Effects of the Short-Circuit Faults in the Stator Winding

th

The 8 International Symposium on ADVANCED TOPICS IN ELECTRICAL ENGINEERING The Faculty of Electrical Engineering, U.P.B., Bucharest, May 23-24, 2013

Effects of the Short-Circuit Faults in the Stator Winding of Induction Motors and Fault Detection through the Magnetic Field Harmonics Alexandru-Ionel Constantin1, Member IEEE, Virgiliu FIRETEANU2, Vincent LECONTE3 1,2 Electrical Engineering Faculty POLITEHNICA University of Bucharest 313 Splaiul Independentei 060042 Bucharest, ROMANIA 3 CEDRAT S.A. FRANCE [email protected], [email protected],[email protected] Abstract- Based on the finite element analysis of the electromagnetic field in time domain, this paper studies effects of the short-circuit faults in the stator winding of an induction motor and the influence of this fault on the magnetic field outside the motor. The detection of the short-circuit fault through the magnetic field is based on the comparison of harmonics of the output voltage of coil sensors for the healthy and faulty motor states. The influence of the magnetic saturation of the motor on the fault diagnose efficiency is studied. Keywords: Induction machine, stator winding short-circuit, fault detection, finite element analysis

I.

INTRODUCTION

The interest for the finite element investigation of the electromagnetic field in electrical machines increases. The numerical simulation of the healthy and faulty operation states, respectively the study and detection of different faults based on the finite element models, offers a deeper understanting of the associated phenomena [1 – 10]. This paper studies short-circuit faults in the stator winding [10] based on Flux2D finite element models [11]. The effects of faults on the time variation of the current, of the electromagnetic torque and of the unbalanced force acting on the rotor are studied. The magnetic field outside the motor is investigated through the time variation of the output voltage of coil sensors in case of healthy and faulty motor states, for no load and for loaded motor operation. II.

nonconductive regions, 48 stator slots - nonconductive, nonmagnetic and source regions, the 32 bars of the rotor squirrel cage aluminum made, the motor frame (8 mm thickness, 0.045 m) and the motor shaft, which are regions of solid conductor type, the motor airgap and the infinitely extended air region outside the motor. In order to investigate the magnetic field in this last region, the computation domain includes two coil sensors around a magnetic core, SensorOx, whose sides in Fig. 1 (b) is blue colored, and SensorOy in red color, located in near proximity of the motor.

(a)

FINITE ELEMENT MODEL AND THE TIME DOMAIN ANALYSYS OF THE ELECTROMAGNETIC FIELD FOR THE INVESTIGATION OF THE S HORT -C IRCUIT FAULTS

The geometry and mesh of the electromagnetic field 2D computation domain in Fig. 1 (a), (b) and the circuit model, Fig. 1 (c), correspond to a four poles squirrel cage induction motor of 11 kW, rated supplied 3 x 380 V, fn = 50 Hz, delta winding connection. The computation domain contains the stator and the rotor cores that are magnetic and

(c) Fig. 1. Geometry (a) and mesh (b) of the electromagnetic field computation domain and the circuit model (c)

