Analysis of Induction Motor with broken rotor bars Using Finite Element Method

Transcription

1 Analysis o Induction Motor with broken rotor bars Using Finite Element Method Salah Eddine Zouzou, Samia Kheli, Noura Halem and M. Sahraoui Electrical Engineering Laboratory o Biskra, Biskra, Algeria, zouzou_s@hotmail.com Abstract - The paper presents the use o the two-dimensional inite element method or modelling the three-phase squirrel-cage induction motor by using circuit-ield coupled method. In order to analyze the machine perormances, the voltage source is considered. The lux 2D magnetic analysis sotware is used or calculating the magnetic ield o an induction motor having a cage ault. The simulation results o transient and steady state are given, which veriies the reliability o this method. The experimental results prove that the proposed approach constitutes a useul tool or the study and diagnostics o induction motors. Keywords - Induction motor, inite element, broken rotor bars, time stepping inite element (TSFE), diagnosis, aults. I. INTRODUCTION Rotor aults o induction machines yield asymmetrical operation o this one, causing unbalanced currents, torque pulsation, increased losses and decreased average torque. The need or detection o rotor aults at an earlier stage, so that maintenance can be scheduled, has pushed the development o monitoring methods with increasing sensitivity and noise protection. For that, a model closer to reality considering aults conditions must be established. An analytical analysis method based on the rotating ield theory and coupled circuit was used []. In works, where the machine inductances are calculated and the machine perormance is studied under aulty conditions, the Winding Function Approach (WFA), is used, where several assumptions and approximations o the actual machine layout are made, like the eects o stator teeth and slots, which are omitted in the calculations[2]. The modelling with inite element method represents a high idelity electromagnetic behaviour. Which leads to more precise results than other models, as the actual geometry and winding layout o the machine are used. The consideration o the behaviour o the local electromagnetic induction machine provides a more accurate modelling. The numerical solution o Maxwell's equations governing the behaviour o electromagnetic ields and the consideration o the equations representing the electrical supply circuit o the machine reduces the simpliications made in the classical models. In analysis o induction motors, the input current, not the voltage, is usually used. The voltage source which is mainly discussed in this paper is more suitable than current source. The external circuit that represents the electrical sources and circuit components are coupled to the FEM. Only the terminal voltages applied to the motor are required as known input quantities, and the total terminal currents are the unknowns to be evaluated. The use o time-stepping inite elements is the most precise way, up to date, or modelling the coupled ield-circuits and motion o induction motors, accounting or both saturation, time and space harmonics. Indeed, the modelling o rotor mechanical motion and stator ield source variation simultaneously allows coupling the instantaneous ields o stator and rotor [3]-[6]. This paper presents the transient state modeling o cage induction motors using the coupled electric circuit with 2D inite element electromagnetic ield analysis. The lux 2D magnetic analysis sotware is used or calculating the magnetic ield o an induction motor or the normal rotor, and or broken bars. II. FINITE ELEMENT MODEL Generally, the electric machine and apparatus are excited by connecting the external constant power source. Thus, it is necessary that the characteristics will be calculated under the constant terminal voltage. In this paper, the three-phase induction motor is analyzed by inite element method taking into account the terminal voltage. All the stator and rotor slots are represented in the circuit domain by deining real constants to conductor area in the FE domain. The motor is excited to its rated voltage and requency using a three-phase voltage source. The ratings o the machine are presented in Table I. TABLE I. CHARACTERISTICS OF THE MACHINE Variable Rated Power Rated Voltage Frequency Rated Speed Value. kw 23 V 5 Hz 425 rpm Number o stator slots 36 Number o rotor bars 28 This work was supported by the DGRST, with PNR (ALGERIA)

2 Fig. shows a detail o the mesh used or simulation. The magnetic circuit o squirrel cage and the geometry are very close to the real machine. same region with no broken bars []. This is due to the act that in the broken bar region there is no localized conductor demagnetization eect since these bars carry no currents []. Fig.. Finite element meshes III. SIMULATION RESULTS In this paper, the induction motor is simulated under rated conditions. Fig. 2 shows the magnetic ield distribution at steady state or healthy rotor. When the slip is small, the eddy current in the secondary conductor is small either. Thereore, the lux passes through the inside o rotor because o small eect o the ield caused by eddy current. But above this, the results show that lux distribution is symmetrical in each pole. Fig. 3. Magnetic lux distribution at the transient state Top: Healthy rotor, Bottom: One broken bar Fig. 4 shows the waveorm o the air gap lux density along a circular contour in the air-gap. The lux densities have a symmetrical distribution in healthy state. The perturbation in the magnetic ield produced by 5 broken bars results in a nonsymmetrical ield [2]. 2. a) Healthy state.5 Radial lux density (T) Air gap (mm) 2. b) Rotor with 5 broken bars Fig. 2. Magnetic ield distribution. Fig. 3 shows the magnetic lux distribution or healthy rotor and with one broken bar at the transient state. When the slip is large, the eddy current shows a large value. This high value o slip is necessary to illustrate the eects o the broken bars on the ield. The concentration o magnetic lux is observed around the broken bar and creates asymmetric magnetic lux distribution [7]-[9]. One can notice that the region around the broken bar o the rotor has a higher degree o saturation in comparison to the Radial lux density (T) Air gap(mm) Fig. 4. Waveorm o the Air gap lux density Once the magnetic ield is determined by the time-stepping inite-element method, the magnetic torque is calculated using

