Unbalance and harmonics detection in induction motors using an optical fiber sensor

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IEEE SENSORS JOURNAL, VOL. 6, NO. 3, JUNE 2006 605 Unbalance and Harmonics Detection in Induction Motors Using an Optical Fiber Sensor Jesus M. Corres, Javier Bravo, Francisco J. Arregui, Member, IEEE, and Ignacio R. Matias, Senior Member, IEEE Abstract—In this work, a new method for the detection of the negative effects of a particular unbalanced voltage and inverter harmonics on the performance of an induction motor using fiber sensors is proposed. Supplying a three-phase induction motor with unbalanced voltages causes an oscillating electromagnetic torque that generates vibrations, increased losses, efficiency reduction, and an extra temperature rise that leads to a reduction on insula- tion life of the machine. A new in-line fiber etalon accelerometer has been designed to detect these vibrations in the range DC-500 Hz. The in-line fiber etalon scheme used provides high robustness and stability, giving enough sensitivity to monitor the low-fre- quency and low-amplitude oscillations in the stator of the machine that exist in a voltage unbalance situation. To prove this claim, a 1.5–kW squirrel cage induction motor is analyzed under different unbalance levels. It is shown that a precise unbalance factor can be detected without accessing to the electric part of the machine and an accurate monitoring can be obtained using the high-resolution analysis proposed. Index Terms—Engine fault detection, Fabry-Pérot interferome- ters, ILFE accelerometer, induction motor, unbalanced voltage. I. INTRODUCTION A CCORDING to the U.S. Department of Energy (DoE), 70% of the electricity is used by industrial motors, and in a typical industry the 80% of the load consists of three-phase AC induction motors [1]. Induction motors are being used more than ever before due to their versatility, dependability and economy. In most cases, condition monitoring schemes have focused on one of three induction motor components: the stator, rotor or bearings. Actually vibration monitoring is accepted for diag- nosis of electrical nature faults for many types of machines since this practice does not require either modification of the machine or the access to the supply lines [2]–[4]. Large systems are often equipped with mechanical sensors, primarily vibration sensors based on proximity probes. Those however are delicate and ex- pensive. While the use of vibration monitoring is currently extensive, moderately little attention has been paid to voltage unbalance in the motor supply. Voltage unbalance is related with the case of an unbalanced distribution system network or the use of single phase loads. Some representative examples are unsymmetrical Manuscript received March 14, 2005; revised July 4, 2005. This work was supported by the Spanish Ministerio de Ciencia y Tecnologia-FEDER under Research Grant CICYT-TIC 2003-00909 and Gobierno de Navarra Research Grants. The associate editor coordinating the review of this paper and approving it for publication was Dr. Subhas Mukhopadhyay. The authors are with the Universidad Pública de Navarra. Campus Arrosadía s/n. Edificio Los Tejos. Departamento Ing. Eléctrica y Electrónica, 31006-Pam- plona (Navarra) Spain ([email protected]; [email protected]; par- [email protected]; [email protected]; www.unavarra.es). Digital Object Identifier 10.1109/JSEN.2006.874441 transformer windings or transmission line impedance, unbal- anced three-phase loads, blow fuses on three-phase systems, or switching significant single-phase loads, just to mention a few. Because of the wide use of the induction motors both in indus- trial and residential areas, the damaging effects on induction motors will cause an important economic impact. Under a voltage unbalance the amplitude of the line currents deviation can be many times larger than the voltage change, creating a torque pulsation. From the electrical viewpoint, vi- brations are due to varying magnetic forces acting between the stator and rotor of the machine. Mechanical vibration of electric machines is a source of troubles because of the faster ageing of the machine. Another cause of machine’s life reduction is the extra tem- perature rise that the induction motor under voltage unbalance experiments because of the efficiency reduction since even a small unbalance in the system severely increases the rotor losses. When functioning at low speed the thermal dissipation capability is low, and the derating can become particularly se- rious. International Electrical Code (IEC) standards [5] restrict the permissible voltage unbalance on induction motors to 1% and obligate to derate if voltage unbalance is greater (5%). The causes for lowering the machine power rating exist in all stages of the electrical energy transformation, from the gen- eration to the final user. As it is well known the reliability of power electronics systems is of paramount importance in in- dustrial, commercial, aerospace and military applications. One of the main problems in pulsewidth modulation (PWM) drives is the current distortion because of the nonideal characteris- tics of GTOs, IGBTs, or MOSFETs in the inverter bridge. The main source of output current distortion, and consequently in the torque ripple in the motor shaft, is the dead time insertion that must be present in order to prevent the short circuit of the inverter bridge. The use of microprocessors gives high quality control but, although the PWM waveforms are becoming more and more complex, these waveforms rarely have the same shape on each phase and, therefore, the three-phase output voltages can be unbalanced. Also, it is well known that from the safety point of view, preventive maintenance, for example of critical re- actor components in nuclear plants, like the refrigeration pumps, has a significative importance. A common characteristic of these large machines, that are the target of this paper, is the pres- ence of high current and voltage levels that create high deriva- tives and electromagnetic interferences. When switching high power levels for machine control, the commutation device can cause unacceptable interferences in the measured signal. Be- cause of that, the electro-magnetic interference (EMI) immunity of fiber-optic sensors is an advantageous candidate to cover the sensing needs in these fields of application. The high electrical 1530-437X/$20.00 © 2006 IEEE

