Rotor Bars Breakage in Railway Traction Squirrel Cage Induction ...

SDEMPED 2005 - International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives Vienna, Austria, 7-9 September 2005

Rotor Bars Breakage in Railway Traction Squirrel Cage Induction Motors and Diagnosis by MCSA Technique Part I : Accurate Fault Simulations and Spectral Analyses Claudio Bruzzese

Onorato Honorati

Ezio Santini

Department of Electrical Engineering University of Rome “La Sapienza” Via Eudossiana 18, 00184 Rome, Italy fax: 06 4883235 [email protected] Abstract - In this paper the rotor bar fault diagnosis problem for a particular induction motor (1.13 MW) employed in high speed-railway traction is considered, by getting realistic simulations of the electromechanical converter behaviour in specified working and feeding conditions. The use of a complete motor phase model and the implementation of the real GTOinverter waveforms (three-pulses PWM modulation) allow accurate computation of the machine currents (both stator and rotor currents), and of the real mechanical internal stresses. The numerous data needed for model settings were obtained by F.E.M. and identification of the inductance parameters was performed starting from few measured values and some informations about internal machine structure. Some simulations are shown, and matched with measured waveforms. Bar breakages are easily recognized as produced by PWMgenerated harmonic torques. The simulated stator phase currents are then analyzed by FFT in healthy and faulty rotor conditions. Finally, all the fault-related harmonic current components (sidebands) are found, and diagnostic criteria are evaluated and discussed. In a companion paper theoretical formulations were developed for frequency and amplitude sidebands prediction and calculation. Keywords – Induction Machine, Low-Frequency PWM, Rotor Fault Diagnosis, Spectral Analyses, Fault-Related Sidebands.

I. A SURVEY OF ROTOR FAULTS IN RAILWAY DRIVES Induction motors are widely used in industrial plants and in traction drives. Cheapness, robustness, and building simplicity are the leading points of strength. On the other hand, reliability has become an important aspect, since industrial outages have increasing costs [1]. Thus, monitoring techniques capable of early and precise fault detection are desirable. This is particularly true for railway traction applications, especially for high speed trains (TAV) or high frequentation trains (TAF). Rotor bars breakage is a classical and frequent kind of fault, which can lead, if not detected, to even much heavier faults (bars can lift out of rotor slots, and strike the stator windings [2]). The stator fault imposes the motor break-down, and consequently the vehicle stopping (the latter being unforeseeable, can happen in critical condition, as in a gallery or tunnel).

Often, rotor bars breakage rises from constructive defects or project errors. Excessive fatigue mechanical solicitations, not properly considered at an early stage of system planning, can rise due to harmonic torques produced by a nonsinusoidal motor feeding (low-frequency inverter feeding). Much research effort and numerous publications have been devoted to broken rotor bars detection and to fault gravity assessment, and effective procedures have been proposed that are of industrial interest [3]. Among them, MCSA (motor current signature analysis) appears as the most developed and proved, due to non-invasive and continuous on-line monitoring capability [2]. This technique is based on the registration and harmonic analysis of the motor phase current, with the aim to evaluate some particular frequency components whose amplitudes are strictly related to a given fault and his gravity. Ulterior aim of this paper is to demonstrate, by complete simulations, the diagnostic capabilities of such a technique for the particular problem considered, and some improvements are also suggested. II. HARMONIC TORQUES AND CURRENT SIDEBANDS In railway traction drives are often employed GTO-based three-phase converters for motor feeding. These converters are characterized by a low switching frequency (hundreds of hertz), thus forcing system designers to make use of a lownumber pulses PWM modulation (typically three-pulses or five-pulses, for the higher output frequencies, Fig.1). fswitch (Hz) 300 250 0-20 Hz: ASYNCHRONOUS 20-50 Hz: SYNCH. FIVE-PULSES 50-100 Hz: SYNCH. THREE-PULSES 100-133 Hz: SQUARE-WAVE

150 100

0

20

50

100

133

ffeeding(Hz)

Fig.1. Switching frequency versus motor feeding frequency. The inverter modulation ranges are shown.