The Phase B and the Phase C of the stator winding are represented in the circuit model, Fig. 1 (c), by four coil components that reflects the four groups representing each the four go- and the four return sides of the elementary coils. Each elementary coil occupies two stator slots and four elementary coils series connected represent one stator pole. The three inductance components in Fig. 1 (c) correspond to the stator winding outside the stator core. It is the Phase A, Fig. 1 (c), of the stator winding where the shortcircuit faults are considered. The part of this winding representing one stator pole, which regroups four elementary coils, is represented in the circuit model, Fig. 1 (c), through eight coil components. These are the go- and the return sides of the four elementary coils. Through the four resistors in the circuit model, Fig. 1 (c), it is possible to simulate the short-circuit of one, of two, of three or of four elementary coils of of the Phase A. For each of the two sensors, the circuit model, Fig. 1 (c), includes two coil components and a resistor of high resistance for the evaluation of sensors output voltage. The state variable of the electromagnetic field - the magnetic vector potential A(x,y,z,t), satisfies the following differential equations: c u r l 1   c u r l A     A  t    J s  x , y , z , t  ; d i v A  0 (1) where  is the magnetic permeability,  is the resistivity and Js is the current density in the stator slots. The term (A/t)/ reflects the density of the induced current in the regions of solid conductor type. In the 2D field model considered in this paper the source current density has the structure Js[0, 0, Js(x,y,t)]. As consequence, the vector potential A[0, 0, As(x,y,t)] is oriented along the Oz axis and does not depends on the coordinate z. The second equation (1) is implicitly satisfied. The investigation of the electromagnetic field inside and outside the motor uses the transient magnetic model of the induction motor [6] with imposed constant speed 1450 rpm for the rated load motor operation and the synchronous speed 1500 rpm for ideal no load motor operation. The value t = 0.05 ms of the time step is considered in the time domain analysis of the electromagnetic field. Thus, the harmonic variations with the frequency equal or less than 1000 Hz are evaluated in at least 20 steps on a period. The results in this paper concern the steady state of the electromagnetic field, in which the amplitudes of all electric and field quantities are time independent. Since the steady state of the transient solution is reached in about 0.5 s from the computation start (t = 0), the time interval (0.52…0.6) s is considered for the results analysis. III.

EFFECTS OF STATOR SHORT-CIRCUIT FAULTS ON MOTOR OPERATION PARAMETERS

Taking into account small values of the resistance for the first, respectively for the last short-circuit resistors in the Phase A of the motor, Fig. 1 (c), the short-circuits of one elementary coil, respectively of four elementary coils series connected are simulated. The time variation of the Phase A current for the loaded motor is different for the healthy state, Fig. 2 (a), for the faulty states with one elementary coil in

shortcircuit, Fig. 2 (b) and with four coils in short-circuit, Fig. 2 (c). The corresponding rms values of the Phase A current are 12.88 A, 13.83 A and 28.29 A respectively. The figures 3 and 4 show amplitudes of the harmonics of the Phase A current for the healthy (cyan) and faulty motors (red) in the cases one coil short-circuit, respectively four coils short-circuit. If in the first case the amplitude of the main harmonic of 50 Hz has only a slight increase, in the second case this harmonic increases 2.2 times.

Fig. 2. Time variation of the Phase A current for the healthy motor (a), one coil short-circuit fault (b) and four coils short-circuit fault (c).

Fig. 3. Amplitude of the Phase A current harmonics. Comparison healthy motor – motor with one coil fault

Fig. 4. Amplitude of the Phase A current harmonics. Comparison healthy motor – motor with four coils fault

Related the harmonics of the Phase A current with frequency higher than 500 Hz, only the 725 Hz harmonic presents an important increase in case of the one coil shortcircuit, Fig. 3. For the second faulty case, Fig. 4, the most important in amplitude over 500 Hz harmonic, the harmonic of 825 Hz increases with 20.36 %. The others harmonics, of 925 Hz, 625 Hz, 550 Hz and 750 Hz, increase from healthy to faulty states with 34.1 %, 246.9 %, 76.0 %, 677.1 %. In comparison with the healthy state, Fig. 5 (a), the time variation of the electromagnetic torque for the loaded motor

is slightly different for the case one elementary coil in shortcircuit, Fig. 5 (b). The difference is much more important in the case four coils in short-circuit, Fig. 5 (c). The corresponding mean values of the electromagnetic torque are 76.78 Nm, 76.26 Nm and 73.01 Nm, respectively.

coil short-circuit to the four coils short-circuit. For example, the amplitude of the 100 Hz harmonic increases 19.55 times.

Fig. 7. Time variation of the module of the electromagnetic force: (a) one coil short-circuit fault, (b) four coils short-circuit fault.

Fig. 5. Time variation of the electromagnetic torque for the healthy motor (a), one coil short-circuit fault (b) and four coils short-circuit fault (c).

