904 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 32, NO. 4, JULYlAUGUST 1996

Instantaneous Signature Analysis of hductio

Stanislaw F. Legowski, Senior Member, IEEE, A. H. M. Sadrul Ula, Senior Member, IEEE, and Andrzej M. Trzynadlowsh, Senior Member, IEEE

Abstruct- Preventive maintenance of electric drive systems with induction motors involves monitoring of their operation for detection of abnormal electrical and mechanical conditions that indicate, or may lead to, a failure of the system. Intensive research effort has been for sometime focused on the motor current signature analysis (MCSA). The MCSA techniques utilize the results of spectral analysis of the stator current. Reliable interpretation of the spectra is difficult, since distortions of the current waveform caused by the abnormalities in the drive system are usually minute. In this paper, an alternate medium for the motor signature analysis, namely the instantaneous power, is proposed. By theoretical analysis, computer simulations, and laboratory experiments, it is shown that the instantaneous power carries more information than the current itself. Utilization of the instantaneous power is thus enhancing the reliability of diagnostics of induction motor drives.

I. INTRODUCTION

NDUCTION MOTORS dominate the field of electro- mechanical energy conversion. Reliability of drive systems

with these motors has a serious economical impact on operation of industrial plants. Often, even a short interruption of a manufacturing process due to a drive failure causes a serious financial setback for the manufacturer. Certain drive systems, such as those of coolant pumps in nuclear reactors, are crucial for safety of the plant. Consequently, the issue of preventive maintenance and diagnostics of induction motor drives has become increasingly important in today's electrical engineering technology.

Monitoring the operation of a drive system allows detection of abnormal electrical and mechanical conditions [ 1]-[4]. Large electromachine systems are often equipped with me- chanical sensors, primarily vibration sensors based on prox- imity probes [5], [6]. Those, however, are delicate and ex- pensive. Therefore, intensive research efforts have recently been focused on the so-called motor current signature analysis (MCSA) [7]-[lo]. The MCSA techniques utilize results of spectral analysis of the stator current (precisely, the supply current) of an induction motor to spot an existing or incipient failure of the motor or the driven system. Of particular interest are broken bars in the rotor cage, rotor imbalance and

Paper IPCSD 96-1 1, approved by the Electric Machines Committee of the IEEE Industry Applications Society for presentation at the 1995 IEEE Industry Applications Society Annual Meeting, Lake Buena Vista, FL, October 8-12. Manuscript released for publication February 5, 1996.

S. F. Legowski and S. Ula are with the Department of Electrical Engineer- ing, University of Wyoming, Laramie, WY 82071 USA.

A. M. Trzynadlowski is with the Department of Electrical Engineering, University of Nevada, Reno, NV 89557-0153 USA.

Publisher Item Identifier S 0093-9994(96)04162-X.

eccentricity, worn or damaged bearings, and resonant torsional vibration [ 111-[ 161. Commercial vendors offer specialized software for interpretation of the current spectra [9]. Such interpretation is not an easy task and the practical results are often unreliable because of the typically small extent of distortions of the current waveform and noisiness of the spectrum. Use of expert systems and neural networks for the diagnostics of induction motor drives has been experimented with and reported in several publications, e.g., [lo], [17], [18].

In this paper, in place of the stator current, the instantaneous power is proposed as a medium for the motor signature analysis oriented toward detection of mechanical abnormalities in a drive system. It is shown that the amount of information carried by the instantaneous power, which is a product the supply voltage and current, is higher than that deducible from the current alone.

11. INSTANTANEOUS POWER AND ITS MODULATION

No abnormalities in stator windings are assumed in further considerations. Indeed, in practice, different techniques than the spectral analysis are employed for detection of such faults [lo], [19]. Also, an ideal three-phase supply voltage is assumed. The instantaneous power, p ( t ) , is defined here as

p ( t ) = V L L ( ~ ) ~ L ( ~ ) (1)

where V L L ( ~ ) is the voltage between any two of the three stator terminals and i ~ ( t ) is the current entering one of these terminals. Taking as a reference a perfectly healthy drive system running with a constant speed, waveforms of the voltage, l i ~ ~ ( t ) , current, i ~ , ~ ( t ) , and instantaneous power, p o ( t ) , are given by

l iLL(t) = AV,, c o s ( w t ) (2)

(3)

where VLL and IL denote rms values of the supply line-to- line voltage and line current, respectively, w is the supply radian frequency, and p is the load angle of the motor. The power spectrum of the current has only the fundamental component at frequency f = w/(27r) , while the spectrum of instantaneous power has a dc component (average power) and the fundamental component at f = 2w/(27r).

