Rotor bar fault diagnosis in three phase induction motors by monitoring fluctuations of motor current zero crossing instants

Electric Power Systems Research 77 (2007) 385–392

Rotor bar fault diagnosis in three phase induction motors by monitoring fluctuations of motor current zero crossing instants Hakan C ¸ alıs¸ ∗ , Abd¨ulkadir C ¸ akır Department of Electronics-Computer Education, The Faculty of Technical Education, Suleyman Demirel University, Isparta, Turkey Received 8 December 2005; received in revised form 30 March 2006; accepted 31 March 2006 Available online 8 May 2006

Abstract This study describes broken bar detection in induction motors without using additional sensor. It is based on observation of the fluctuations of stator current zero crossing times (ZCT). Instead of sampling motor current with a high resolution A/D converter, zero crossing instants are recorded as waveforms cross zero. Fluctuations in the intervals between successive zero crossings of the three phase current waveforms are analysed using Fast Fourier Transforms (FFT). Diagnostic information is found in the spectrum of the ZCT signal through the presence of specific fault related frequencies. A rotor bar fault is manifested as an increase in the amplitude of the 2sf and other spectral components. This paper analyses the effect of an electrically unbalanced rotor on the ZCT spectrum of stator current, and discusses the various frequency components associated with rotor bar faults seen in the ZCT spectrum. It is important to eliminate the dependence of the index on the parameters of the induction motor. Particularly, the effect of motor inertia, supply harmonics, and variable load are discussed to increase the reliability of the rotor fault index, and simulation results are presented. It is found that the 2sf frequency component is independent of inertia, load, and harmonics, and thus it is suitable as an index for broken rotor bar. © 2006 Elsevier B.V. All rights reserved. Keywords: ZCT signal; Fault diagnosis; Rotor fault; Broken rotor bar; Induction motors

1. Introduction Induction motors are most commonly used electrical rotating machine in industry. However, it is becoming increasingly important to use condition monitoring techniques to give early warning of imminent failure. Many of motor faults have an electrical reason. Rotor bar faults are usually associated with high temperatures, high mechanical loading particularly during the starting time, or any defective casting or poor jointing during the manufacturing process. Initially, they started as high resistance causing high temperature and then progress as cracking or small holes in the rotor bars. They are more likely to take place near the cage end rings. Although rotor bar faults covers approximately 10% of overall fault conditions in squirrel-cage induction motors, many research works have been implemented for detection of induction motor rotor faults during the past years. Therefore, many monitoring algorithms have been proposed in ∗

Corresponding author. E-mail addresses: [email protected] (H. C ¸ alıs¸), [email protected] (A. C ¸ akır). 0378-7796/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2006.03.017

the literature. Now, there is a good understanding for the rotor bar fault mechanism. Rotor bar fault detection has been implemented by monitoring pulsations in speed, airgap flux, axial flux, vibration, and current [1–7]. The main disadvantage of these methods is that they all require using additional sensor for the monitoring. Additionally, the sensitivity of fault detection mainly depends on the inertia of the load, and it is difficult to determine the degree of fault level. The preferred and widely used approach to rotor bar fault detection is the analysis of stator current in the frequency domain, due to its non-invasive accessibility [7]. A sensorless zero crossing times method, observing the changes on the motor current zero crossing instants, has also been shown to be able to use for speed measurement and fault detection [8]. The conventional indicator of the broken rotor bars in the single phase of motor current spectrum is well recognized by sidebands displaced by 2sf Hz around the mains peak at full load working conditions with high slip, where f is the supply frequency and s is the motor slip. In practice, motor load may not be steady and if current is sampled when the motor load changes, sidebands may not be