In this paper we focus on the synchronous three-pulses modulation. The typical voltage waveform produced by the

inverter is shown in Fig.2-left. By varying the "notch" length ‘x’ the fundamental harmonic amplitude can be modulated. Unfortunately, this waveform contains large lowfrequency harmonicas such us 3rd, 5th, 7th (odd frequencies), that produce correspondent large harmonic currents, with exception of 3rd and her multiples (since the motor is threewire connected). 5th and 7th current harmonicas are particularly harmful, since they generate heavy 6th harmonic torques. These torque harmonicas produce strong adjunctive solicitations on the rotor, and they can eventually excite some cage resonant vibration modes, when forcing torque frequency matches a mechanical resonance frequency. v AO (V )

notch (x)

Fig.3. Stator phase current (left) and motor torque (right), three broken bars.

ω sω

Vdc 2 O

s T/2 T

with frequency (1+2s)f, (7+2s)f, (5-2s)f. In the case of a massive vehicle such as a train, the large inertia should suppress the sidebands produced by speed fluctuations.

sω* (ω-2sω)* 5ω (6ω-sω)* (6ω-sω) (7ω-2sω)* 7ω (6ω+sω) (6ω+sω)* (5ω+2sω)* ω-sω

III. CIRCUITAL MODEL Each stator phase of the particular motor considered is made up by four parallel polar windings (Fig.4-left), [4]: ROTOR

Fig.2. Left: three-pulses inverter voltage waveform. vAO is voltage of motor phase A with respect to inverter dc-link middle-potential point O. The fundamental harmonic is shown. Right: harmonic torques and current sidebands basic generation mechanisms. A machine with two poles is considered for simplicity. Continuous and sketched arrows are referred to stator and rotor field waves, respectively. Asterisks outline component waves produced by a rotor asymmetry.

6th harmonic torques rise from interaction between stator and rotor time-harmonic polar wheels (Fig.2-right). 5thharmonic stator polar wheel (5ω electrical speed backward rotating) excites an analogous rotor reaction polar wheel (with electrical speed (6ω-sω) regressive with respect to the rotor), whose interaction with 1st harmonic stator polar wheel (ω-speed forward rotating) generates a 6f frequency pulsating torque. 7th harmonic stator polar wheel produces a similar effect, and another 6th harmonic torque rises. These two pulsating torques add together by constructive interference. Fig.2-right also shows the fault-related current sidebands generation mechanism: when one or more bars are broken, or with end-ring damaged, the cage symmetry is lost and the multi-phase rotor currents system loses his symmetry as well. So, some reverse rotating fields rise in the air-gap (whose speeds in Fig.2 are sω*, (6ω-sω)*, (6ω+sω)*, with respect to the rotor), that are superimposed to direct ones (sω, (6ω-sω), (6ω+sω)). The reverse fields link with stator windings inducing currents with frequencies (1-2s)f, (7-2s)f, (5+2s)f. Such currents are limited by stator impedances (resistances and leakage reactances) and by feeding system impedances (VSI converter) generally very low. Super-imposition of the "normal" current components (without fault) with the faultrelated ones makes raise a current modulation with frequency 2sf, Fig.3. As a consequence a pulsating torque appears, that produces some rotor mechanical speed oscillations with the same frequency (2sf) and with amplitude limited by global drive inertia. These fluctuations reduce the (1-2s)f, (7-2s)f, (5+2s)f sideband amplitudes but make raise current sidebands

ib3 ib4

iR4 iR,k-1

ib,k-1

iRk ibk

iR3

ie

iR55

ib2 iR2

ib1 iR1

iR56

ib56

ib55

Fig.4. Left: transverse section of the induction motor (1.13 MW). The four polar windings of one phase are schematically shown. Right: topological circuital scheme for the rotor fifty six-bars squirrel cage.