Transcript of Unbalance and harmonics detection in induction motors using an optical fiber sensor

IEEE SENSORS JOURNAL, VOL. 6, NO. 3, JUNE 2006 605

Unbalance and Harmonics Detection in InductionMotors Using an Optical Fiber Sensor

Jesus M. Corres, Javier Bravo, Francisco J. Arregui, Member, IEEE, and Ignacio R. Matias, Senior Member, IEEE

Abstract—In this work, a new method for the detection of thenegative effects of a particular unbalanced voltage and inverterharmonics on the performance of an induction motor using fibersensors is proposed. Supplying a three-phase induction motor withunbalanced voltages causes an oscillating electromagnetic torquethat generates vibrations, increased losses, efficiency reduction,and an extra temperature rise that leads to a reduction on insula-tion life of the machine. A new in-line fiber etalon accelerometerhas been designed to detect these vibrations in the range DC-500Hz. The in-line fiber etalon scheme used provides high robustnessand stability, giving enough sensitivity to monitor the low-fre-quency and low-amplitude oscillations in the stator of the machinethat exist in a voltage unbalance situation. To prove this claim, a1.5–kW squirrel cage induction motor is analyzed under differentunbalance levels. It is shown that a precise unbalance factor can bedetected without accessing to the electric part of the machine andan accurate monitoring can be obtained using the high-resolutionanalysis proposed.

Index Terms—Engine fault detection, Fabry-Pérot interferome-ters, ILFE accelerometer, induction motor, unbalanced voltage.

I. INTRODUCTION

ACCORDING to the U.S. Department of Energy (DoE),70% of the electricity is used by industrial motors, and in a

typical industry the 80% of the load consists of three-phase ACinduction motors [1]. Induction motors are being used more thanever before due to their versatility, dependability and economy.In most cases, condition monitoring schemes have focused onone of three induction motor components: the stator, rotor orbearings. Actually vibration monitoring is accepted for diag-nosis of electrical nature faults for many types of machines sincethis practice does not require either modification of the machineor the access to the supply lines [2]–[4]. Large systems are oftenequipped with mechanical sensors, primarily vibration sensorsbased on proximity probes. Those however are delicate and ex-pensive.

While the use of vibration monitoring is currently extensive,moderately little attention has been paid to voltage unbalance inthe motor supply. Voltage unbalance is related with the case ofan unbalanced distribution system network or the use of singlephase loads. Some representative examples are unsymmetrical

Manuscript received March 14, 2005; revised July 4, 2005. This work wassupported by the Spanish Ministerio de Ciencia y Tecnologia-FEDER underResearch Grant CICYT-TIC 2003-00909 and Gobierno de Navarra ResearchGrants. The associate editor coordinating the review of this paper and approvingit for publication was Dr. Subhas Mukhopadhyay.