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clearly identified. The left-hand sideband (1 − 2s)f is produced directly by rotor asymmetry due to the electrical or magnetic unbalance in the rotor. In addition, its amplitude is affected by cyclic variation in the torque at 2sf Hz, which causes load dependent speed pulsation at the same frequency. The effect of this 2sf pulsation on the left-hand sideband causes decrease in its amplitude and produces a right-hand sideband at (1 + 2s)f [7]. Research presented in [9–12] discusses methods of distinguishing unbalanced mechanical loads from rotor bar faults, while research in [13] eliminates the effect of the fluctuating speed and states a direct relation between the magnitude of the rotor fault index and the number of broken rotor bars. Artificial intelligence based techniques are used to eliminate load effect and speed ripple effect in [14–17]. Also, Park’s vector approach based on the observation of Park’s complex vector module, and space vector angular fluctuations, based on measuring the displacement of the space vector, methods are proposed to detect stator and rotor faults including determination of failure’s degree [18,19]. They use the sum of sidebands amplitudes to eliminate the effect of speed ripple and inertia. In the literature it is also shown that a novel method of space vector angular fluctuation (SVAF) is used as off-line rotor fault detection [20–22]. In that study, the effects of system inertia and load are discussed, and simulation results are presented. In this paper, broken rotor bars are detected only through the monitoring of fluctuations in the motor current zero crossing instants (ZCT) in frequency domain. This only requires the use of a current sensor, which is already in place in many drives. The induced characteristic frequencies in the motor current due to the rotor asymmetry are discussed in this paper. The ZCT method for the rotor fault detection is based on the measurement of motor current zero crossing times. The time difference between successive zero crossing times is stored as a data file for monitoring purpose. The spacing between successive zero crossings is unequal due to motor abnormalities. From the ZCT data motor slip and motor status information are estimated. The data values represent the fluctuations in the motor current zero crossing times and motor running at the constant speed under balanced supply, stator winding, would be equal to zero. Hence, the fluctuations in load or speed from any cause will be encoded as modulation of ZCT data values. These data are analysed in frequency domain for fault diagnosis purposes. Fault detection algorithm used in this study is tested for various conditions. It is proven that for the broken bar diagnosis, the monitored frequency component (2sf) in ZCT spectrum is independent of unbalanced supply voltage, supply harmonics, variable load, and motor or load inertia. Thus, the ZCT signal can be chosen as a reliable and distinctive diagnostic parameter for the rotor bar fault detection. ZCT method is implemented in simulation model in which rotor phase resistance is made unbalanced by adding extra resistance. Results obtained are presented in this work together with a diagnostic parameter for condition monitoring of rotor bar faults.

2. An explanation on status or origins of broken bar indicator component in the motor current spectrum Rotor unbalance such as broken bars produces positive and negative sequence currents in the rotor. Frequency of current flowing in the broken rotor bar is sf, where f is the frequency of supply phase current and s is the slip. It can be resolved into positive and negative sequence components. It follows that the positive sequence rotor current results in positive sequence emfs and positive sequence currents on the stator of angular frequency wr + sw = w(1 − s) + sw = w

(1)

while negative sequence rotor current results in emfs and currents of frequency in the stator, wr − sw = w(1 − s) − sw = (1 − 2s)w

(2)

where ωr (rad/s) is the angular frequency of rotation of the rotor shaft. It is seen that the each stator current consists of positive sequence current and additional current component. The rotor asymmetry induces the current in the stator of the angular frequency (1 − 2s)ω. On the other hand, spectrum of the ZCT signal contains a 2sf frequency component and its harmonics at 2ksω, k = 2, 3, . . . (with decreasing amplitude at higher values of k) as frequencies of broken bar. The amplitude of this spectral component increases as the degree of rotor asymmetry rises. These components and their effects on fluctuations of motor zero crossing instants are discussed in this section. Due to interaction of (1 − 2s)f component with the flux, an oscillation is going to be seen in the torque at 2sf frequency (see Eq. (3)) [21]. T (t) =

