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A Research Survey of Induction Motor Operation With

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Electric Power Systems Research 75 (2005) 200–213 A research survey of induction motor operation with non-sinusoidal supply wave forms G.K. Singh ∗ Department of Electrical Engineering, Indian Institute of Technology, Roorkee 247667, India Available online 10 May 2005 Abstract The developments in the power electronics field have lead to an ever-increasing use of static switching devices to control the torque and speed of ac motors. Invariably, the output voltage and current waveforms of these de
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  Electric Power Systems Research 75 (2005) 200–213 A research survey of induction motor operation withnon-sinusoidal supply wave forms G.K. Singh ∗  Department of Electrical Engineering, Indian Institute of Technology, Roorkee 247667, India Available online 10 May 2005 Abstract The developments in the power electronics field have lead to an ever-increasing use of static switching devices to control the torque andspeed of ac motors. Invariably, the output voltage and current waveforms of these devices contain numerous harmonics and these harmonicshave detrimental effects on the motor performance in form of derating and torque pulsation, especially at low speed. The order and magnitudeof these harmonics depend on the design as well as nature of load being supplied. The extensive research has been underway for a long timein order to assess the effects these harmonics have on induction motor performance, and to investigate the various issues related to the use of induction motor to improve the drive performance and reduce the losses. This paper, therefore, presents a comprehensive review of researchand developments in the induction motor operation with non-sinusoidal supply waveforms since its inception. Attempts are made to highlightthe current and future issues involved in the development of induction motor drive technology to impart good dynamic stability with improvedperformance. A list of 167 research publications on the subject is also appended for a quick reference.© 2005 Elsevier B.V. All rights reserved. Keywords:  Analysis; Adjustable-speed drives; Induction motor; Harmonic torque; Harmonic; Non-sinusoidal; Noise; Speed estimation 1. Introduction Prior to the advent of solid-state controllers for the speedcontrol of induction machines, the supply voltage used tobe sinusoidal in nature, being practically free from the timeharmonics. The standard integral slot windings, having sim-ilar pattern of conductor distribution for all the phases, havebeen used with these machines giving reasonably good per-formance [1,2]. At present time, the induction motors arewidely supplied from several types of solid-state adjustablevoltage–frequency controllers with a wide range of oper-ating features. However, in any case, the motor has to bederated for the harmonic effects due to the non-sinusoidalnature of the voltage supply. The magnitude and the distri-bution of the additional losses and the related motor derat-ing, in steady state, depends on the harmonic contents of the applied voltage and, in some way, on the motor design.The output voltage of the present day static controllers de-viates substantially from the sinusoidal form and contains ∗ Tel.: +91 1332 285070; fax: +91 1332 273560.  E-mail address:  gksngfee@iitr.ernet.in. wide spectrum of time harmonics of which the lower or-der time harmonics in general, having frequency closer tothe wanted output frequency and the sub-harmonics in par-ticular, are found to be potentially objectionable in prac-tice [3–5] and are at the same time found difficult to befiltered off  [6,7]. Besides directly reducing the rating of the machine, these time harmonics produce other undesir-able effects on the performance. Attempts have, however,been constantly made to modify the design of controller cir-cuit for improving waveform of the output voltage [8–11].The success has been achieved to a limited extent at thecost of added complications, which has reduced the relia-bility and increased the cost of controller unit besides anincrease in switching losses [12–16]. This paper, therefore, deals with a state-of-the-art discussion on performance of induction motor operating on non-sinusoidal supply wave-forms, highlighting the analytical and technical considera-tions as well as various issues addressed in the literature to-wards the practical realization of this technology for betterdrive stability with improved performance. One hundred andsixty-seven publications [1–167] are reviewed and classifiedin 11 parts. 