The authors are with the Universidad Pública de Navarra. Campus Arrosadías/n. Edificio Los Tejos. Departamento Ing. Eléctrica y Electrónica, 31006-Pam-plona (Navarra) Spain ([email protected]; [email protected]; [email protected]; [email protected]; www.unavarra.es).

Digital Object Identifier 10.1109/JSEN.2006.874441

transformer windings or transmission line impedance, unbal-anced three-phase loads, blow fuses on three-phase systems, orswitching significant single-phase loads, just to mention a few.Because of the wide use of the induction motors both in indus-trial and residential areas, the damaging effects on inductionmotors will cause an important economic impact.

Under a voltage unbalance the amplitude of the line currentsdeviation can be many times larger than the voltage change,creating a torque pulsation. From the electrical viewpoint, vi-brations are due to varying magnetic forces acting between thestator and rotor of the machine. Mechanical vibration of electricmachines is a source of troubles because of the faster ageing ofthe machine.

Another cause of machine’s life reduction is the extra tem-perature rise that the induction motor under voltage unbalanceexperiments because of the efficiency reduction since evena small unbalance in the system severely increases the rotorlosses. When functioning at low speed the thermal dissipationcapability is low, and the derating can become particularly se-rious. International Electrical Code (IEC) standards [5] restrictthe permissible voltage unbalance on induction motors to 1%and obligate to derate if voltage unbalance is greater (5%).

The causes for lowering the machine power rating exist inall stages of the electrical energy transformation, from the gen-eration to the final user. As it is well known the reliability ofpower electronics systems is of paramount importance in in-dustrial, commercial, aerospace and military applications. Oneof the main problems in pulsewidth modulation (PWM) drivesis the current distortion because of the nonideal characteris-tics of GTOs, IGBTs, or MOSFETs in the inverter bridge. Themain source of output current distortion, and consequently inthe torque ripple in the motor shaft, is the dead time insertionthat must be present in order to prevent the short circuit of theinverter bridge. The use of microprocessors gives high qualitycontrol but, although the PWM waveforms are becoming moreand more complex, these waveforms rarely have the same shapeon each phase and, therefore, the three-phase output voltagescan be unbalanced. Also, it is well known that from the safetypoint of view, preventive maintenance, for example of critical re-actor components in nuclear plants, like the refrigeration pumps,has a significative importance. A common characteristic of theselarge machines, that are the target of this paper, is the pres-ence of high current and voltage levels that create high deriva-tives and electromagnetic interferences. When switching highpower levels for machine control, the commutation device cancause unacceptable interferences in the measured signal. Be-cause of that, the electro-magnetic interference (EMI) immunityof fiber-optic sensors is an advantageous candidate to cover thesensing needs in these fields of application. The high electrical

1530-437X/$20.00 © 2006 IEEE

606 IEEE SENSORS JOURNAL, VOL. 6, NO. 3, JUNE 2006

Fig. 1. Schematic diagram of the electro-mechanical system.

isolation allows the use of fiber-optic probes in places wherethe use of electrical instrumentation is dangerous or inoperative,such as under highly explosive atmospheres, for example in thepetrochemical industry.

There are several fiber-optic based techniques for vibrationmeasurement [6]. Widely speaking they can be classified intofiber Bragg gratings (FBGs) [7], intensity modulation [8], andFabry-Pérot interferometry (FPI) [9]. The highest sensitivity isprovided by the interferometric techniques, and among them themost attractive probably is the FPI, because of its easy imple-mentation, low size and robustness. The intrinsic configuration[10] uses semi reflective surfaces on the faces of a segment offiber fused to the lead fibers in order to create the interfero-metric cavity. The extrinsic configuration [11] consists of a mi-crometric alignment tube that provides mechanical stability tothe pair of cleaved fiber end faces. The main disadvantage ofthis scheme comes from the difficulty to protect adequately thecavity in order to obtain robust and long term usable sensors.

An alternative configuration that produces robust devices,used in this study, is the in-line fiber etalon (ILFE) proposed bySirkis et al. [12], [13]. This sensor is built by fusing a segmentof hollow core fiber between two standard single-mode fibersto create the interferometric cavity. As the outer diameter ofthe hollow core segment match with the single-mode fibers, thestress at the discontinuities is significantly low.