3 pψInr sin(2sωt − (φψ − φnr )) 2

(3)

where p is the number of pole pairs, Inr (A) the amplitude of stator current component originating from the negative sequence rotor current, φψ and φnr (rad) the displacements referring to fundamental current component, and ψ (Wb) is amplitude of magnetic flux in the induction motor. This torque ripple produces a speed ripple as shown in the following equation: J

dωr = T (t), dt

(4)

where J (kg m2 ) is induction motor’s inertia, T(t) (N m) the pulsating torque, and ωr is its rotor speed. Eq. (4) can be solved for ωr and following expression obtained, when torque from Eq. (3) is substituted into Eq. (4) and integrated [21]:  1 3pψInr ωr (t) = T (t) dt = − cos(2sωt − (φψ − φnr )) J 2J2sω (5) where 3pψInr /J4sω = ωr is the amplitude of speed ripple. Variation in the speed induces an emf in the stator when it interacts with the magnetic flux. The main effect of the speed fluctuation, which is a function of motor’s inertia, is the appearance of two voltages on the fundamental emf. These two voltages induce two

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additional currents of the (1 − 2s)f and (1 + 2s)f frequency and  , in the stator. These induced currents the same amplitude, Inr depend only on the operating conditions and motor’s inertia. New component of the stator current at frequency (1 − 2s)f is a reaction of the initial component with the same frequency, induced by the rotor asymmetry itself, so the final component at frequency (1 − 2s)f in the stator current spectrum is the sum of the two components at frequency (1 − 2s)f. The new component of the stator current at frequency (1 + 2s)f is also visible in the spectra of stator current. A rotating magnetic field continues to produce the stator current components at frequencies (1 ± 2ks)ω, k = 1, 2, 3, . . . [21]. Components of the stator current, appeared due to the reaction to the rotor asymmetry, are expected to reflect in the fluctuations of motor current zero crossing instants. To investigate their effects, firstly additional stator current component at frequency (1 − 2s)ω, whose amplitude is Iadd = Inr , is considered. It appears in the ZCT spectrum at frequency 2sf, as well as the initial component of the same frequency originating in the rotor asymmetry. The effect of the newly induced stator currents, which are reaction of the induction motor to the oscillating torque and speed, is not felt in the ZCT spectrum. So, ZCT spectral component at 2sf is influenced only by the negative sequence current in the rotor and not by the reaction of the induction motor to the rotor asymmetry involving torque pulsation and speed ripple. Since 2sf component in the ZCT spectrum is independent of motor inertia, it can be used as good indicator of the rotor bar fault.

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of broken bar faults should reflect the amount of the broken bar and various locations of them. However, this process is very complicated [23]. Rotor bar fault can be simulated by increasing one of rotor phase resistances [22–24]. If end-ring contribution is neglected, the phase rotor equivalent resistance, referred to as stator, can be computed as [25] (2Ns )2 Rb Rr ∼ = Zr /3 where Ns is turn number stator phase winding, Zr the number rotor bar number, and Rb () is the bar resistance. In case of n contiguous broken bars, one of the phase rotor resistances becomes [24] (2Ns )2 Rrf ∼ Rb = Zr /3 − n which will correspond to an increment (see Eq. (6)) R = Rrf − Rr =

n Rr Zr /3 − n

(6)

with this assumption, rotor bar fault is simulated by externally adding three star connected rotor resistors. Each value of added rotor phase resistance is changed between 0.10  and 0.205 , in 0.0175  steps (this value corresponds to equivalent resistance of the approximately half broken bar, and it is increased to the value of the three broken bar resistances). In addition, in the simulation model zero crossing detection circuit, power spectrum estimation of ZCT and motor current signals are included with displaying and storing in data file blocks.

3. Simulation of the ZCT method for the detection of broken bar faults using Matlab/Simulink model

3.1. Simulation results for broken rotor bar

In this study, 3 hp, four pole squirrel-cage induction motor is used for simulations. Block diagram of an induction motor’s Simulink model is shown in Fig. 1. It is required that the model

Simulation results for the broken rotor bar fault are presented in the ZCT signal spectrum. Also, all frequencies induced in the stator current spectrum are displayed as a comparison of

Fig. 1. Simulink model of sensorless broken bar detection for induction motor.

