1 resistance is theone that allow calculating the mechanical power of the When some deficiency in the isolation state of the statormotor, 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 theshown 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 appearsfield, the equivalent circuit for the inverse sequence could a short circuit affecting only a pair of turns. This methodbe obtained substituting the sliding, s, in the direct sequence has not been implemented to an industrial level, because thecircuit by the quantity (2-s). In the figure 2 (lower) the development of equipments based on microcontrollers thatresulting circuit is shown. Now, the impedance variable allow making inverse sequence impedance calculus ofcomponent 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 theas is shown in the equation 4. Taking into account that most winding were obtained by fragmenting a real motor, inof the induction motors works with very low sliding, of 3% which field test were performed. Figure 3 shows theorder, two main observations could be done. The first is machine geometry entirety, in which stator and rotor corethat 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 inversesequence voltage low levels, high inverse sequence currentlevels are circling. This is a problem when is time tomonitoring the line current, because this is affected by littlevoltage unbalances, and hide any symptom of incipient fail. Another interesting observation is that, unlike the directsequence impedance, the inverse sequence impedance of aninduction motor is less sensible to the sliding changes. Inconsequence the inverse sequence impedance is practicallyconstant to the load variations and the inverse sequencecurrent flux. This impedance value could be calculated as the quotientbetween the voltages inverse sequence component and the Fig. 3. Geometry and mesh of NEMA B motorcurrent inverse sequence component, as shown in theequation 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 turnsVr2 e Ir2 are the voltages and currents inverse sequence motor, the winding was divided in two parts, onecomponents respectively, calculated with the symmetrical corresponding to the short-circuit turns and the othercomponents 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 .
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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 theFig. 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 inversethe MEF simulations, in the starting and maximum torque sequence impedance in the motor MEF simulations. Fromzone, is shown. The change in the torque curve is not the obtained data in the transitory simulations, it’s possibleconsiderable when the motor has short-circuited phase A to find the magnitude and phase angle for both voltage andturns. 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 workpoint (1740 rpm) are light. The curves between the values0.001 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-
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circuit turns increases; it increases the inverse sequenceflow in one of the phases. Thereby when the inversesequence impedance is inversely proportional to thesequence current, it decreases (Z= V/I). V. MOTOR CURRENT SIGNATURE Given below are the results of inter-turn short-circuitfrom a statoric phase winding by means of theimplementation of spectral current analysis applied to thegotten results by running simulations through MEF. Thesimulation was implemented on magneto-transient modefrom 0 to 0.4 seconds, time steps of 0.0005 seconds,everything was carried out looking for enough data to applyFFT. 5 failure states were simulated, each one with 5different 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 withoutthe limiting resistance, it means a direct short-circuit. In thelaboratory the resistance had to be implemented to limit thecurrent caused by the fault due such a high risk representedfor personnel that perform the test and for the machine aswell. Therefore, to validate the results(facing simulatedresults with field tests) a resistance was introduced in thecircuit model corresponding to the motor under study bymeans of MEF.. Due to the amount of data, only the results for theslightest and severe failure will be shown (5 and 14 short-circuited turns). The progress for the fault current can beobserved 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 forthe 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)