The sensor used in this work is based on the seismic mass ef-fect with two different ranges of operation. Below the resonancefrequency it works as an accelerometer, and for higher frequen-cies the output is proportional to the displacement, working asa vibrometer.

The paper structure will start with some definitions about thesystem under voltage unbalance. Then the transducer construc-tion and the main properties of its performance will be shown.After that, the experimental results will be presented and the ca-pacity of the proposed system to detect the electrical unbalancein three-phase induction machines will be tested.

II. THEORETICAL BACKGROUND

The system under study is schematized in Fig. 1. The prin-ciple of operation consists of the presence of an electromagneticmotor torque, created by the angle between the rotor and statorflux angles of any electrical machine, which is present both inthe stator and rotor of the machine. The torque on the statorserves to induce the change in the speed of the load, as requiredby the power controller. Part of this torque can be detected usinga gauge torque transducer in the couplings with the load. The re-action torque is transmitted by the mechanical assembly to thesupporting base, inducing undesirable oscillations that can bedetected with the use of adequate vibrometers.

Below, the method of the symmetrical components is ex-posed. It is used here to calculate the motor torque underdifferent voltage unbalance degrees.

A. Symmetrical Components

Classical fault analysis of unbalanced power systems hasutilized a symmetrical component based approach [14] toobtain the zero, positive and negative sequence model forsystem components. Given the sequence line to neutral voltages

, the sequence voltages are computedwith [15]

(1)

where . As zero-sequence components are neverpresent in the line-to-line voltages regardless of the unbalancelevel, negative sequence voltage is the primary cause of voltageunbalance.

The electrical model of [16] can be reduced further to theelectrical networks shown in Fig. 2, for the positive and negativesequences. The negative sequence equivalent circuit has inputimpedance similar to that of the locked rotor, in which even asmall amount of negative sequence voltage causes a large cur-rent and the stator losses increase.

The electromagnetic torque is given by the following expres-sion [17]:

(2)where is the synchronous electrical frequency, is the rotorelectrical frequency, and is the slip.

B. Voltage Unbalance Definitions

Comprehension of how voltage unbalance influences thesteady-state performance of induction motors is the theoreticalroot of standards related to induction motor operation andprotection. The voltage unbalance factor (VUF) of a sinusoidalthree-phase voltage system is defined by the IEC as the quotientbetween the negative and positive sequence components [18]

(3)

Normally positive sequence voltage is very close to the ratedvoltage, and the negative sequence voltage is very close to theVUF. Thus, VUF can indeed be considered as the negative se-quence component per unit.

Also, the phase voltage unbalance rate (PVUR) is defined inthe IEEE Standard 141

(4)

where .

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Fig. 2. Sequence models of the induction motor.

Fig. 3. Schematic diagram of ILFE.

C. Harmonics Influence on the Sensing Scheme

Harmonics produced by inverters can be in some casesa main source of vibration and oscillations in AC motors.The fundamental harmonic component is positive-sequence,second harmonic is negative-sequence, and third harmonic iszero-sequence, repeating this pattern higher order harmonics.Negative sequence harmonics produce a pulsating torque thatcauses excess of power losses in the winding as it works againstthe fundamental component. This is the case of the harmoniccomponent created by the voltage unbalance. Those withpositive sequence have a forward rotation and also increasethe losses due to skin effect and eddy currents. Finally, triplenharmonics are zero-sequence harmonics that are multiples ofthird harmonic and they have no effect on torque pulsation.