0093-9994/96$05.00 0 1996 IEEE

LEGOWSKI et al.: INSTANTANEOUS POWER AS A MEDIUM FOR THE SIGNATURE ANALYSIS OF INDUCTION MOTORS

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If a mechanical abnormality develops in a drive system, harmonic torques are generated in the motor, accompanied by slip and speed oscillation, and modulation of the stator current. Frequency components characteristic for the type of abnormal- ity appear in the power spectrum of stator current. Location of these components allows identifying the abnormality.

For simplicity, it is assumed that a fault in the motor causes sinusoidal modulation of amplitude of the stator current, while the phase modulation of the current is negligible. The latter assumption is justified by the fact that practical motors are so designed that within a wide range of the load torque, the load angle does not change significantly, staying at a low level to maintain a high power factor. The modulated current, i ~ ( t ) , can be expressed as

"1 = i L , O ( t ) + -{cos MIL [(w - w1)t - p - - Jz 6

( 5 ) "

(w - w1)t - cp - - I} 6

where M is the modulation index and w1 is the modulating radian frequency. Clearly, in the power spectrum of current, two sideband components will appear about the fundamental, at frequencies f = (w + w1)/(27r) and f = (w - w1)/(27r).

The expression for the modulated instantaneous power, obtained by multiplying (2) and (3, is

" (2w - w1)t - p - -1

6

+ 2cos (p + E) cos (w l t ) } .

It can be seen that besides the fundamental and two sideband components at f = ( 2 w + w l ) / ( 2 ~ ) and f = ( 2 w - w 1 ) / ( 2 " ) , the power spectrum of instantaneous power contains an ad- ditional component directly at the modulation frequency f = f l = (w1)/(27r) . The latter component, subsequently called a characteristic component, provides an extra piece of diagnostic information about the health of the motor.

111. COMPUTER SIMULATIONS

Advantages of the power signature analysis have been confirmed by computer simulations of an example lo-hp, 230- V, 60-Hz, six-pole, wye-connected induction motor. Initially, the motor drives a load with a constant torque equal half the rated torque, and a mass moment of inertia equal to that of the rotor of the motor. Power spectra of the stator current and instantaneous power are shown in Figs. 1 and 2, respectively. These and the subsequent spectra, obtained using fast Fourier transform with 213 samples taken over one second of operation of the drive system, have been drawn in the logarithmic magnitude scale and normalized format, i.e., the magnitude of the fundamental had been assigned the value of 0 dB. Obviously, only the fundamental 60-Hz component appears in the spectrum of current, while the spectrum of power contains only the 120-Hz fundamental component and a dc component.

SPECTRUM OF CURRENT

Fig. 1. load.

Power spectrum of stator current of the simulated motor with constant

SPECTRUM OF POWER 0

4

Fig. 2. constant load.

Power spectrum of instantaneous power of the simulated motor with

When the load torque is changed to that shown in Fig. 3, the previously constant speed and slip of the motor begin oscillating due to the pulsating 25-Hz component of that torque. This situation may represent, in a simplified manner, torsional vibration of the shaft of the motor. As illustrated in Fig. 4, the speed oscillation is barely perceptible, as its peak-to-peak amplitude is 0.6 r/min only, i.e., about 0.05% of the average speed. The associated slip oscillation is, however, relatively stronger since the value of 0.6 r/min represents as much as 1.7% of the average slip speed of 36 r/min. As a result, the spectra of current and power significantly differ from those in Figs. 1 and 2.

In the power spectrum of stator current, shown in Fig. 5, prominent sideband components appear at 35 Hz and 85 Hz, i.e., at 60 Hz (fundamental frequency) plus and minus 25 Hz (frequency of speed oscillation). A frequency component at 110 Hz, i.e., 60 Hz +2 x 25 Hz, generated by the second harmonic of the pulsating torque, is also visible. The 35-Hz

906 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 32, NO. 4, JULYIAUGUST 1996

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- - m : w :

w : n - 3 : i-: z x: c3 1 : 4 1 2 -

n D. *: 'U': A -

0. U -

...................... ................................................................ ..

............................................ I ..................... J .....................

...................... ; ...................... L......... ..................................