Thus, stator electrical equations are twelve: vAi = RpwiAi + pψAi (1) (2) vBi = RpwiBi + pψBi (3) vCi = RpwiCi + pψCi with i = 1,2,3,4, and where: Rpw= single polar winding resistance = Rphase*4; p = derivative operator = d/dt. Rotor topological circuital scheme is shown in Fig.4-right. Electrical balance of kth rotor loop is [5]: 0 = -RbiR,k-1+2(Rb+RE/NR)iRk-RbiR,k+1-Re/NRiE+pψRk (4) Rotor bars currents are obtained by the equations: ibk = iRk – iR,k+1 (5) End-ring electrical equation is: (6) 0 = RE iE - ∑ RE/NR iRk + pψE The previous equations are reassumed by the following matrix system (matrix dimension is 69x69): [v] = [R] [i] + p[ψ] (7) where column vectors are: [v] = [vA1…vA4 vB1…vB4 vC1… vC4 0 0…… 0 0 ]t (8) [i] = [ iA1… iA4 iB1… iB4 iC1… iC4 iR1 iR2… iR,Nr iE ]t (9) [ψ]= [ψA1…ψA4 ψB1…ψB4 ψC1…ψC4 ψR1ψR2…ψR,Nr ψE]t (10) The flux linkages are expressed in matrix form by eq.(11):

[ψ] = [L(ϑ)] [i] (11) The comprehensive machine inductance matrix is: [LSR(ϑ)] [LSE] [LSS] [LRE] (12) [L] = [LRS(ϑ)] [LRR] [LES] [LER] [LEE] whose elements where evaluated by FEM analysis. Structure of [LSS] can be achieved by exploiting its circular symmetry: [LSS] = Lss =

LAA =

LAB =

LAC =

LAA LBA LCA

LAB LBB LCB

LAC LBC LCC

=

LA1A1 LA2A1 LA3A1 LA4A1




LA1B1 LA2B1 LA3B1 LA4B1




LA1C1 LA2C1 LA3C1 LA4C1




LAA LABt LACt =

=

=

LAB LAA LABt

LAC LAB LAA

(13)

L0 L90 L180 L90

L90 L0 L90 L180

L180 L90 L0 L90

L90 L180 L90 L0

L60 L30 L120 L150

L150 L60 L30 L120

L120 L150 L60 L30

L30 L120 L150 L60

L120 L30 L60 L150

L150 L120 L30 L60

L60 L150 L120 L30

L30 L60 L150 L120

(14)

(15)

(16)

where L0, L30, L60, L90, L120, L150, L180 are auto and mutual inductances between stator polar windings. We have: (LphaseA)equivalent = (L0 + 2L90 + L180)/4 (17) Note that [LSS] has not a circulant structure, but a nominal one, so simplifying the elimination of the neutral connection (Section V, C). On the contrary, [LRR] is circulant [6]. IV. PARAMETERS IDENTIFICATION BY F.E.M. Exact air gap length and iron and wedge permeabilities were accurately evaluated by computing the real total energy of the magnetic field produced by one phase by the formula: Em = ½ LA iA2 (18) (LA is the measured stator phase auto-inductance) and matching this value with that obtained by FEM analysis, Fig.5-left, [7]. [LSS] and [LSR(ϑ)] inductance sub-matrices were calculated by magnetic vector potential AZ slot values distributions obtained by feeding one stator polar winding (Fig.5-center), and by using the following formulas: Lkh = ψkh / ih (19) ψkh = [AZ(slot k1)-AZ(slot k2)]Nk (20) where k1 and k2 identify the slots of kth loop with Nk turns.

Fig.5. Left: field analysis performed by FEM to match the measured stator phase inductance with the model one. Center: field of a single stator polar winding. Right: field of a single rotor loop.

A similar procedure was used to obtain [LRR] matrix, starting from a FEM analysis for a single rotor loop, Fig.5-right. Being [LSR(ϑ)] function of the rotor angle, a cubic interpolation was used to compute its elements (Fig.6).

Fig.6. Cubic interpolation of computed inductance values.