The harmonics caused by inverters, in practice, are odd andnot a multiple of three. In [19] the impact of harmonics on in-duction motors is analyzed, and for example, for the lowestharmonic frequencies, which are fifth and seventh in a three-phase square wave inverter, they produce a torque that pulsatesat a sixth harmonic frequency. In addition, as higher order har-monics produce torque components at higher frequencies, theyhave a lower impact on the speed ripple because of the integra-tive effect of the system inertia. The harmonic content of theinverter output depends on the type of control. For the six-stepdrives, which basically have a square wave output, torque rippleis a problem, because at low frequencies the stepped nature ofthe stator rotating field causes the torque to be applied in pul-sations. However, on modern sinusoidal PWM the problem oftorque pulsations is greatly reduced, because the output waveis near-sinusoidal, even at very low speeds. In [20] we can seehow the PWM modulation pushes the harmonics into a high-fre-quency range around the switching frequency and its side-bands (5–10 kHz). A PWM drive produces little heating andtorque precisely because of the high frequency. The leakage in-ductance of the motor goes up in proportion to frequency, sohigher frequency voltage harmonics result in very little currentand very little torque and heating effect.

As far as we know, the second order torque ripple harmonicis not involved in the electromagnetic nature oscillations causedby the switching nature of power inverters, unless when theoutput have voltage unbalance, for example caused by a dead-time problem. Nevertheless, if a symmetrical system with har-monics becomes unbalanced, a second harmonic negative-se-quence current will flow independent of the existing harmonics.The resulting unbalanced (negative sequence) currents inducedouble system frequency currents in the rotor that quickly causerotor overheating.

Under voltage unbalance, thermal, mechanical and magneticstresses appear and cause the majority of rotor faults, which fi-nally are due to broken rotor bars. In [21], a simulation study ofan induction motor with rotor broken bars is reported. The spec-trum of the torque ripple, and in consequence of the vibrationspectrum, gives , components, where is the speed slipand is the line frequency. As the slip is low in normal oper-ation, the vibration harmonics are in the low-frequency range,around 4 Hz.

III. SENSOR FABRICATION AND CHARACTERIZATION

The seismic mass effect is the principle of operation of thedeveloped sensor, where the system is created by the opticalfiber and a concentrated mass. The optical fiber works as thespring in the spring-mass system, and its deformation is regis-tered using interferometry of the light reflected by the mirrorsof a Fabry-Pérot etalon.

The etalon scheme is shown in Fig. 3. The first step for thefabrication of the sensor consists of cleaving a standard single-mode fiber and a 50/125 hollow core fiber. As the cleaving angleis of vital importance in order to maintain the amount of lightthat reaches the detector, each cleaved fiber is tested launchingthe beam of a laser source and measuring the power of the re-flected light. Then the cleaved end face of the single-mode-fiber(SMF) is fused to the hollow core. The next step consists of cut-ting the hollow core fiber attached to the SMF, setting at this

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Fig. 4. Schematic diagram of unbalance monitoring system.

point the length of the cavity. The final step is the fusion of thehollow core fiber end face to another single-mode fiber.

This technique has the advantage that both mirrors are pro-tected against external factors and parallelism between both sur-faces can be fitted with high accuracy. Nevertheless, due to thehigh sensitivity required for the measurement of rotating ma-chine vibrations, it has been necessary to build sensors with acavity on the millimeter range.

The schematic setup of the measurement system is shown inFig.4.The light froma1-mWlaserat1310nmpasses throughoneinput of a 2 1 SMF coupler. The output arm is attached to theILFE sensor and the other input is connected to a photodetectorthat detects the light reflected by the sensor containing the vibra-tion information, with a gain of 10 . The photodetectoris connected to an oscilloscope with a FFT module to show thefrequency domain representation of the vibration applied signal.An ILFE of 500- cavity length with a lead concentrated massof 40 g bonded to the end of the fiber was used.

When acceleration is impressed to the frame where one pointof the fiber is bonded, a strain caused by the inertial force ap-pears in all the sections of the fiber. Particularly in the hollowcore fiber the strain causes a deformation, changing the lengthbetween both ends of the cavity. Also, the deformation generatesa change in the optical power reflected because of the light inter-ference. This is basically the operation of the proposed sensor.The ILFE sensor exhibits a good linearity in the measurementrange, as it can be seen in Fig. 5. The output can be consideredapproximately linear in the range 20%–80%, with a typical de-viation of less than 2%. The minimum detectable accelerationdepends on the sensor range and on the amplifier of the signalconditioning system. The limiting factor is the resolution of thephotodetector signal conditioning. The optical-power meter hasan inherent random noise of 8.8 . The minimum detectableamplitude acceleration was assumed when the noise was of thesame amplitude as the output of the sensor. In this situation thesensor was put under a sinusoidal oscillation using the electro-dynamic shaker. However, using an appropriate filter, the noisecan be reduced consequently increasing the signal-to-noise ratio(SNR) of the recovered signal. The minimum detectable accel-eration amplitude was found to be 0.5 , which correspondsto a 300-nm displacement amplitude, measured at 200 Hz. Hys-teresis was negligible.