35 Hr I

0 I " " ' I ' I , I " ' " " ' I b b " " " " " " " " " " " ' 0.1 0.2 0.3 0 4 0.5

TIME ( sec )

Fig. 4. Speed oscillation due to the variable torque of Fig. 3 .

e : c3 + 3 Q :

11:

c,

component, at -52 dB, has the highest magnitude after that of the fundamental. In contrast, in the spectrum of instantaneous power, shown in Fig. 6, the highest magnitude nonfundamental frequency component (not counting the dc component) appears directly at the 25-Hz frequency of speed oscillation. Moreover, its magnitude, at -47 dB, is higher by 5 dB than that of the strongest nonfundamental spectral component of the stator current. This can be attributed to the synergistic effect of phase modulation of the current, disregarded in the theoretical analysis in the previous section of the paper.

IV. EXPERIMENTAL RESULTS

To verify the generality of the presented considerations, the computer simulations described were followed by laboratory experiments with an induction motor that was purposefully different from the simulated one. The investigated drive system is shown in Fig. 7. A 7.5-hp, 220-V, 60-Hz, four-pole, wye- connected motor drives a 5-hp dc compound generator. Two resistor banks serve as a load for the generator. The first bank is used as a fixed load, while the second one can be periodically

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

SPECTRUM OF CURRENT

c.,

- - m - u :

w - o- v -

n : 3 : e : z% c3 1 : Q : 2 :

.......................................................................................

...................... J ........................................... 1 ....................

0

Fig. 5. load torque.

Power spectrum of stator current of the simulated motor with variable

SPECTRUM OF POWER

Fig. 6. variable load torque.

Power spectrum of instantaneous power of the simulated motor with

RESISTOR D C GENERATOR

CURRENT INDUCTION SHAFT SENSOR PIOTOR POSITION - SENSOR

1 I I I #I~VOLTAGE TRANSDUCER 1 '

, PROGRANMABLE

FREOUENCY

D I V I D E R MULTIPLIER

INSTANTANEOUS STATOR POWER AWL1 F I E R

STATUR CURRENT

Fig. 7. Experimental setup.

switched on and off by a power electronic switch based on an insulated-gate bipolar transistor (IGBT). In this way, periodic torque oscillation of any frequency and duty cycle can be

LEGOWSKI et al.: INSTANTANEOUS POWER AS A MEDIUM FOR THE SIGNATURE ANALYSIS OF INDUCTION MOTORS

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Fig. 8. motor with constant load.

Oscillogram of the stator current and instantaneous power of the

produced. An optical sensor of the motor shaft’s position and a programmable frequency divider are employed to make the torque oscillate either synchronously with the position of the shaft, or asynchronously. In practice, synchronous torque oscillation is typical for such mechanical abnormalities as rotor imbalance and eccentricity and, in an extreme case, a rub between the rotor and stator. Asynchronous torque oscillation, on the other hand, may result from abnormalities in a load that is geared to the motor, or from torsional vibration of the motor shaft.

To obtain an analog signal representing the instantaneous power, laboratory current and voltage probes were initially used, specifically the A6303 current probe with the AM503 amplifier and P.5200 differential voltage probe, all from Tek- tronix. Later, a dedicated system was built using the current sensor IHA-100 from F.W. Bell and differential voltage probe ADFlS from Test Probes Inc. The Burr-Brown’s MPYlOO analog multiplier performed the multiplication according to ( I ) , Circuits interfacing the sensors with the multiplier were based on instrumentation amplifiers. The HP3S82A spectrum analyzer was employed for determination of the power spectra

The first experiment involved the drive system driving a constant load, realized by the first resistor bank. As shown in the oscillogram in Fig. 8, the waveform of the stator current is slightly distorted, mainly due to the nonideal supply voltage and minor motor imperfections. The power waveform, also shown in Fig. 8, displays even stronger distortions because of the cumulative effect of multiplication of the voltage and current. Power spectra of the current and power are shown in Figs. 9 and 10, respectively. The distortions introduced by the supply voltage manifest themselves in the spectrum of current as a small second harmonic, at 120 Hz, and a prominent third harmonic, at 180 Hz. Interaction of the first three harmonics of the voltage and current produce frequency components at 0 Hz (average power), 60 Hz, 120 Hz (fundamental), 180 Hz, 240 Hz, 300 Hz, and 360 Hz (the latter two not shown). The 60-Hz component is additionally strengthened by the “antenna effect,” i.e., the

Fig. 9. Power spectrum of stator current of the motor with constant load.

