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JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN ELECTRICAL ENGINEERING COMMONLY OCCURRING FAULTS IN THREEPHASE INDUCTION MOTORS – CAUSES, EFFECTS AND DETECTION - A REVIEW 1 1 Department DR. SHASHI RAJ KAPOOR of Electrical Engineering, University College of Engineering, Rajasthan Technical University (RTU), Kota (RAJ.), India. [email protected] ABSTRACT: This paper expounds an elementary delineation of the tangible verities and occurrences associated to induction motors and induction motor faults. Besides, it explicates the underlying tenet, causes and consequences of frequently occurring faults in induction motors. The paper attempts to discuss different types of induction motor faults, their causes and detection techniques. It is found that the detection techniques which evaluate the dynamic behaviour of the signal (such as Wavelet Transform analysis) are best suited for the purpose. Keywords— Fault detection and identification (FDI), Mechanical and electrical faults, Condition monitoring. I: INTRODUCTION Induction motors are intricate electro-mechanical devices that are widely used in industrial processes and commercial installations. Such motors have extensive usage in consequence of their sturdy edifice, unpretentious installation, undemanding control strategies, and adaptability to various industrial applications. Furthermore, induction motors may plausibly be fed from an unswerving sinusoidal power supply or by an inverter fed variable frequency drive. Most of the faults in the induction motors may be detected in the nascent stages so as to prevent untimely failures [3]-[7]. This paper addresses induction motor faults, their causes-effects and various detection techniques that are used for incipient fault detection in three-phase induction motors. II: MAJOR DAMAGE TYPES OF INDUCTION MOTORS The probable reasons for induction motor impairment can be a multiplicity of factors such as filth and dirt instigated temperature intensification; unwarranted vibrations due to faulty bearings; thermal stresses due to rotor rub, rotor skewing, and end ring heating; mechanical stresses due to air gap eccentricity, frequent startups, rapid acceleration and deceleration; long persistent overload conditions; transient torques due to faulty bearings, poor supply quality, and unbalanced stator phase winding; flaws in manufacture or design; imperfect installation; deterioration due to abrasion, erosion and aging. Most of the time there are copious factors that beget motor breakdown. The most unequivocal basis for motor breakdown is damage of the bearings or winding or rotor but the paramount rationale that is often an attribute to such failures is overheating prompted through dirt, filth and grime.The literature point out that majority of the failures in the threephase induction motors are mechanical in nature such as bearing faults, misalignment or eccentricity faults and balance related faults [1], [8]. The commonly occurring electrically detectable Induction motor faults are as follows [1], [4]-[7], [14]-[15], [31]: (A) Unbalanced Supply Condition: The unbalanced supply condition [15] is the most commonly occurring electrical anomaly in the Induction motors. The unbalanced supply condition might be due to the poor power quality resulting from unequal phase voltage and/or currents, poor or damaged terminal contacts to motor, unbalanced load distribution on one or more phases, faulty power factor correcting equipment installed on one or more phases etc. The unbalanced supply fault although external to motor, might result in damage to motor foundation, bent shafts, rotor eccentricity, damaged bearings, and burnt motor terminals. These fault conditions, under extreme situations, might result in severe and objectionable motor vibrations, oscillating torque, and unsymmetrical phase currents. The phase unbalanced condition causes increase in current in one or more phases and might result in blown fuse in affected phase circuit. This subsequently turns up into single phasing of the motor which need necessarily be checked to avoid severe motor damage. (B) Broken Rotor Bars: Outsized squirrel cage induction motors are assembled using copper rotor bars and end-rings, whereas small and medium sized cage motors are by and large crafted using die-cast aluminum rotor and end rings. Therefore, there is preponderance of diecast aluminum rotors in the induction motors on account of its distinctive light weight and low cost. These die-cast rotors bring in numerous predicaments, ISSN: 0975 – 6736| NOV 12 TO OCT 13 | VOLUME – 02, ISSUE - 02 Page 178 JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN ELECTRICAL ENGINEERING such as rotor eccentricity and temperature instigated softening of bars and end-rings. The alternative approach to fabricate the cage rotors is by using brazed or welded copper rotor bars. The rotor failures get trigger off by an assortment of diverse stresses and strains that appear in the rotor. Stresses can be electromagnetic, thermal, residual, dynamic, environmental