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both methods. Obtained spectral results are classified for the following conditions: 1. Motor having various number of broken rotor bar for the case of balanced supply and symmetrical stator windings. 2. Motor having broken rotor bar and running in the case of unbalanced supply but symmetrical stator windings. 3. Broken rotor bar fault in the case of balanced supply including odd harmonics condition. 4. Faulty rotor operating under different levels of motor inertia. 5. Asymmetrical rotor operating under variable motor load. 3.1.1. Results for the motor having broken rotor bars In Fig. 2, spectra of current and ZCT signals are presented, respectively, for symmetrical and asymmetrical rotor operating under balanced supply and symmetrical stator winding conditions. Rotor fault is simulated by adding extra resistance to the single phase resistance of rotor circuit in steps of 0.0175 . Induction motor was operating at ωr = 1440 rpm, so slip was s = 0.04. Thus, stator current component which is a direct consequence of negative sequence rotor current is of frequency (1 − 2s)f = 46 Hz. Components that are induction motor’s reaction to the asymmetrical rotor are: (1 − 2s)f = 46 Hz and (1 + 2s)f = 54 Hz. ZCT spectrum then contains spectral lines at 2sf = 4 Hz. Due to balanced operating conditions no component appears at 2f frequency, where a spectral line caused by negative sequence stator current is expected.

3.1.2. Results for the motor having broken rotor bars operating under unbalanced supply condition In Fig. 3, spectra of current and ZCT are given, respectively, for the motor operating under unbalanced supply, balanced stator conditions, and having asymmetrical rotor. In the spectrum of ZCT signal, a spectral line at 2f = 100 Hz is noticed. Also, negative sequence current is induced on the stator operating under unbalanced supply voltage; thus, negative sequence currents of stator current components are induced. Since the rotor speed of the induction motor has remained the same as in conditions described by Figs. 2 and 3 with slip s = 0.04, all rotor asymmetry characteristic frequencies remain the same. New frequency, emerging in the ZCT spectrum, due to the unbalanced supply voltages is 2f = 100 Hz, and sidebands of ±2sf around 2f due to rotor fault, and frequency in the lower part of the spectrum 2sf remains unaffected by the unbalanced supply. Current spectrum reacts to new unbalanced condition by appearance of spectral lines at 3f = 150 Hz due to the unbalanced supply and with (3 ± 2s)f = 154 Hz and 146 Hz due to the unbalanced rotor operating under unbalanced supply. Current ZCT spectrum also contains the same frequencies as previously. Difference with respect to previous condition with unbalanced supply is in the degree of unbalance and it is reflected in the change of the amplitudes of frequencies, which depend on negative sequence. So, spectral components at frequencies 2f and 2k(1 ± s)f have changed their amplitude, while spectral components at frequencies 2ksf remained unaffected. When the spectrum of the stator current in the case of asymmetrical rotor is analysed, it is noticed that the newly induced

Fig. 2. Power spectra of current and ZCT signals for symmetrical and asymmetrical rotor, respectively. For: (a) healthy rotor and (b) rotor have broken bars.

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Fig. 3. Power spectra of current and ZCT at working condition with 0.6% unbalanced supply, balanced stator, and asymmetrical rotor.