The increase of the number of harmonics of the electromagnetic torque with frequency lower than 2500 Hz is evident when pass from the healthy, Fig. 6 (a), to one coil short-circuit fault, Fig. 6 (b), and to four coils short-circuit, Fig. 6 (c). The amplitude of the 100 Hz harmonic increases 963.8 times from case (a) to case (b) and 4052.8 times from (a) to (c).

Fig. 6. Amplitude of the electromagnetic torque harmonics: (a) healthy motor ; (b) one coil short-circuit fault; (c) four coils short-circuit fault

The most important effect of the short-circuit faults in the stator winding concerns the unbalanced electromagnetic force on the rotor. The mean value in time of the module of this force, which is under 1 N for the healthy motor state, is 145.64 N for the one coil short-circuit fault, Fig. 7 (a), and 1102.8 N for the four coils shortcircuit fault, Fig. 7 (b). There is an important increase of the low frequency harmonics, under 300 Hz, Fig. 8, when pass from the one

Fig. 8. Amplitude of the harmonics of the module of the electromagnetic force on the rotor: (a) one coil short-circuit; (b) four coils short-circuit

IV.

THE SHORT-CIRCUIT FAULTS IN THE STATOR WINDING AND THE OUTPUT VOLTAGE OF THE COIL SENSORS

This section analyses results related the time dependence of the output voltage of SensorOx and SensorOy coil sensors and the changes in amplitude of harmonics of this voltage in the ranges [0 … 1000] Hz and [500 … 1000] Hz when pass from the healthy state to one of the faulty states , one coil short-circuit, respectively four coils short-circuit. The main interest is to choose an efficient solution for the detection of faulty states of the motor through the magnetic field outside the motor. The loaded motor having the speed 1450 rpm is considered in the first part and the ideal no load operation with 1500 rpm after. Loaded motor. The rms value of the SensorOx output voltage corresponding to the time dependences in Fig. 9 is as follows: 1148.0 mV for the healthy motor (a), 1154.9 mV for the one coil short-circuit fault (b) and 1708.0 mV for the four coils short-circuit (c).

Fig. 9. Time variation of SensoOx voltage for the healthy motor (a), one coil short-circuit fault (b) and four coils short-circuit fault (c).

The comparison of the amplitude of different harmonics in Fig. 10 for the healthy state and the one coil short-circuit faulty state of the motor does not enphasizes important differences. Contrarely, the same comparison for the four coil short-circuit, Fig. 11, shows an important increase in the faulty state of the amplitude of the 50 Hz harmonic and the increase of the amplitude of an important number of harmonics in the range [500 ... 1000] Hz. The most important as amplitude, the harmonic of 925 Hz, increases roughly two times, and the 550 Hz, 650 Hz, 850 Hz and 950 Hz harmonics increases more than two times in the faulty state. Fig. 12. Time variation of SensoOy voltage for the healthy motor (a), one coil short-circuit fault (b) and four coils short-circuit fault (c).

Fig. 10. Amplitude of harmonics of SensorOx voltage. Comparison healthy motor - one coil shortcircuit fault.

Similar results for the SensorOy coil sensor, related the time variation of the output voltage are presented in Figs. 12 and 13. The rms value of the SensorOy output voltage are as follows: 1448.5 mV for the healthy motor (a), 1396.5 mV in case of the one coil short-circuit fault (b) and 870.4 mV in case of the four coils short-circuit (c).

Fig. 13. Amplitude of harmonics of SensorOy voltage. Comparison healthy motor – motor with one coil shortcircuit fault

The finding issued from the comparison of the amplitude of different harmonics for the healthy state and the two faulty states, Figs. 13 and 14, is different from those corresponding to SensorOx. The amplitude of an important number of harmonics generated by the short-circuit fault decreases..