0378-7796/$ – see front matter © 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.epsr.2005.04.001  G.K. Singh / Electric Power Systems Research 75 (2005) 200–213  201 2. Modeling and analysis A basic paper for induction machine analysis has beenreported by Stanley [17]. Later on, many researchers made their contributions on the basis of the machine model givenbyStanleywithsomemodifications.HughesandAlderd[18]have suggested a general model for transient and unbalancedoperation of two- and three-phase induction machine. Themachineequationsareexpressedwithrespectto αβ – dq coor-dinate. The model is simulated using analogue computer andthe obtained results are compared with practical ones. SarkarandBerg[19]havepresentedadirectthree-phasemodelusing phasevariablesandtwoaxismodelsforthree-phaseinductionmachine. The models are simulated using digital computer.The machine performance under rectangular waveform sup-ply is also included. Jacobides [20] has reported the modelof a drive consisting of three-phase induction motor fed froma full bridge cycloconverter. The model based on phase vari-ables and Gaussian elimination method is used to reduce theorder of the connecting matrix. Murthy and Berg [21] havepresented a dynamic model based on instantaneous symmet-rical components theory. The model is used to obtain thetransient behavior of thyristor-controlled three-phase induc-tion motor. The model covers most of the operating modesand the analysis is done without reference to the rotor posi-tion. Krause and Lipo [22–25] and many other researchers have reported different analytical techniques based on phasevariablesandreferenceframetransformationsforthree-phaseinduction machine. Different machine and supply conditionshave been included.Fallside and Wortley [26] and Ueda et al. [27] have stud- ied the effect of supplying the machine from variable fre-quency source from the point of view of stability. The effectof machine parameters variation on the machine stability hasbeen discussed. Levi [28,29] have reported the modeling of  induction motor and synchronous machine considering si-nusoidal and non-sinusoidal supply. The models are basedon  d  – q  axes and the analysis includes the effect of machinesaturation and core loss. Different control strategies of in-duction motor are also considered. Neto et al. [30] have pre-sented a mathematical model of three-phase induction mo-tor using phase variables. The model is based on the har-monic impedance concept and accordingly the voltage andtorque equations are derived. Two cases are included in theanalysis, supplying the machine from sinusoidal supply andfrom non-sinusoidal supply using PWM inverter. Toliyat etal. [31–33] have developed analysis method for modelingthe multiphase cage induction motor. The model considersthe mmf harmonics using winding function approach. Themodel is used effectively to simulate different types of ma-chine faults such as asymmetry in the stator winding, air gapeccentricity and rotor bar fault. Joksimovic and Penman [34]have presented an induction motor model based on windingfunctionapproachtoinvestigatetherelationbetweenthema-chine faults and the current harmonics. One of the commonmethods used to simulate the supply faults and unbalance instatorandrotorcircuitisthesymmetricalcomponentmethod[35].The formulation of machine dynamic and steady stateequations and the role of transformations in the analysis of  m – n  winding induction machine with space harmonics havebeen reported by Fudeh and Ong [36,37]. In another study [38], the authors have derived the voltage equations in termsof  ∝ – β  and  dq  components for a three-phase cage rotor in-duction machine with space harmonics. In the same study,skin effect, skewing of rotor bars and the influence of slotopening on the mmf are all taken into account in the deriva-tion of the parameters for the machine. Krause and Lipo [39]have presented the analysis and simplified representation of a rectifier-inverter induction motor drive. A semi-empiricalinduction motor loss model as a function of motor powerrating has been given by Buck et al. [40]. Oguchi [41] has reportedaclosed-form,analyticalsolutionforthecurrentandtorque waveform for a three-phase induction motor, suppliedwith multiple phase-shifted voltage source inverter system.Motor performance, such as the torque ripple factor and thepeak stator current ratio, has been calculated for the inverteroutput voltage waveforms with 6–48 steps. A guideline forthe design of multiple inverter systems has been given anda comparison between motor performances of multi-steppedvoltage-fed and a PWM voltage-fed design has been made.Belmans et al. [42] have presented the analysis of the audible noise of three-phase squirrel-cage