components occur if stator is unbalanced, either due to the unbalanced supply or unbalanced stator itself. In addition, stator currents will have positive and negative sequence components, rotating in the positive and negative directions. Therefore, the spectrum of the ZCT will only hold additional spectral lines when asymmetrical rotor operates under asymmetrical stator occurring at frequencies of 2k(1 ± s)f, k = 1, 2, 3, . . . components due to the unbalanced stator currents originating in rotor asymmetry. When observed real time, the amplitude of 2f spectral component oscillates at 2sf frequency, indicating asymmetry both in the stator and in the rotor. In a real practical situation, the stator of an induction motor can be considered as asymmetrical; thus, presence of these frequencies can be expected in the ZCT spectrum. However, since ZCT components 2(1 − s)f and 2(1 + s)f depend on the degree of stator unbalance and in addition 2(1 + s)f depends on the motor’s inertia, they can be used only as an indication of rotor unbalance, but not as a rotor fault index. The phenomenon of unbalanced rotor currents induces a number of additional components in the stator phase current, as shown in previous sections. They all contribute to fluctuations and appear as frequency components: 2ksf, 2k(1 − s)f, 2kf, and 2k(1 + s)f in the ZCT spectrum. It is mentioned that 2sf spectral component of the ZCT spectrum is independent of the motor’s inertia. In order to verify this, motor model is simulated for increasing levels of inertia with two different levels of rotor faults. Initially, 17.5% additional rotor resistance and later 100% variation in rotor resistance are added to one phase of the rotor circuit, running under balanced supply condition (see Table 1). Fig. 4 presents characteristic frequency from the ZCT spectrum for increasing inertia and for Rr = 0.0175 , plotted in the line with star, and Rr = 0.205 , plotted in the line with diamond. It can be clearly seen in Fig. 4 that amplitude of spectral component at frequency 2sf does not vary. Thus, 2sf spectral component in the current ZCT spectrum can be taken as reliable index of the rotor fault because it is independent of the supply unbalance and stator asymmetry. Even though in real situation where always some degree of unbalance

Table 1 Amplitude of 2sf component for variable inertia in case of broken rotor bar J (kg m2 )

0.089 0.1 0.2 0.3 0.4 0.5 0.6

Amplitude of 2sf (s) Rr = 0.1175 

Rr = 0.205 

0.8048e−6 0.8188e−6 0.9373e−6 1.038e−6 1.117e−6 1.176e−6 1.217e−6

4.895e−6 4.984e−6 5.736e−6 6.36e−6 6.839e−6 7.182e−6 7.414e−6

of the supply or stator is existing, the 2sf component is not overshadowed by any other major peak, such as f or 2f. However, there is a single deficiency for this fault indicator; for low slip induction motors or motors operating at the no load condition it may then be difficult to read its value. 3.1.3. Results for asymmetrical rotor under balanced supply including unbalanced harmonics Fault indicator parameters used to detect broken bar and supply unbalance are tested in case of unbalanced supply harmonics. For this purpose, third harmonic with amplitude of 10% of supply voltage is added to the supply. Fifth and seventh harmonics are also injected in the same way. The model is then executed in this case with various loads and different rotor bar fault levels. Monitored amplitude levels of components are given in Table 2. There is approximately 11 times increment in the amplitude level of the fault indicator component 2sf. Motor current and ZCT spectra are shown as in Fig. 5 for this condition. It is seen that when the motor is running without load,

Fig. 4. The effect of inertia on the 2sf fault indicator component at two different rotor bar fault levels.

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Table 2 Amplitudes of fault related components in motor current and ZCT signal spectra at supply with balanced harmonics Amplitudes of fault indicator components a

2f (1 − 2s) f a (1 + 2s) f a

b

2 sf 4sf b 6sf b 2fb (1 − s)2 fb (1 + s)2 fb a b

Rotor resistance variation () 0.1

0.1175

0.135

0.1525

0.17

0.1875

0.205

32.23 0.001168 0.001045

32.24 0.06618 0.03317

32.24 0.1317 0.07585

32.24 0.1935 0.1278

32.24 0.2495 0.188

32.24 0.2979 0.2554

32.24 0.3374 0.3283

0.1

0.1175

0.135

0.1525

0.17

0.1875

0.205

1.508e−6 0.09567e−6 0.2706e−7 0.0007367 1.318e−5 0.6512e−5

2.904e−6 2.904e−6 0.41e−7 0.0007362 1.318e−5 0.6545e−5

5.861e−6 5.861e−6 1.2e−7 0.0007359 1.318e−5 1.065e−5

8.794e−6 3.677e−6 2.78e−7 0.0007356 1.801e−5 1.589e−5

11.68e−6 5.218e−6 2.275e−7 0.0007354 2.382e−5 2.128e−5

14.5e−6 6.926e−6 8.416e−7 0.0007353 2.927e−5 2.683e−5

17.25e−6 8.798e−6 11.99e−7 0.0007352 3.43e−5 3.257e−5

Current (A). ZCT (s)