Fig. 5. Amplitude response of the optical fiber accelerometer at f = 200 Hz

with a sensitivity of 1.76 nWs m .

It has to be taken into account that the fiber is an elastic ma-terial that can be modeled as a spring, with the recovery con-stant , given by the area of the hollow core section and theglass Young’s module. Also, the presence of damping is usefulto reduce the impact of resonances and stabilize the mass-springsystem. Therefore, applying modal analysis to the proposed me-chanical system for the steady-state sinusoidal movement, theamplitude of the sinusoidal deformation of the fiber, is given by[22]

(5)

where , , . The vari-able is the frequency of the sinusoidal vibration wave, isthe inertial mass in Kg, is the damping in kg/s, and is theamplitude of the absolute displacement of the mounting. Thisdisplacement amplitude is given by , where isthe acceleration amplitude.

According to this mathematical model the frequency re-sponse of the sensor has been simulated and the results can beseen in Fig. 6, where a resonance peak around 85 Hz can beappreciated. For frequencies below the resonance frequency,the output of the sensor is proportional to the acceleration, evenfor DC values. The resonance frequency depends on severalfactors, but the main variable for its adjustment is the overalllength of the fiber that is between the concentrated mass andthe frame to which it is bonded. The resonance peak establishesthe working range as accelerometer and as vibrometer for the

CORRES et al.: UNBALANCE AND HARMONICS DETECTION IN INDUCTION MOTORS USING AN OPTICAL FIBER SENSOR 609

Fig. 6. Theoretical analysis of the frequency response of the ILFE sensor.

sensor. When working as a vibrometer (for frequencies threetimes higher than the resonance), the relative displacementbetween the mass and the base (sensed by the transducer) isessentially the same as the displacement of the base. In thiscase, the output of this sensor is proportional to the absolutedisplacement of the machine. In order to extend the measure-ment range of the system, an easy signal processing of thespectrum can be used to obtain the same magnitude (accel-eration, velocity or displacement) in all the measuring range,whenever the worst-case SNR (for the highest frequency) beadequate for the application of interest.

IV. EXPERIMENTAL RESULTS AND DISCUSSION

Based on the theoretical studies explained in [22], and onboth theoretical and experimental results, a linear relationshipbetween the current harmonics and vibration level can be as-sumed. However it is important to note that the vibrations tendsto be nonstationary in time and due to the complex relationshipbetween the stator frame and the airgap permeance the ampli-tudes of the harmonics can behave in a different way. This re-lationship is highly dependent on the mechanical system, as itdiffers greatly for each vibration frequency.

A robust and well-balanced test-rig, implemented in our lab-oratory and shown in Fig. 7, was used. Nominal and electricalmodel parameters of the AC induction motor are shown inTable I. With the use of a TMS320C30 digital signal processorcontrol card and IGBT inverter, any failure of electro-magneticorigin that can exists in a real machine, can be recreated on thetest-rig because it controls the instantaneous electromagneticflux and, in consequence, the instantaneous torque applied.More details about the experimental test can be found in [23].

A. Test of the System With Square Waveform

In order to verify the capacity to detect vibrations generatedby a failure of the electrical system, a twin machine has beenemployed to introduce an electromagnetic disturbance torque.An electromagnetic torque square waveform of 3.5 nm was in-troduced using the DSP-based field oriented vector control al-gorithm [23]. In spite of the high test-rig robustness, the Fig. 8shows how the ILFE sensor detected the 10-Hz fundamental andits main harmonics.

As expected, odd harmonics are detected due to the squaredisturbance waveform applied with the load motor. The most

Fig. 7. Motor test-rig with 1.5-kW three-phase induction machine.