and mechanical [2]. The foremost reason for the rotor failure typically resides in flaws related to imperfect casting or substandard jointing during manufacturing. Whilst the rotor bar is slighter than the bar slot, slot harmonics will surface that subsequently initiate radial advance of the bar, particularly during starting-up, accelerating and braking periods. This might beget frailty consequently ensuing in fractured and ruptured rotor bar(s). Thermal stress is an additional quandary, occurring when the bar cannot progress longitudinally in the rotor slot. Sustained motor overloads and frequent starts, acceleration and deceleration contribute to cultivate substantial currents that bring forth considerable mechanical and thermal stresses, consequently prompting damage to the rotor and the stator as well. Even so, the induction motor rotor faults by and large onset from a minuscule crevice or a high resistivity spot in the rotor bar. This spot shows temperature intensification which worsens the damage until the rotor bar is absolutely conked out. Subsequent to a solitary rotor bar breakage, the rotor current reassigns to the other co-existing healthy bar(s) causing the over current and ultimately a cluster of broken bars. Another frequently occurring source for the rotor failures is the over-current typically due to rotor clog up condition of the motor. It is on the whole not beneficial or feasible to mend the rotor. A broken rotor bar brings about assorted outcomes of concern in induction motors. A documented consequence of a broken rotor bar is the advent of the purported sideband components [4, 9, 10]. Bar failure progression that induces sideband frequencies in current and power spectrum of the induction motors involves an intricate mechanism. The precursors of rotor faults encompass the twofold slip frequency side bands flanking the supply frequency in a frequency spectrum of the stator current. The lower side band component to the left of the fundamental is prompted by electrical and magnetic disparity in the rotor cage of an induction motor [9], whilst the lower sideband component to the right is attributable to ensuing speed undulations on account of the varying air-gap torque [4, 16]. The frequencies of these sidebands, fSB, can be formulated as: (1) Where k = harmonic index = 1, 2, 3, ----s = per unit slip p = number of fundamental pole-pairs fe = fundamental supply frequency On account of the configuration of the windings in an induction motor, only the frequency components with harmonics k =1, 5, 7, 11, 13, and so forth will figure in the current. Then, the equation (1) can be transformed as: (2) For harmonic index k = 1, the equation (2) gets further altered as: (3) The spectral sideband components are availed of to a large extent for induction motor fault classification [9, 10, 20, 29, 48]. At high voltage or low inertia, the upper sideband takes the limelight owing to speed undulations churned out of the defective bar. Air-gap space harmonics brought into being due to tooth or core saturation influence the upper spectral sideband component. Other correlated effects of broken rotor bars that are used for motor fault diagnosis and detection purposes include speed undulations [16], torque ripples [19], stator power swings [24], and stator current envelopes [49]. (C) Damaged Bearing Faults: Four major types of bearing faults [3] are material deterioration in inner race, outer race, cage, and ball defects. The bearing faults can be classified into cyclic faults and non-cyclic faults. Cyclic faults emerge when the rolling element and the race or the rolling element cage of the bearing passes through the point of flaw. The deep scratches in a race or in a rolling element are a type of cyclic fault. The material abrasion, qualitative degradation of the lubricant due to contaminants, insufficient lubrication, slither and skid amongst the movable bearing components cause mutilation of the contact areas, which is a non-cyclic fault category. The bearing defects induce non-stationary and fault specific frequency components in the stator current and the engendered vibrations. a) Cage Defect: The bearing cage of a ball bearing upholds the balls at evenly balanced positions and assists the confined rolling of the balls along the raceways. When the motor shaft is rotating, the bearing cage revolves at a constant angular velocity that is mean of the inner and outer race angular velocities. The cage angular velocity can be exploited to work out the value of dominant fault frequency due to cage defect, fCD as given below: (4) Where ωi = Angular speed of the inner race in RPM ωo= Angular speed of the outer race in RPM D = Pitch Diameter d = Ball Diameter Φ = Ball contact angle ri = Inner race radius, ro = Outer race radius In case of motors, the outer race is connected to the casing that is stationary. The inner race and the shaft ISSN: 0975 – 6736| NOV 12 TO OCT 13 | VOLUME – 02, ISSUE - 02 Page 179 JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN ELECTRICAL ENGINEERING are mounted together