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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 theq 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 moduleslocated in the origin and its diameter equals to (√6⁄2)I, as it for a component at twice the fundamental frequencycan 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 themotor load varies. In addition, current modules for no-fault TABLE I INDICADORES DE FALLA SEGÚN LA CURVA DE LISSAJOU Y EL ESPECTRO DEmotor only have a DC component. LOS MÓDULOS DE PARK Condition The Lissajou’s curve Spectrum ofB. Faulty condition Park’s In a faulty condition, due to the particular components modulusinfluenced from faults on stator currents, the shape of Healthy Circle DC Broken rotor Círcle, thicker DC, 2 , 4Lissajou’s curve becomes distorted. In [8,9], detection of bar sor Endrotor asymmetry by monitoring the Lissajou’s curve has ringsbeen presented. The rim of the Lissajou’s curve becomes Mix eccentricity Circle (Thicker for DC, ,2thicker when the rotor is asymmetrical. For example, the high degree ofLissajou’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 2acquired patterns. The results have shown that the sidebandcomponents in the stator currents influenced from the rotor VII. ASSEMBLY TEST BENCHasymmetry could be transformed to place at the frequency2sf1 ,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 veryuseful for the detection of eccentricity [11,12] because thecurve 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 thepower modules and Lissajou curve. In normal conditions(without fail), the stator currents contain only the positivesequence component, so that the circular form Lissajoucurve is still valid. However, under abnormal condition, theimpedance of the phases are unbalancing by the defect inwindings, causing unbalanced currents and introducesnegative sequence component. Due to this negative
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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 limitingresistor of 0.14 Ohms. As expected, due to the asymmetry Analyzing the results achieved by the MEF wasin the stator field caused by the failure, the curve takes the observed that in the current spectrum there are harmonics atform of an ellipse instead of a circle, which is indicative of frequencies 180, 300, 400, 520, 760, 880 Hz. It is seen thatthe 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 [1] D. F. Percy, J. L. Oslinger, “Pruebas de impulso y de alto voltaje de A summary on a single graph the curves for short and 14 CD para la evaluación de devanados de maquinas rotativas.” Energy
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Conversion Chair, Engineering Faculty, Universidad del Valle. Cali, [11] A.J.M. Cardoso, E.S. Saraiva, “Predicting the Level of Airgap Colombia 1998. Eccentricities in Operating Three-Phase Induction Motors, by Park’s[2] D. F. Parra, G. O. Ocampo, “Estudio del comportamiento de motores Vector Approach”, Conference Record of the Industry Applications de inducción ante fallas estatóricas”. Degree thesis. Universidad de Society Annual Meeting, 1992., IEEE, 4-9 Oct. 1992 page(s):132 - Antioquia. Medellín, Colombia 2004. 135 vol.1.[3] M. F. Cabañas, M. García Melero, G. A. Orcajo, J. M. Cano [12] A.J.M. Cardoso, E.S. Saraiva, “Computer-Aided Detection of Airgap Rodríguez, J. S. Sariego. “Técnicas para el mantenimiento y Eccentricities in Operating Three-Phase Induction Motors by Park’s diagnóstico de máquinas eléctricas rotativas”. Marcombo S.A. Vector Approach”, IEEE Transactions on Industry Applications, Barcelona, Spain 1998. Volume 29, Issue 5, Sept.-Oct. 1993 page(s):897 – 901.[4] FLUX2D®. Application software based on finite elements method, [13] S. M. A. Cruz, A. J. M. Cardoso, “Stator Winding Fault Diagnosis in trade mark from CEDRAT group, information available on Three-Phase Synchronous and Asynchronous Motors, by the http://www.cedrat.com/. Extended Park’s Vector Approach”, IEEE Transactions on Industry[5] J. C. Urresty, “Diagnóstico de rotura de barras en un motor de Applications, Volume 37, Issue 5, Sept.-Oct. 2001 page(s):1227 – inducción de Jaula de ardilla mediante la aplicación del método de 1233. Elementos finitos”. Degree thesis. Universidad del Valle. [14] A. J. M. Cardoso, S. M. A. Cruz, D. S. B. Fonseca, “Inter-Turn Engineering Faculty. Electronic and Electrical Engineering School. Stator Winding Fault Diagnosis in Three-Phase Induction motors, by Cali, Colombia 2006. Park’s Vector Approach”, IEEE Transactions on Energy Conversion,[6] D. Díaz, R. Díaz, “Diagnóstico de fallas estatóricas en un motor de Volume 14, Issue 3, Sept. 1999 page (s):595-598. 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. X. BIOGRAPHIES Cali, Colombia 2007. Martha Cecilia Amaya Enciso: Electrical Engineer from the Universidad[7] FLUX users guide, www.cedrat.com del Valle-Colombia. Master of Power Generation Systems from the same[8] N. Benouzza, A. Benyettou, A. Bendiabdellah, “An Advance Park’s institution. Diplôme d’Études Approfondiees DEA of the Institut National 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 2004, page(s):461 – 464. Electronic Engineering School of the Universidad del Valle, Cali,[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 Cage Fault Diagnosis in Three-Phase Induction Motors, by Park’s electrical machines in Energy Conversion Research Group. E-mail : Vector Approach”, Industry Applications Conference, 1995. IEEE, martha.amaya@univalle.edu.co Volume 1, 8-12 Oct. 1995 page(s):642 - 646 vol.1.[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 masters 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 .
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