V. MODEL IMPROVEMENTS A. Partition of the Model Matrices Equation (7) was partitioned [8] to achieve effective algorithms, eliminating the end-ring current (healthy rings): VS = RSSIS + GSR(ϑ)pϑ⋅IR + LSSpIS + LSR(ϑ)pIR (21) 0 = RRRIR + GRS(ϑ)pϑ⋅IS + LRS(ϑ)pIS + LRRpIR (22) (23) Tem = IRtGRS(ϑ)IS (note the use of bold letters for matrices) which can be arranged in the following form for simpler computing: pIS = (LSS – LRStA)-1(LRStC - RSSIS - GRStIRpϑ + VS) (24) pIR = – C – ApIS (25) Tem = IRtB. (26) The following synthetic matrices were introduced, to avoid repetitions and to speed-up calculations: A = LRR-1LRS ; B = GRSIS ; C = LRR-1(Bpϑ+RRRIR) (27) Note that LRR submatrix is constant: his inversion is needed only once, by pre-calculation. Therefore, only a (11x11) matrix inversion is needed for every integration step. B. Improvement of the Model Differential Class Difficulties raised when a low-class model was used to simulate the motor [8]. Employing step functions to represent the 3-pulse PWM voltages, and linear interpolation for LRiAj(ϑ), the model class is only generally C0 (that is, the "f" function of system dy/dt=f(y,t) is generally continuous, and y(t) is a generally C1 class function). With this model, the 1th order Euler formula was successfully used to do integration: (28) yk+1 = yk + f(yk, tk)∆t However, the number of iterations needed to get simulations convergence was excessive. So, an higher-class model employing cubic-splines was made up to implement PWM waveforms and mutual inductances. If the Lrs elements are C2 class functions, then Grs elements class is C1. Voltage waveforms reach C1 class. Then eqs. (24), (25) are C1 class functions, and y(t) is C2. This allows to use 2nd-order quadrature formulas (Adams-Bashforth) to do integration: yk+1 = yk + [3f(yk, tk) - f(yk-1, tk-1)]∆t/2 (29) By using (29) the simulation time was reduced to about 10%. C. Elimination of the Neutral Connection Since the studied motor is three-wire connected, the model needed to be re-arranged to simulate the star-connection with insulated neutral [8]. A gauge exists on the stator currents: iC4 = -(iA1+...+iA4+iB1+...+iB4+iC1+iC2+iC3) (30) Substituting the latter in (21),(22),(23), and subtracting the

12th eq. from the first eleven, a reduced system was obtained containing independent currents and concatenated voltages: (VS)red = [vAC vAC vAC vAC vBC vBC vBC vBC 0 0 0]t (31) VI. SIMULATIONS FOR MOTOR IDENTIFICATION Simulations were performed to complete the healthy motor identification, by using equations (24)-(27), together with the mechanical torque balance: ppϑ = (Tem-Tload)/J. Motor feeding frequency was fixed to 50Hz, and a threepulses PWM was built in the model to match the simulated current waveforms with the measured ones. A load torque ramp with constant slope (500Nm/s) was applied, to reproduce quasi-steady-state operating conditions over the wall load range (Fig.7, up). Fig.7 (down) shows electromagnetic motor torque for rated load. A large 6thharmonic ripple (6000Nm peak-peak) superimposed to the mean torque (5126Nm, rated torque) is evident, which is the principal responsible of frequent bar breakages.

Fig.10. Simulated phase current spectra. Measured values are marked by ‘X’.

In Fig.10 and in Table I a comparison between simulated and measured current spectra is reported. Fig.11 shows the trajectories of the simulated stator current space vector. TABLE I. MEASURED AND SIMULATED HARMONIC CURRENT AMPLITUDES (A)

order measured simulated

1 556 583

5 71 55

7 233 194

11 96 85

13 24.5 17

17 4.5 0.2

19 20 14

23 4.5 2

A Fig.11. Stator current space vector trajectory: (a): starting, (b) detail for no-load and rated operating. Fig.7. Simulation of a constant slope ramp (500Nm/s) load torque.

The simulated current waveform (Fig.8-b) for rated load shows good agreement with the recorded current (Fig.9).

Fig.12. Motor slip versus time. A

Fig. 9. Real motor phase current (measured).

A

Fig.12 shows the slip time-evolution; since the load torque rate of change is constant, the shown curve approximates the motor torque-slip mechanical characteristic curve. Fig.12 shows a good agreement with motor data.

A

Fig.8. Motor phase current during load increasing (simulated).

25 16 13

Fig.13. Left: rotor bar current. Right: a detail is shown.

Fig.14. Rotor bar current spectra (healthy motor).