it is not possible to detect rotor bar fault in ZCT spectrum. It is only possible to implement broken bar detection when the motor loaded at least quarter of rated load. Balanced or unbalanced supply harmonics does not affect fault detection algorithm. 3.1.4. Results for the unbalanced rotor resistance motor operating under variable load In this section, to show whether fault indicator parameter is valid in existence of variable motor load condition or not, constant motor load used in the model is replaced with sinusoidal changing load. It is put in model as shown in Eq. (6). TL (t) = 28.19 + 2.819 sin(155t)

(6)

Then load amplitude and frequency are changed sequentially as shown by following equations: TL (t) = 55.84 + 5.584 sin(153.93t)

(7)

TL (t) = 109.46 + 102.946 sin(150.79t)

(8)

Amplitude and frequency of the load are chosen as completely an assumption. The results for these cases are given in Table 3. Current and ZCT spectrums are given in Fig. 6. It is shown that 2sf fault indicator is still detectible and remained unaffected unless variation frequency in load is exactly equal to frequency of 2sf component.

Fig. 5. Amplitudes of (a) motor current and (b) ZCT signal spectral components for harmonically effected supply in the case of broken rotor bar.

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Table 3 Amplitudes of fault related components in motor current and ZCT signal spectra at variable motor load Amplitudes of fault indicator components 2 sf a 2fa (1 − 2s) fa (1 + 2s) fa

2 sf b 4 sf b 2fb (1 − s)2 fb (1 + s)2 f b a b

Rotor resistance variation () 0.1

0.1175

0.135

0.1525

0.17

0.1875

0.205

0.001041 32.93 0.001169 0.001082

0.001061 32.93 0.06655 0.06646

0.001081 32.93 0.1299 0.1302

0.0011 32.93 0.1874 0.1882

0.001118 32.93 0.2374 0.2388

0.001197 32.93 0.2783 0.2807

0.001216 32.93 0.3479 0.3539

0.1

0.1175

0.135

0.17

0.17

0.205

0.205

3.194e−11 3.194e−11 5.448e−9 1.424e−8 1.196e−11

0.8048e−6 3.282e−7 5.333e−9 1.394e−8 1.753e−11

1.622e−6 4.689e−7 5.228e−9 1.366e−8 3.725e−11

2.445e−6 1.072e−7 5.13e−9 1.341e−8 6.251e−11

3.269e−6 1.914e−7 5.04e−9 1.317e−8 9.696e−11

4.087e−6 2.972e−7 4.956e−9 1.296e−8 14.86e−11

4.895e−6 4.21e−7 4.88e−9 1.276e−8 21.95e−11

Current (A). ZCT (s)

Fig. 6. Amplitudes of motor current and ZCT signal spectral components for motor running under variable load in the case of broken rotor bar. For: (a) healthy rotor and (b) motor having broken bars in the rotor.

4. Conclusion The application of the ZCT method for the rotor fault detection was discussed in this study. Initially, the phenomenon of asymmetrical rotor was presented and all the characteristic frequencies occurring in the stator current due to cracked or broken induction motor bars are explained. Their reflection and corresponding frequencies in the ZCT spectrum are identified. The 2sf frequency component from the current ZCT spectrum is considered as a reliable index of rotor fault, since it has been shown through results that it is independent of motor’s inertia, supply

harmonics, and variable motor load. Accurate prediction of rotor faults depends on the ability of precise reading of motor slip in order to extract the right frequencies from spectrum. Having only one diagnostic index enables the use of a diagnostic system with minimum requirements. Also, pre-history of the motor is not demanded by such diagnostic system. Diagnostic system as simple as look-up table could be implemented. Similar approach, based on one diagnostic index, has been proposed before as based on a sum of three spectral components extracted from stator phase current. The ZCT rotor fault detection has the advantage that it requires single diagnostic index

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