Fig. 10. Power spectrum of instantaneous power of the motor with constant load.

impact of the 60-Hz electric field of neighboring power lines on the insufficiently screened measuring equipment. Frequency components at multiples of the supply frequency can, generally, be disregarded, since the rotational frequency of an induction motor is asynchronous with respect to the supply frequency. Therefore, mechanical abnormalities affect the analyzed spectra at frequencies unrelated to the supply frequency.

In the second experiment, the load torque was varied periodically by adding the second resistor bank and switching it on and off with a frequency of 10 Hz and a duty cycle of 0.5. Although the investigated motor and its operating conditions were different from those employed in the simulations, the power spectra of stator current and instantaneous power shown in Figs. 11 and 12 bear distinct resemblance to those in Figs. 6 and 7. As expected, the sideband components appear in both spectra, and in the spectrum of instantaneous power, the characteristic component, pointed at by the arrow, coincides exactly with the 10-Hz frequency of torque oscillation. Note

908 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 32, NO. 4, JULYIAUGUST 1996

Fig. 11. Power spectrum of stator current of the motor with variable load.

Fig. 12. load.

Power spectrum of instantaneous power of the motor with variable

an adjacent small frequency component at the 29.1 Hz (1746 r/min) rotational frequency of the motor, generated by the mechanical imperfections in the drive train, such as imbalance and eccentricity of the rotating parts and misalignment of the motor and load shafts.

V. CONCLUSIONS

It has been demonstrated that the instantaneous electric power, proposed as a medium for signature analysis of induc- tion motors, has definite advantages over the traditionally used current. The characteristic spectral component of the power appears directly at the frequency of disturbance, independently of the synchronous speed of the motor. This is important in automated diagnostic systems, in which the irrelevant frequency components, i.e, those at multiples of the supply frequency, are screened out. Consider, for instance, a case of torsional vibration in a drive system, always very dangerous on the long run, since it causes material fatigue and, ultimately, cracking of the shaft. The torsional vibration usually occurs

when the rotational frequency, or one of its even multiples, coincides with the first natural frequency of the torsional mode of the drive train [16]. If this frequency is low, e.g., if the vibration is excited at the rotational speed of a low-speed high-inertia motor, the frequency of speed oscillation of the motor is also low, and the resultant sideband components are close to the fundamental. Similarly, broken rotor bars generate sideband components at frequencies differing from the fundamental by only the double slip frequency [ 101-[13]. Clearly, in both the described cases, it would be difficult to filter out the fundamental without affecting the sideband components. In contrast, the characteristic component in the spectrum of power can easily be separated from the dc component by compensation of the latter component, similar to, for instance, a dc offset voltage in an operational amplifier circuit. Thus, the spectrum of power provides easier filtering conditions than that of the stator current.

Generally, not denying the diagnostic value of the sidebands components, the characteristic component provides a precious additional piece of information, which enhances the reliability of the diagnosis of health of an induction motor drive. As seen in Figs. 6 and 12, the characteristic component also tends to be stronger than the sideband components.

Extensive experimental studies are necessary to fully assess usefulness of the instantaneous power for the preventive- maintenance diagnostics and failure prevention in drive sys- tems with induction motors. Nevertheless, it can already be asserted that use of this variable as a medium for motor signature analysis deserves serious consideration. It is worth mentioning that application of the instantaneous input power for detection of electrical faults in the stator has already been proposed in [ 191.

APPENDIX PARAMETERS OF MOTORS USED IN

THE SIMULATIONS AND EXPERIMENTS

Rated power Rated voltage Rated current Rated frequency Rated speed Number of poles Stator connection Stator resistance Rotor resistance Stator inductance Rotor inductance Magnetizing inductance

Simulations 10 hp 230 V 23.8 A 60 Hz 1164 r/min 6 WYe 0.294 Rlph 0.156 Rlph 42.4 mWph 41.7 mH/ph 41.0 mWph

Experiments 7.5 hp 220 v 20.1 A 60 Hz 1735 r/min 4 WYe 0.403 Rlph 0.354 Wph 36.0 mWph 36.0 mWph 34.8 mWph

ACKNOWLEDGMENT

The authors would like to thank S. Tallapaneni, an M.S. degree graduate of the University of Wyoming, for setting up the experimental system and making measurements.

LEGOWSKT et al.: INSTANTANEOUS POWER AS A MEDIUM FOR THE SIGNATURE ANALYSIS OF INDUCTION MOTORS 909

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vol. IA-21, pp. 324332, 1985.