and both rotate at the same angular speed. Accordingly, it can be assumed that: ωo = 0 and ωi = ωr (5) Where ωr = Rotor angular speed in RPM Incorporating the above mentioned assumption as depicted in equation (5) fetches equation (6) as given below: (6) Empirically, the cage defect fundamental frequency for a ball bearing with six to twelve balls in it is given as: (7) Where b) Inner Race Defect: The inner race defect frequency, fIRD, depends on the rate at which bearing balls pass through the point of defect on the inner race. Each ball move across the flaw point at a rate that is proportional to the difference of angular speed of the cage and inner race. The fault frequency of the inner race defect is also proportional to the number of balls in the bearing. The fundamental fault frequency for the inner race defect (for conditions ωo = 0 and ωi = ωr ) is given as: (8) Where the used variables have definition as mentioned along with eqn. (4) The empirical formula for inner race defect fault frequency of a ball bearing consisting of six to twelve balls in it is given as: (9) Where ωrs is as mentioned along with eqn. (7) c) Outer Race Defect: The outer race defect frequency, fORD, depends on the rate at which bearing balls cross the point of defect on the outer race. Each ball move across the point of defect at a rate that is proportional to the difference of angular speed of the cage and outer race. The fault frequency of the outer race defect is also proportional to the number of balls in the bearing. The fundamental fault frequency corresponding to the inner race defect is given as: (10) Where the used variables have definition mentioned along with eqn. (4) Using equation (5), i.e. ωo = 0 and ωi = ωr (Where ωr = Rotor angular speed in RPM), yields: fODR = (0.4).n.ωrs (11) Where ωrs is as mentioned in eqn. (7) (D) Inter-Turn Short Circuits: In Induction motors the Inter-turn short circuits occur as short circuits between turns of one phase, or between turns of two phases, or between turns of all phases, or between winding conductors and the stator core. Inter-turn short circuits between turns of same phase, winding short circuits, short circuits between winding and stator core, short circuits between different phases is usually caused by stator voltage transients and abrasion. Burning of winding insulation and complete winding short circuits of all phase windings are usually caused by motor overloads and blocked rotor, stator energising by subrated voltage, overrated voltage power supplies, frequent starts and rotation reversals. Inter-turn short circuits are also caused due to voltage transients because of the successive reflections resulting from the cable connection between induction motor and induction motor drives. Inter-turn short circuits in stator windings constitute a category of faults that is most common in induction motors. Typically, short circuits in stator windings occur between turns of one phase, or between turns of two phases, or between turns of all phases. Moreover, short circuits between winding conductors and the stator core also occur. The different types of winding faults are summarizes below as follows [37]: Inter-turn short circuits between turns of the same phase, winding short circuits, short circuits between winding and stator core, short circuits on the connections, and short circuits between phases are usually caused by stator voltage transients and abrasion. Stator faults originate in the stator core or in the stator windings. Stator winding faults can be due to several different reasons. The insulation damage can be, for example, due to impact damage during installation, movement due to repeated starting, slack core laminations, thermal damage due to over current and finally due to thermal aging. The stator winding faults, in a case of a low voltage induction motor, are often not repaired. If repaired, the machine is taken to a special service establishment or to a manufacturer for re-winding. Stator faults are indicated by analysing e.g. the phase unbalance of the stator currents or the axial leakage flux. The unbalance is calculated with the aid of symmetrical components. The negative sequence current or impedance is used as a fault indicator. (E) Air gap eccentricity: The presence of static and dynamic eccentricity can be detected by monitoring the behaviour of the fundamental sidebands of the supply frequency. The frequencies of interest are given as: (12) Where fe = supply frequency s = per unit slip m = 1, 2, 3, --P = number of poles The air gap eccentricity is also detected by monitoring the behavior of sidebands of the slot frequencies in stator current. The sideband frequencies of interest are given as: ISSN: 0975 – 6736| NOV 12 TO OCT 13 | VOLUME – 02, ISSUE - 02 Page 180 JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN ELECTRICAL ENGINEERING (13) Where k = 1, 2, 3, ---------, R (R = number of rotor slots) nd = order of the rotating eccentricity nw = order of the stator MMF harmonics III: INDUCTION MOTOR FAULT MONITORING The features used in fault detection