Fig.13 shows a rotor bar current; two large 6th-harmonicas are superimposed to the slip-frequency component; their frequencies are (6-s)f and (6+s)f (Fig.14), thus generating beats with frequency 2sf. 6th-harmonic rotor currents notably increase thermal power generation, and thermal bar stresses. VII. SPECTRAL ANALYSES FOR HEALTHY MOTOR Fig.15 shows spectral analysis of simulated phase motor current (no-fault condition). Inverter feeding is 50Hz, threepulses modulated. The load is increased from 0% to 200% of rated value. As expected, 1st harmonic amplitude is essentially load-dependent; 5th and 7th harmonicas, that produce 6th harmonic torques, are indifferent to load variations. Interaction of 11th and 13th with 1st produces 12th harmonic torques. No sidebands compare in the spectrum.

Fig.15. Phase current spectrum, versus load torque.

Figure 16 shows spectral analysis of the electromagnetic torque. Mean motor torque balances the load torque. Alarming levels of 12th and especially of 6th harmonic are clearly present, that are not dependent from load condition.

lower sideband (ILSB) of the phase current fundamental component (If), since this sideband is directly produced by the rotor asymmetry correspondent to the broken bars [2]. Number (n) of broken bars can be approximately estimated by the empirical relation (32), (P = pole pairs), [9]: I LSB (32) n = 2N r

I f + 2 P ⋅ I LSB

Peculiar drawbacks of this method are a) dependence of sideband amplitude from actual load, b) dependence of sideband position (frequency) from slip (and therefore from load) and c) incidence of global drive inertia on slip fluctuations and, then, on (1+2s)f frequency sideband amplitude (which reduces the lower sideband amplitude by a feedback reaction [2]). In fact, eq. (32) is better satisfied with drive having large inertia [3]. Figure 17 shows 1st, 5th and 7th harmonic spectra, when no inertial load is added to motor shaft (only the rotor inertia is considered), and with rated torque. Motor feeding is 50Hz, three-pulses modulated. One rotor bar is broken by increasing the resistance 200 times. Sidebands are present with frequencies furnished by eq.(33): f = hf ± ksf, h=1,5,7,11,..., k=2,4,6,... (33) All sidebands are observable in Fig.17, thanks to the low inertia. Naturally, this is not the case of the real drive. When a large inertial load was considered (railway traction drive, constant speed), spectra in Fig.18 were obtained. Sidebands disappear with frequencies: hf - sf(1± k), h=1,7,13,19,..., k=3,9,15,21,... (34) hf + sf(1± k), h=5,11,17,23,..., k=3,9,15,21,... (35) and sidebands remain with frequencies: hf - sf(1± k), h=1,7,13,19,..., k=1,5,7,11,13,… (36) hf + sf(1± k), h=5,11,17,23,..., k=1,5,7,11,13,… (37) Eq. (32) is now more reliable; by using this formula, Table II was carried out by inspecting Figs.18-20. TABLE II. ESTIMATED NUMBER OF BROKEN BARS BY EQ. (32)

# broken bars 1 2 3

Fig.16. Electromagnetic torque spectrum, versus load torque. The mean value balances the load torque; 6th-harmonic is responsible for bar faults.

VIII. SPECTRAL ANALYSES FOR FAULTY MOTOR Some spectral analyses were carried out starting from simulated waveforms, with the aim to study the applicability of MCSA as a diagnostic tool for bar breakages. We can observe that, the same physical phenomenology that produce bar breakages (harmonic currents that excite harmonic torques), is than useful to detect rotor faults as well (by using broken bar-related sidebands of harmonic currents), as shown in the following spectral diagrams. MCSA technique is normally used to discover and measure the (1-2s)f frequency

If (50%) 300A 300A 300A

I(1-2s)f (50%) 4A 8.5A 13A

n (50%) 1.42 2.85 4.14

If (100%) 583A 583A 593A

I(1-2s)f (100%) 8.5A 19A 30A

n (100%) 1.5 3.2 4.7

Table II shows a modest agreement of eq.(32) with reality. Eq.(32) produces results variable with load torque and inertia. By inspecting Figs.17-20, it appears evident that a lot of sidebands arise, other than (1-2s)f, suitable for fault diagnosis. I.e., (5+2s)f sideband is a good fault indicator. In fact, its amplitude is insensible to load inertia, as results comparing Figs.17, 18. Moreover, it is insensible to load torque variations (Figs.18, 19). 5th harmonic upper sideband is only variable with broken bars number, Table III. The dependence relationship seems to be quite linear. Absolute magnitude of this sideband is large enough to be easily detected. It stays only one decade under 5th harmonic peak. TABLE III. FIFTH HARMONIC UPPER SIDEBAND AMPLITUDE.