3 the Maxwell stress tensor. The mechanical equation determines a new angular and radial position o the rotor. The time increment used or the numeric integration was.. The evolution o the stator current, speed and torque transients during the irst second ater the connection, or the case o healthy rotor are shown, respectively in ig. 5, 6 and 7. Fig. 8 shows the stator current at steady state or loaded machine o simulation analysis and experimental results. We can notice a good agreement between the results. 4 Srator current (A) Stator current (A) a) Time(s) Speed (rpm) Fig.5. Stator current Fig.6. Speed Stator current (A) b) Fig.8. Stator Current at steady state a) Computed b) Measured 2 Torque (Nm) V. SPECTRUM ANALYSIS OF STATOR CURRENT An induction machine rotor asymmetry introduced by broken bars produces spectrum lines o stator current at requencies: Fig.7. Electromagnetic torque s ( 2ks) = () bb ± Where s is the electrical supply requency, s is the slip, k =,2,3,..., respectively. IV. EXPERIMENTAL RESULTS In order to validate the simulation results, a special test model was used. It is a.kw 22/38V 5Hz our pole induction motor whose stator windings were modiied in order to have accessible several tapping. That can be used to introduce interturn short circuits with dierent number o turns. This test bench is available at the LAII in Poitiers, France. In Fig. 9, the spectra o the simulated stator current with healthy rotor and with one broken bars are presented. In case o broken rotor bar, the rotor is electrically asymmetric and the backward rotating ield is created. The current spectrum reveals sidebands expected around the supply requency given by () [3]-[4].

4 a) Magnitude(dB) Magnitude(dB) Fig.. Simulated current spectrum b) Fig. 9. Simulated current spectrum a) Healthy rotor b) Rotor with broken bar In order to have a better understanding o rotor broken bar, it may be necessary to examine the higher requency components o the requency spectra. When we took into account the space harmonics, additional requency appear at requencies given by: k = s ( s ± s p bb ) 2 (2) Where, p is the number o pole pairs and k/p =, 3, 5, 7. The spectra o the stator current o a loaded machine when it runs in healthy conditions are shown in Fig.. It is obvious that besides the supply requency component, higher requency components exist around the principal slot Harmonics as was predicted. Some requency components (25Hz, 35Hz, etc.) exist which are a result o the saturation o magnetic material. Due to the coniguration o three phase windings, harmonic orders that exist are: k/p =, 5, 7, In this simulation, magnetic saturation patterns cause the 3 rd harmonic and it s multiple to appear as non-zero components in the spectra o the phase currents. The spectra o the stator current o a loaded machine when it runs in aulty conditions are shown in Fig.. The stator current requency described by () and (2) can be detected over the observation bandwidth between Hz and Hz. The spectrum o Fig. 2 shows the measured current waveorm spectra with healthy rotor and with one broken bar. The current spectrum reveals sidebands expected around the supply requency. Even or a motor in a healthy state, there are always requency components but o low amplitudes, this is due to the natural asymmetry o the motor, and on the other hand rom the power supply (distortion in the power supply voltage waveorm). As can be clearly seen through Fig. 2, the occurrence o one broken rotor bar increases signiicantly the magnitudes o several sidebands around the undamental Fig.. Simulated current spectrum with one broken bar Fig.2. Measured Current spectrum Top: Healthy rotor, Bottom: one broken bar