TABLE IEXPERIMENTAL TEST-RIG PARAMETERS

Fig. 8. ILFE sensor output (FFT), 3.5-nm square-wave disturbance torque ap-plied.

important it is the third harmonic because the electromagneticfield created by this component of the flow in the rotor of theinduction machine produces as well a torque that it opposes tothe direction of rotation of the fundamental component.

B. Three-Phase Voltage Unbalance Test

For this test, the induction motor has been fed with three-phase sinusoidal waveforms. A variable degree ofvoltage unbalance on phase was introduced reducing the am-plitude of the waveform. The state of the machine was loggedmeasuring the shaft speed, the torque given by the gauge trans-ducer and the electrical magnitudes (currents and voltages). Thepower factor was also monitored. Initially, a balanced three-phase voltage system (200 , 45 Hz) was applied. Then the

610 IEEE SENSORS JOURNAL, VOL. 6, NO. 3, JUNE 2006

Fig. 9. Electrical performance of the induction machine under voltage unbal-ance (0%–10%).

Fig. 10. Supply voltage waveform (200 V , 45 Hz) applied and filteredILFE vibration waveforms obtained under unbalance operation (5%).

PVUR was increased in 0.5% steps up to a 10%, reducing forthis the amplitude of . In Fig. 9, the performance of the elec-trical magnitudes can be appreciated through the power factor ofthe machine, which relates the active power with the total (activeand reactive) power. The motor was left to rotate freely withoutexternal load torque. In steady state, the motor torque remainsequal to the torque caused by the friction forces. As the powerfactor measures the real power consumption, it increases withthe unbalance degree, because of the additional losses causedby the speed change of the shaft inertia.

When running without unbalance, basically only vibrationsdue to friction or other mechanical causes should be appreciated.In the motor under test, a very low oscillation was detected inthe balanced situation. The reason for this circumstance is theinherent unbalance present in any real machine because of thefact that the windings of the three-phase circuit are not exactlymatched, but after adjusting the phase voltages, this oscillationis easily cancelled.

The theoretical study indicates that the positive sequencecomponent gives a constant torque in the forward direction,while the negative sequence component generates a secondorder harmonic [24]. In Fig. 10, under a 5% of voltage un-balance, we appreciate how the vibration measured has aperiodic waveform (90 Hz) with a frequency that doubles thefundamental waveform, as it was expected.

Fig. 11. Transient response to a voltage unbalance PVUR (0%–5%).

Fig. 12. Speed waveforms and ILFE output amplitude for five unbalance de-grees in steady state.

C. Transient and Steady-State Operation

In Fig. 11, the transient response of the ILFE vibrometer isshown for a change in the supply voltages at . In thisfigure, only the phase is shown, because the other componentsamplitude remains at a constant RMS value of 200 V. The low-frequency oscillations are caused by the sudden operation pointchange.

In Fig. 12, the speed of the shaft was detected using a digitalencoder of 4096 pulses per revolution. Using an oscilloscopewith FFT module, the 90-Hz harmonic of the ILFE output wasalso logged for different steady-state unbalance degree. It can beseen in this figure how the speed ripple and the external vibrationincrease with the unbalance. In Fig. 13, this harmonic compo-nent is represented over the voltage unbalance, and as it can beseen, it exhibits a monotonic performance, increasing with theapplied distortion. This means that the measurement obtainedcan be used in the condition monitoring of the machine to de-tect electrical nature faults, and in particular the ones caused byvoltage unbalance.

D. Harmonics Caused by Inverters

In Fig. 14, the response of the ILFE sensor is representedwhen the power inverter injects harmonics to the motor. The

CORRES et al.: UNBALANCE AND HARMONICS DETECTION IN INDUCTION MOTORS USING AN OPTICAL FIBER SENSOR 611

Fig. 13. Steady-state amplitudes of the ILFE sensor for an unbalance range of[0%–10%].

Fig. 14. Steady-state amplitudes of the ILFE sensor measured in the sixth har-monic frequency when a fifth and seventh harmonics are injected in the voltagewaveform.