#broken bars I(5+2s)f

1 2A

2 5A

3 7.5A

Fig.17. Phase current first, fifth and seventh harmonic spectra. Sampling frequency 24kHz. One broken bar; 100% rated torque applied; no inertial load.

Fig.18. One broken bar; 100% rated torque applied; inertial load applied.

Fig.19. One broken bar; 50% rated torque applied; inertial load applied.

Fig.20. Two broken bars; 100% rated torque applied; inertial load applied.

IX. CONCLUSIONS A complete phase model was used to simulate an induction motor employed in a railway traction GTOinverter-fed drive. Parameter identification was performed by FEM. Simulations of healthy and faulty machine under realistic feeding and loading conditions were performed, which show the superiority of (5+2s)f sideband with respect to (1-2s)f as fault indicator. Many other sidebands can be investigated for diagnostic purposes. In a companion paper [6] theoretical formulas were developed for sideband amplitudes and frequencies calculation. REFERENCES [1]

[2] [3]

A. H. Bonnett, G. C. Soukup, "Cause and Analysis of Stator and Rotor Failures in Three-Phase Squirrel-Cage Induction Motors", IEEE Transactions on Industry Applications, vol. 28, No.4, pp.921937, July-Aug. 1992. W. T. Thomson, M. Fenger, "Current Signature Analysis to Detect Induction Motor Faults", IEEE Industry Applications Magazine, vol.7, pp. 26-34, July/Aug. 2001. C. Kral, T. G. Habetler, R. G. Harley, F. Pirker, G. Pascoli, H. Oberguggenberger, C. J. M. Fenz, "A Comparison of Rotor Fault

[4]

[5] [6]

[7]

[8]

[9]

Detection Techniques with Respect to the Assessment of Fault Severity", in Proc. SDEMPED 2003, Atlanta, GA, USA, Aug. 2003, pp. 265-270. C. Bruzzese, O. Honorati, E. Santini, P. Sordi, "Improved Squirrel Cage Induction Motor Phase Model for Accurate Rotor Fault Simulation and Parameters Identification by F.E.M.", in Proc. ACEMP 2004, Istanbul, Turkey, May 2004, pp. 94-100. J. Manolas, J. Tegopoulos, “Analysis of Squirrel Cage Induction Motors with Broken Bars and Rings”, IEEE Transactions on Energy Conversion, vol.14, no.4, Dec. 1999. C. Bruzzese, C. Boccaletti, O. Honorati, E. Santini, “Rotor Bars Breakage in Railway Traction Squirrel Cage Induction Motors and Diagnosis by MCSA Technique. Part II: Theoretical Arrangements for Fault-Related Current Sidebands”, in Proc. SDEMPED 2005, Vienna, Austria, Sept. 2005. C. Boccaletti, C. Bruzzese, O. Honorati, E. Santini, “Accurate Finite Elements Analysis of a Railway Traction Squirrel-Cage Induction Motor for Phase-Model Parameters Identification and Rotor Fault Simulations”, in Proc. SPEEDAM 2004, Capri, Italy, June 2004, pp. 827-832. C. Boccaletti, C. Bruzzese, S. Elia, O. Honorati, "A Procedure for Squirrel Cage Induction Motor Phase Model Parameters Identification and Accurate Rotor Faults Simulation: Mathematical Aspects", in Proc. ICEM 2004, Cracow, Poland, Sept. 2004. R. Hirvonen, "On Line Condition Monitoring of Defects in Squirrel Cage Motors", in Proc. ICEM 1994, Paris, France, 1994, pp.267-272.