methods are intended to classify the motor condition as faulty and healthy and also to identify the motor fault type. The detection technique is intended to identify electrically detectable faults in the induction motors and also identify the fault severity. The classifier technique classifies the Induction motor as either healthy or faulty. The fault features are extracted from a suitable motor parameter. Good number condition-monitoring propositions have concerted explicitly with sensing related failure methodologies. All of the currently accessible techniques entail the user to acquire some competence in making a distinction amongst normal operating condition from a prospective fiasco. Ideally, it is aspired to create a diagnostic procedure that endow with a clear inference of machine health in minimum time through processing of minimal measurable inputs [8]. Various different parameters such as temperature, current, voltage, vibration, flux and acoustics have been in force for monitoring electrical machines. Good number condition-monitoring propositions have concerted explicitly with sensing related failure methodologies. All of the currently accessible techniques entail the user to acquire some competence in making a distinction amongst normal operating condition from a prospective fiasco. Ideally, it is aspired to create a diagnostic procedure that endow with a clear inference of machine health in minimum time through processing of minimal measurable inputs [8]. Expediency, consistency, and sensitivity are the basis of sensor signals. The existing methods of condition monitoring of electrical machines are [6], [7], [14]: 1. Noise Monitoring: Acoustic noise from air gap eccentricity in induction motors can be used for fault detection. Noise monitoring is accomplished by measuring and analyzing the acoustic noise spectrum. However, the application of noise measurements in a plant is not practical because of the noisy background from other machines operating in the vicinity. 2. Torque Monitoring [25]: Almost all motor faults cause harmonics with specific frequencies in the air gap torque. However, air gap torque cannot be measured directly. From the input terminals, the instantaneous power includes the charging and discharging energy in the windings. Therefore, the instantaneous power cannot represent the instantaneous torque. From the output terminals, the rotor, shaft, and mechanical load of a rotating machine constitute a torsional spring system that has its own natural frequency. The attenuations of the components of air gap torque transmitted through the torsional spring system are different for different harmonic orders of torque components. Generally, the waveform of the air gap torque curve is different from the torque measured at the shaft. The fault condition can be identified by monitoring the specific harmonics in the air gap torque. The air gap torque in terms of measurable motor terminal quantities is given as: (14) Where iA, iB , and iC are three-phase line currents of an induction motor, VCA and VAB are line-to-line voltages r is half of the line-to-line resistance p is the number of pole pairs Frequencies of major torque harmonics associated with the certain defects in induction motors are as follows: Under normal operation: Angular frequency of torque = 0 With a single-phase stator: Angular frequency of torque = -2ωs With a single-phase rotor: Angular frequency of torque = 2sωs Where ωs is the supply frequency in rad/s, and s is the slip. Therefore, the fault condition can be identified by monitoring the special harmonics in the air gap torque. 3. Flux Monitoring: Air gap flux of induction motors contains rich harmonics. A flux monitoring scheme can give reliable and accurate information about electrical machine conditions. Any change in air gap, winding, voltage, and current can be reflected in the harmonic spectra. The change of air gap flux is a function of static eccentricity. Air gap flux can be measured by search coils installed in the stator core. Because of the enclosed structure of induction motors, this operation requires the disconnection of induction motors from the main supply before dismantling. As such, this is neither practical nor economical for the motors that are in service. 4. Vibration Analysis: Vibration monitoring [5], [21]-[24] is one of the oldest condition monitoring techniques and is widely used to detect mechanical faults such as bearing failures or mechanical imbalance. A piezo-electric transducer providing a voltage signal proportional to acceleration is often used. This acceleration signal can be integrated to give the velocity or position. 