5 The spectrum o Fig. 3 shows the measured current waveorm spectra with healthy rotor. We notice the presence o the slot harmonics in addition to the harmonics due to saturation. The lower rotor slot harmonic is visible at 62 Hz. As envisaged during simulation, we show the presence o the harmonics components o high requencies. In order to avoid any misinterpretation, all spectral components having magnitudes less than -7 db are assumed as noise Fig.3. Measured current spectrum Furthermore, the Fig. 4 shows, clearly, considerable changes in magnitude or the sidebands around the 3rd, 5th and 7th current time harmonics, or a motor with one broken bar Fig.4. Measured current spectrum with one broken bar VI. CONCLUSION This paper presents the circuit coupled inite element method used to modeling the Three-Phase Squirrel Cage Induction Motor. For this purpose, the time-stepping inite element method (TSFE) was proposed. The determination o magnetic lux density waveorm, magnetic lux distribution was obtained. The perturbation in the air-gap magnetic ield produced by broken bars results in a non-symetrical ield. The stator current waveorm obtained with simulation was in good agreement with the experimental results. The simulation waveorms o speed and torque transients o induction motor during start-up conirm the known experimental results. As envisaged during simulation, the presence o harmonics in current spectra at low and high requency conirm the experimental results, proving that the proposed approach constitutes a useul tool or the study and diagnostics o induction motors. It will be mentioned that this approach is limited only to the evaluation o the component requencies induced by the broken bars ault. ACKNOWLEDGMENTS The authors would like to thank Proessor Champenois at the LAII laboratory, Poitiers, France, or his help. REFERENCES [] A. Ghoggal, M. Sahraoui and S. E. Zouzou, Analytical and experimental study o a squirrel cage induction motors with rotor bar aults, Advances in Modelling, Measurement and Control,A : General Physics and Electrical Applications, AMSE, vol. 8, no. 2, pp. 43-6, 28. [2] S. E. Zouzou, A. Ghoggal, A. Aboubou, M. Sahraoui, and H. Razik, Modelling o induction machines with skewed rotor slots dedicated to rotor aults, presented at the IEEE International Symposium on Diagnostics or Electric Machines, Power Electronics and Drives, Vienna, Austria, 7-9 Sep. 25. [3] Y. Ouazir, N. Takorabet, R. Ibtiouen, and M. Benhaddadi, Time-stepping FE analysis o cage induction motor with air-gap interace coupling taking Into account phase-belt harmonics, IEEE Trans. Magn, vol. 45, pp , Mar. 29. [4] J. Faiz, B. M. Ebrahimi, and M. B. B. Shariian, Time stepping inite element analysis o broken bars ault in a three-phase squirrel-cage induction motor, Progress In Electromagnetics Research, vol. 68, pp. 53-7, 27. [5] J. F. Bangura, N. A. Demerdash, Diagnosis and characterization o eects o broken bars and connectors in squirrel-cage induction motor by time-stepping coupled FE state space modeling approach, IEEE Trans. Energy Convers., vol. 4, pp , Apr [6] X. Ying, Characteristic perormance analysis o squirrel cage induction motor with broken bars, IEEE Trans. Magn, vol. 45, pp , Feb. 29. [7] R. Fiser, S. Ferkolj, Application o a inite element method to predict damaged induction motor perormance, IEEE Trans. Magn, vol. 37, Part, pp , September 2. [8] G. H. Jang, S. J. Park, Simulation o the electromechanical aults in a single-phase squirrel cage induction motor, IEEE Trans. Magn, vol. 39, pp , Sep. 23. [9] C. J. Aileen, S. Nagarajan and S. R. Reddy, Detection o broken bars in three phase squirrel cage induction motor using inite element method, presented at the International Conerence on Emerging Trends in Electrical and Computer Technology (ICETECT), Nagercoil, India, Mar. 2. [] J. Sprooten, J. C. Maun, Inluence o saturation level on the eect o broken bars in induction motors using undamental electromagnetic laws and inite element simulations, IEEE Trans. Energy Convers., vol. 24, pp , Sep. 29. [] L. Weili, X. Ying, S. Jiaeng, L. Yingli, Finite-element analysis o ield distribution and characteristic perormance o squirrel-cage induction motor with broken bars, IEEE Trans. Magn., vol. 43, pp , Apr. 27. [2] K. J. Hammadi, D. Ishak, and W. Salah, Rotor ault diagnosis based on current signatures in squirrel-cage induction motor, presented at the International Conerence on Electronic Devices, Systems and Applications (ICEDSA), Kuala Lumpur, Malaysia, pp. 2-25, -3 Apr. 2. [3] M. Riera-Guasp, M. F. Cabanas, J. A. Antonino-Daviu, M. Pineda- Sanchez, and C. H. R. Garcia, Inluence o nonconsecutive bar breakages in motor current signature analysis or the diagnosis o rotor aults in induction motors, IEEE Trans. Energy Convers., vol. 25, pp.8-89, March 2. [4] J. Faiz, B. M. Ebrahimi, Locating rotor broken bars in induction motors using inite element method, Energy Conversion and Management, vol. 5, pp. 25-3, Jan. 29.