Fig. 15. Steady-state amplitudes of the ILFE sensor measured in the sixth har-monic frequency when the inverter is in the overmodulation range.

digital signal processor that controls the voltages applied to thestator was reprogrammed in order to create a sinusoidal wave-form superposed to the fundamental voltage. The fundamental

is 10 Hz and 50 and the fifth (reverse rotation) and sev-enth (forward rotation) harmonics were created in order to em-ulate the performance of the proposed sensor for measuring themain components that appears in inverter-fed motors. As wasshown in Section II-C, the mechanical oscillation produced canbe measured at the sixth harmonic.

In Fig. 15, the power inverter is overmodulated and also in-jects fifth and seventh harmonics. For this, the controller is de-manded with a voltage higher than the maximum for the linearrange (modulation index higher than the unity). The sinusoidaloutput of the inverter in this case tends to work as a six-step [19].

V. CONCLUSION

In this paper, a new comprehensive and generalized procedureis presented to predict the steady-state performance of three-phase motors under unbalanced conditions. This is the first timethat an ILFE fiber-optic sensor has been used as a vibrometerfor unbalance detection. It is well known that voltage unbalancecauses extra loads to the utilities and additional charges to con-sumers. With the high-sensitivity scheme proposed, specificallydesigned for operation in the low-frequency range, the applica-tion to voltage unbalance detection is feasible. The interfero-metric mechanism of the sensor allows to measure nanometricscale oscillations, with the well-known additional properties ofEMI immunity and high dielectric isolation of fiber-optic sen-sors. These properties could make the ILFE vibrometer espe-cially appropriate to prevent faults in high-power machines lo-cated in nuclear plants. The same sensor can also be used to de-tect inverter harmonics and other critical machine defects likebroken bars or winding short circuits whenever they are in thesensor frequency range.

ACKNOWLEDGMENT

The authors would like to thank the Mechanics and Physics(Electro-acoustics) Departments of the Universidad Pública deNavarra for the materials lent and G. Ghanshyam for his ines-timable help.

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Jesus M. Corres received the M.S. degree in elec-trical engineering in 1996 and the Ph.D. degree in2003, both from the Public University of Navarra(UPNA), Pamplona, Spain.

He has been a member of the Department of Elec-trical and Electronics Engineering, UPNA, for eightyears, and has been involved in different projects withindustry, including power systems design and motioncontrol. His main research interests include opticalfiber sensors and nanostructured materials.

Javier Bravo received the M.S. degree in electricalengineering from the Public University of Navarra(UPNA), Pamplona, Spain, in 2003. He is currentlypursuing the Ph.D. degree in the CommunicationsDoctoral program in the Electrical and ElectronicEngineering Department, UPNA.

His research interests are mainly in fiber-optic sen-sors.

Francisco J. Arregui (M’01) received the M.S.degree in electrical engineering from the CatholicUniversity of Navarra, San Sebastian, Spain, in 1994and the Ph.D. degree from the Public University ofNavarra (UPNA), Pamplona, Spain, in 2000.

He has been a member of the CEIT ResearchCenter, San Sebastian, for two years and has beeninvolved in different projects with industry, includingmedical instrumentation and monitoring of highpower lines and communications hardware. Since1995, he has been with the UPNA. During 1998 and

2000, he was a Visiting Scientist at the Fiber and Electro Optics ResearchCenter, Virginia Polytechnic Institute and State University, Blacksburg. Hismain research interests include optical fiber sensors, sensor materials, andnanostructured materials.

Dr. Arregui is a member of SPIE. He is an Associate Editor of the IEEESENSORS JOURNAL.

Ignacio R. Matías (M’01-A’01-SM’03) received theM.S. degree in electrical and electronic engineeringand the Ph.D. degree in optical fiber sensors from thePolytechnic University of Madrid, Madrid, Spain, in1992 and 1996, respectively.

He became a Lecturer at the Public Universityof Navarra, Navarra, Spain, in 1996, where hs ispresently a Permanent Professor. He has coauthoredmore than 200 book chapters and journal and con-ference papers related to optical fiber sensors andpassive optical devices and systems.

Dr. Matías is an Associate Editor of the IEEE SENSORS JOURNAL.