Fig. 14. Amplitude of harmonics of SensorOy voltage. Comparison healthy motor – motor with four coils shortcircuit fault. Fig. 11. Amplitude of harmonics of SensorOx voltage. Comparison healthy motor – motor with four coils shortcircuit fault

No load motor operation. The rms value of the SensorOx output voltage corresponding to the time variations in Fig. 15, are as follows: 1620.2 mV for the healthy motor (a) and 1570.6 mV for the one coil short-circuit fault (b) .

Similarly with the SensorOx case, the amplitude of some harmonics in the range [500 ... 1000] Hz, Fig. 18, have a very important increase when pass from the healthy state to the faulty state.

Fig. 15. Time variation of SensoOx voltage for the healthy motor (a) and for the motor with one coil short-circuit fault (b). No load motor operation.

Fig. 18. Amplitude of harmonics of SensorOy voltage. Comparison healthy motor – motor with one coil shortcircuit fault. No load motor operation.

The amplitude of some harmonics in the range [500 ... 1000] Hz, Fig. 16, have a very important increase when pass from the healthy state to the faulty state.

The comparison of the results for the cases Loded motor and No load motor operation shows that the last one must be the choice for the short-circuit fault detection based on harmonics of the magnetic field outside the motor. The 650 Hz is the frequency of the most appropriate harmonics for the fault detection with both sensors. V.

Fig. 16. Amplitude of harmonics of SensorOx voltage. Comparison healthy motor – motor with one coil shortcircuit fault. No load motor operation.

The rms value of the SensorOy output voltage corresponding to the time variations in Fig. 17 are as follows: : 1682.5 mV for the healthy motor (a) and 1504.3 mV for one coil short-circuit fault (b).

Fig. 17. Time variation of SensorOy voltage for the healthy motor (a) and motor with one coil short-circuit fault (b). No load motor operation.

INFLUENCE OF THE MAGNETIC SATURATION ON THE EFFICIENCY OF THE SHORT-CIRCUIT FAULTS DETECTION

The motor without frame is considered for the study of the influence of the magnetic saturation. The one coil shortcircuit fault is considered. All simulations whose results were previously analysed correspond to the rated value 380 V of the rms voltage of the three voltage sources in Fig. 1 (c). The corresponding maps of the magnetic flux density, Fig. 19 (a), and of the relative magnetic permeability, Fig. 20 (a), emphasise an important level of the magnetic saturation of the motor magnetic cores. If the supply voltage decreases from 380 V to 220 V, the saturation decreases and the mean value of the magnetic permeability, Fig. 20 (b), increases. The time variation of the magnetic field outside the motor will be less influenced by the magnetic nonlinearity of the motor laminations.

(a) (b) Fig. 19. Maps of the magnetic flux density for 380 V (a) and for 220 V supply (b)

(a) (b) Fig. 20. Maps of the relative magnetic permeability for 380 V (a) and for 220 V supply (b)

Loaded motor. The most important harmonic of the coil sensors output voltage for motor operation at 1450 rpm has the frequency 525 Hz. The results in Table 1 show the decrease of the amplitude of this harmonic when the short-circuit fault appears, SensorOy being more sensitive. The decrease of the amplitude of the 525 Hz harmonic when pass from the healthy state to the faulty state is more important when the level of the magnetic saturation decreases, respectively when the 380 V supply is replaced by 220 V. Table 1. Amplitude of SensorOx and SensorOy 525 Hz harmonic in [mV] SensorOx SensorOy Supply [V] Healthy Faulty Faulty / Healthy

380 553.6 519.8 0.94

220 8.232 6.917 0.84

380 622.6 266.7 0.43

220 11.78 3.473 0.295

No load motor operation. In case of 1500 rpm motor speed, two harmonics were considered in Tables 2 and 3. The increase of the amplitude when the fault appears is much more important for the 650 Hz than for 550 Hz. This increase is much more important for the 550 Hz harmonic when pass from the 380 V supply to 220 V. Consequently, the no load motor operation with supply voltage lower than the rated value it is a better solution to detect the appearance of a shortcircuit in the stator winding through harmonics of the magnetic field outside the motor with frequency in the range [500 … 1000] Hz Table 2. Amplitude of SensorOx and SensorOy 550 Hz harmonic in [mV] SensorOx SensorOy Supply [V] Healthy Faulty Faulty / Healthy