- .. pp. i ~ o - 1 2 8 6 , 1995. W. Deleroi, “Broken bar in squirrel cage rotor of an induction motor, Part 1: Description by superimposed fault currents” (in German), Arch. fur Elektrotechnik, vol. 67, pp. 91-99, 1984. K. R. Cho, J. H. Lang, and S. D. Umans, “Detection of broken rotor bars in induction motors using state and parameter estimation,” in Con$ Rec. 1989 IEEE-ZAS Annu. Meeting., pp. 1-6. F. Filipetti, G. Franceschini, C. Tassoni, and P. Vas, “Broken bar detection machines: Comparison between current spectrum approach and parameter estimation approach,” in Con$ Rec. I994 IEEE-fAS Annu. Meeting, pp. 95-102. J. R. Cameron, W. T. Thomson, and A. B. Dow, “On-line current monitoring of induction motors-A method for calculating the level of airgap eccentricity,” in Proc. Con$ Elec. Mach. and Drives, 1987,

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pp. 173-178.

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sor. His main research quantities and automated

Stanislaw F. Legowski (SM’84) received the M.S. and Ph.D. degrees in electronic engineering from the Technical University of Gdansk, Poland, in 1962 and 1971, respectively.

From 1958 to 1962 he was a Research Assistant at the Oceanographic Institute of the Polish Academy of Sciences in Sopot, Poland, where he conducted research in instrumentation and measurement meth- ods used in hydrography. From 1962 to 1983, he was with the Technical University of Gdansk as a Teaching Assistant, Lecturer, and Assistant Profes-

areas were electrical measurement of nonelectrical measurement methods for analog integrated circuits.

In 1983, he joined the faculty of the University of Wyoming, Laramie, where he is currently Professor of Electrical Engineering. His research interests entail analog and digital system design and power electronics.

Dr. Legowski was elected the Best Teacher for the 1979-1980 academic year in the Electronics Department of the Technical University of Gdansk. and the Outstanding Faculty Member of the College of Engineering of the: University of Wyoming for the 1983-1984 academic year. He is a member. of the IEEE-IAS Industrial Drives Committee.

A. H. M. Sadrul Ula (M’77-SM’86) received B.S. and M.S. degrees in Bangladesh, and the Ph.D. degree from the University of Leeds, Leeds, U.K., all in electrical engineering.

Between 1977 and 1982, he worked at the Depart-. ment of Electrical Engineering and Computer Sci- ence, Massachusetts Institute of Technology, C a m bridge, MA, where he was involved in the develop ment of superconducting generators. He joined the University of Wyoming, Laramie, in 1982, where he is Professor of Electrical Engineering and founding

Director of the Wyoming Electric Motor Training and Testing Center. Since 1992, with funding from the U.S. Department of Energy’s Denver Regionall Support Office, he has been conducting studies on oil-field electric motor efficiency improvements at the Naval Petroleum Reserves. As a part of this technology transfer initiative, energy efficiency improvement protocols are being developed for use by the oil field operators.

Dr. Ula is active in several professional organizations. He was instrumental in setting up the Centennial Subsection of the IEEE. He was awarded the 1987 Oustanding Branch Counselor Award by the Technical Activities Board ancl the US. Activities Board of the IEEE. He is the Student Activities Chairman for IEEE Region 5. He also served as Chairman of the Energy Conversion ancl Conservation Division of the American Society for Engineering Education. His fields of interest are power engineering, energy education, and energy policies and management.

Andrzej M. Trzynadlowski (M’83-SM’86) received the M.S. degree in electrical engineering in 1964, the M.S. degree in electronics in 1969, and the Ph.D. degree in electrical engineering in 1974, all from the Technical University of Wroclaw, Wroclaw, Poland.

From 1966 to 1979 he was a faculty member at the same university. In the following years, he worked at the University of Salahuddin in Iraq, the University of Texas-Arlington, and the University of Wyoming. Since 1987 he has been . -

with the University of Nevada, Reno. where he is now Professor of Electrical Engineering and Assistant Director of the Industrial Assessment Center. He has authored or coauthored over eighty publications in the areas of poweir electronics and electric drive systems and has been granted eleven patents. He is the author of The Field Orientation Principle in Control of Induction Motors (Norwell, MA: Kluwer, 1994).

Dr. Trzynadlowski is a member of the Industrial Drives and Industrial Power Converters Committees of the IEEE Industry Applications Society. He was the recipient of the 1992 IEEE-IAS Myron Zucker Student-Faculty Grant.