5. Current Monitoring: One of the, most economically attractive technology in motor condition monitoring is stator current monitoring [11]-[20]. The stator current of an induction motor is readily available since it is used to protect machines from destructive over-currents, ISSN: 0975 – 6736| NOV 12 TO OCT 13 | VOLUME – 02, ISSUE - 02 Page 181 JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN ELECTRICAL ENGINEERING ground current, etc. Therefore, current monitoring is a sensor less detection method that can be implemented without any extra hardware. The vibration monitoring [5], [21-24] is one of the widely used techniques for detection of electrical and mechanical faults in electrical machines. The stator current monitoring [11]-[20] is relatively a recent technique that is fast gaining importance due to its non-invasive nature, cost-effectiveness, preciseness in analysis, easy and efficient signal processing, and convenient installation [34]. The stator current monitoring and analysis can provide as much information as the vibration monitoring provides [14], [22]. The motor stator current analysis is based on the fact that the stator and rotor faults are ultimately reflected in the stator current and in most of the cases cause unbalanced phase currents or introduces a distinct signature in the stator current. The motor stator current analysis being non-intrusive, comparatively simple to implement, load and operating point independent - prove out to possess an advantageous edge over the other analysis techniques. Various stator current analysis methods that are commonly employed for fault detection in Induction motors are as shown below: Motor stator current analysis: Time domain techniques Statistical parameter analysis – Root Mean Square (RMS), mean, variance, crest factor, skewness, kurtosis etc Time synchronous averaging based methods – Time synchronous averaged (TSA) signal, Residual signal analysis (RSA) etc. Spatial angular vector (SAV) analysis Negative sequence component analysis Filter based methods– Demodulation, enveloping etc. Stochastic methods – Thresholding, Autoregression based methods Frequency based techniques Spectrum analysis Fast fourier transform (FFT) Discrete fourier transform (DFT) Short term fourier transform (STFT) Power cepstrum analysis Time-frequency based techniques Spectrogram analysis Wigner distribution (WD) analysis Continuous wavelet transform analysis Discrete wavelet pocket analysis Time-averaged wavelet spectrum (TAWS) Time-frequency-scale (TMS) domain The commonly employed artificial intelligence based interpreting techniques are as follows [15,17,18]: Neural network based inference Feed forward networks Multi layer perceptron Radial basis function (RBF) Principal component analysis (PCA) Recurrent networks Kohonen Self-organising maps (SOM) Fuzzy set based inference Expert system based inference Neuro-fuzzy computing based inference Adaptive Neuro-fuzzy inference Fuzzy expert system based inference Bayesian classifier Support vector machines (SVM) IV: Causes of Faults in Induction motors The reason for induction motor impairment [2] can be a multiplicity of factors such as filth and dirt instigated temperature intensification; unwarranted vibrations due to faulty bearings; thermal stresses due to rotor rub, rotor skewing, and end ring heating; mechanical stresses due to air gap eccentricity, frequent startups, rapid acceleration and deceleration; long persistent overload conditions; transient torques due to faulty bearings, poor supply quality, and unbalanced stator phase winding; flaws in manufacture or design; imperfect installation; deterioration due to abrasion, erosion and aging. Most of the time there are copious factors that beget motor breakdown. The most unequivocal basis for motor breakdown is damage of the bearings or winding or rotor but the paramount rationale that is often an attribute to such failures is overheating prompted through dirt, filth and grime. The rotor failures get trigger off by an assortment of diverse stresses and strains that appear in the rotor. Stresses can be electromagnetic, thermal, residual, dynamic, environmental and mechanical [2], [22]. The foremost reason for the rotor failure typically resides in flaws related to imperfect casting or substandard jointing during manufacturing. Whilst the rotor bar is slighter than the bar slot, slot harmonics will surface that subsequently initiate radial advance of the bar, particularly during startingup, accelerating and braking periods. This might beget frailty consequently ensuing in fractured and ruptured rotor bar(s). Thermal stress is another quandary, occurring when the bar cannot progress longitudinally in the rotor slot. Sustained motor overloads and frequent starts, acceleration and deceleration contribute to cultivate substantial currents that bring forth considerable mechanical and thermal stresses, consequently prompting rotor and the stator damage. Even so, the induction motor rotor ISSN: 0975 – 6736| NOV 12 TO OCT 13 | VOLUME – 02, ISSUE - 02 Page 182 JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN ELECTRICAL ENGINEERING faults by and large onset from a minuscule crevice or a high resistivity spot in the rotor bar. This spot shows temperature intensification which worsens the damage until the rotor bar is absolutely conked out. Subsequent to a solitary rotor bar breakage, the rotor current reassigns to the other co-existing healthy bar(s) causing the over current and ultimately a