380 64.4 76.7 1.19

220 0.199 4.861 24.43

380 31.1 130.3 4.19

220 0.157 10.66 67.90

Table 3. Amplitude of SensorOx and SensorOy 650 Hz harmonic in [mV] SensorOx SensorOy Supply [V] 380 220 380 220 Healthy 85.2 0.583 67.2 1.689 Faulty 748.7 7.183 659.1 25.97 Faulty / Healthy 8.78 12.32 9.81 15.38

VI.

CONCLUSIONS

The short-circuit fault in the stator winding is reflected in the rms values and the spectrum of stator currents harmonics and in the harmonics spectrum of the electromagnetic torque. But the most

important effect of this fault related the motor operation concerns the unbalanced electromagnetic force on the rotor armature. The detection of the short –circuit fault in the stator winding based on the evaluation of the harmonic s in the range [500 --- 1000] Hz of the magnetic field outside the motor represents a simple and very efficient solution. It was proved that the change of the amplitude of some harmonics of the output voltage of coil sensors placed near the motor when the short-circuit appears is more important in case of motor no-load operation than in case of loaded motor. A better efficiency of the fault detection is obtained if the magnetic core of the motor is characterized by a lower magnetic saturation. It rest to verify in perspective if similar conclusions are valid for motors with another number of poles or with other numbers of stator and rotor slots. REFERENCES [1]

J. Penman, H.G. Sedding and W.T. Fink, “Detection and location of interturn short circuits in the stator windings of operating motors,” IEEE Trans. Energy Conversion., vol. 9, No. 4, pp. 652-658, Dec. 1994. [2] M. E. H. Benbouzid, “A review of induction motors signature analysis as a medium for faults detection,” IEEE Trans. Ind. Electron., vol. 47, no. 5, pp. 984–993, Oct. 2000. [3] H. Henao, C. Demian, and G.A. Capolino, “A frequency-domain detection of stator winding faults in induction machines using an external flux sensor”, IEEE Trans. Ind. Appl., vol. 39, pp. 1272–1279, Sept/Oct. 2003. [4] T. Assaf, H. Henao, G.A. Capolino, “Simplified axial flux spectrum method to detect incipient stator inter-turn short-circuits in induction machine”, in Proc. IEEE ISIE. 2004, Ajaccio, France, pp. 815–819, vol. 2, 2004. [5] M. D. Negrea, “Electromagnetic Flux Monitoring for Detecting Faults in Electrical Machines”, doctoral disertation at Helsinki University of Technology, Laboratory of Electromechanics, November, 2006. [6] V. Fireteanu, P. Taras, “Teaching induction machine through finite element models”, Proc. of XVIII ICEM Conf., Sept. 6-9, 2008, Vilamoura, Portugual. [7] B. Vaseghi, N. Takorabet, and F. Meibody-Tabar, "Transient finite element analysis of induction machines with stator winding turn fault," Progress In Electromagnetics Research (PIER) Journals, vol. 95, pp. 118, 2009. [8] A. Ceban, “Methode globale de diagnostique des machines electriques” , PhD Thesis, LSEE Lab., Université d’Artois, France 2012. [9] L. Frosini, A. Borin, L. Girometta, G. Venchi, “A novel approach to detect short circuits in low voltage induction motor by stray flux measurement”, 20th International Conference on Electrical Machines (ICEM ’12), pp. 1536 – 1542, Sept. 2012. [10] R. Pusca, R. Romary, A. Ceban, “Detection of Inter-turn Short Circuits in Induction Machines Without Knowledge of the Healthy State”, Proc. of ICEM Conf., September 2-5, 2012, Marseille, France. [11] FLUX V11.1 Users Guide - CEDRAT