cluster of broken bars. Another frequently occurring source for the rotor failures is the over-current typically due to rotor clog up condition of the motor. It is on the whole not beneficial or feasible to mend the rotor. Bearing faults are one of the prominent causes that instigate the failures in induction motors [1, 8]. The indications of bearing mutilation are bumpy running with jerks, abridged exactness of producing shaft movement with very less rotational tolerance and an atypical noise. The bearing faults in the electrical motors can on the whole be attributed to the material attrition and abrasion at contact points, ageing and exhaustion, misalignment, sustained load overstresses and pressure induced welding. The erosion, attrition and abrasion of the material crop up as a result of presence of contaminants and impurities, friction induced overheating and subsequent occurrence of hot spots on the bearing balls or rolls, inner and outer races. The duration of bearing life span is also reliant on the quality of the lubricant, stresses due to mechanical load and electrical starts. The frequent start ups and rapid accelerating and decelerating periods cause repeated over stressing of the bearings. Besides unfeigned overloading, the lumber on the bearing in induction motors can be due to improper alignment or rotor unbalance, and sooner or later bring forth a state of the bearing that is not appropriate for unblemished operation of the machine. Under ideal state of affairs, the rotor potential is believed to be zero which is not practically the case. A potential relative to the ground emerge at the rotor due to inequality in phase capacitances. The rotor voltage set off a difference of potential crosswise the bearings. This leads to a current flowing through the bearing and brings about an alteration in the chemical composition of the lubricant, consequently resulting in degradation of the quality of the lubricant. This further brings in abrasion in the bearing and may sometimes set in electrical discharges between inner and outer races, eventually leading to the inopportune bearing failures. Stator faults originate in the stator core or in the stator windings. Stator winding faults can be due to several different reasons. The insulation damage can be due to impact damage during installation, movement due to repeated starting, slack core laminations, thermal damage due to over current and due to thermal aging. Stator faults are indicated by perceiving parameters such as phase unbalance of the stator currents or the axial leakage flux or the vibration content of the motor etc. V: Schematic block diagram for fault detection in Induction motors The motor under test (MUT) is made to run as linefed induction motor or an inverter fed adjustable speed induction drive (ASID), as the case may be, by feeding an apposite 3-phase supply. The data acquisition and analysis software (the popular ones are dSPACE-Matlab or National Instrument’s DAQ – Matlab etc.) along with the pertinent control card is used to develop the data acquisition setup. The input signals are processed and analysed through suitable signal processing and analysis tools so as to extract fault features and present them in a format acceptable to the successive classifier stage. The interpreter stage takes a decision on the basis of fault features presented to it as regards the motor health status. The general schematic of an experimental setup for fault detection in three-phase induction motors is as shown in fig.1 below: Data Acquisition Hardware and software Data Acquisition and Control Hall Effect current and voltage Transducers Three-phase Inverter/On-Off Arrangement Speed Measur ement 3-Φ Induction motor Loading arrangement Fig. 1: General schematic of the experimental setup VI: CONCLUSION The brief review of the commonly occurring induction motor faults has been presented. The relevant references have been mentioned for ready reference. The conventional and recent signal analysis, fault extraction and interpreter techniques have been discussed. The outcome and conclusions buoy to support the author’s assumption that it is possible to employ certain new techniques so as to improve the consistency of existing, well reported, ISSN: 0975 – 6736| NOV 12 TO OCT 13 | VOLUME – 02, ISSUE - 02 Page 183 JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN ELECTRICAL ENGINEERING and established strategies for fault detection. Furthermore the techniques that are apt in processing non-stationary signal analysis have a definite edge over the conventionally employed techniques based upon current monitoring alone. It is worth to be mentioned that recent works in motor fault detection are anchored in analysis of stator current based on time-frequency (or time-scale) methods. REFRENCES [1] Albrecht P.F., J.C. Appiarius, and D.K. Sharma,”Assessment of the reliability of motors in utility applications-Updated,” IEEE Transactions on Energy conversion, Vol. 20, Pp. 719-729, 2005. [2] Bonnett A. H. and George C. 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