induction motors suppliedby inverters. In the study, a way for predicting the spectrumcomponents produced by the motor and for relating it to theairgapfluxdensitydistributiontimeharmonicscausedbythenon-sinusoidal supply have been given. Enjeti and Lindsay[43] have developed a direct three-phase model for analyti-cal investigation on steady state and transient behavior of aninduction motor fed from non-sinusoidal supply. An analyt-ical procedure for computing the exact nature obtained fromPWM inverter has been described.In another study, a simulation procedure for investigat-ing problems concerning road traction drives based on three-phase induction machines supplied by modulated invertershas been presented by Denegri et al. [44]. Bonnet [45] has reported the analysis of the impact of the PWM inverter volt-age waveforms on ac induction motors. The effects of themaximumvoltage,rateofrise,switchingfrequencies,capac-itors, resonance and harmonics have been considered in thestudy. Wang and Liu [46] have discussed the steady stateharmonic modeling and simulation of a cycloconverter drivesystem (CSD). The operation and control of a cycloconverterdrive and a synchronous motor load were modeled in timedomain. The theme of this paper is to understand harmonicproblem associated with a CDS from an integrated point of view, with special attention given to harmonics filtering andcancellation effect of converter coupling transformers. Fre-quency domain methods useful for traction drives design andharmonic generation mechanism understanding have beengiven by Lordache et al. [47]. An iterative solving algorithm is used for load flow and converter operating point calcula-  202  G.K. Singh / Electric Power Systems Research 75 (2005) 200–213 Table 1Comparison between induction machine modelsMachine model Complexity CharacteristicsSuitable for all machines conditionsPhase variable model (6 × 6) Matrix Direct presentation of machine variablesBetter suited for unbalanced condition of supply and statorStationary reference frame ( ω =0) (4 × 4) Matrix Better suited for unbalanced condition of supply and statorTransformations needed of machine variableRotor reference frame ( ω a  = ω r ) (4 × 4) Matrix Better suited for unbalanced condition of rotor faultsTransformations needed of machine variableSynchronously rotating reference frame ( ω a  = ω s ) (4 × 4) Matrix Better suited for non-sinusoidal supplyTransformations needed of machine variable tion. A numerical application is developed and results arecompared with time domain simulation results. Dell’Aquillaet al. [48] have presented an analytical method to model andcalculate the line side currents produced by variable speedinductionmotordrives.InapaperbyGersenetal.[49],time- harmonic finite-element simulation, as commonly applied tothe three-phase induction machine model, is used to simu-lateasingle-phasecapacitorstart/runmotorbydecomposingthe air gap field in two revolving fields in the opposite direc-tion. A comparison of various reference frame models withphase variable based model is depicted in Table 1. Although, the complexity of phase variable model and time needed forsimulation of the machine behavior is high as compared tothe other models, it can be used to cover all the machineconditions with ease of implementation. 3. Induction motor losses on non-sinusoidal supply DoggettandQueer[3]f orfirsttimein1929havepresented thepreliminaryinvestigationofaninductionmotoroperationwith non-sinusoidal impressed voltages and suggested thatfor a known pattern of non-sinusoidal supply, the voltageprofile can be analyzed into a fundamental component and aseries of time harmonics. If magnetic saturation is neglected,a motor operating on such a supply system may be regardedas a linear device and the principle of superposition can beapplied. The overall response to the non-sinusoidal voltageis then obtained as aggregation of responses to the individualcomponents. Klingshirn and Jordan proposed a three-phaseinduction motor performance under a non-sinusoidal voltagesource [5]. In 1968, Chalmer and Sarkar studied the induc-tion motor losses due to non-sinusoidal supply waveforms[50]. In 1972 and 1979, Linders investigated the effects of poor quality power sources on ac motors and proposed thehidden costs and containment due to the electric wave dis-tortion [51,52]. Raphael discussed the additional losses and torque pulsations in PWM inverter-fed squirrel-cage induc-tionmotors[53].In1986,Cummingssimplifiedtheharmonic equivalent circuit and proposed a method to estimate motorloss and temperature rise [54]. In 1987, Fuchs et al. inves- tigated the sensitivity of appliances of harmonics [55]. Sen and Landa in 1990, according to material of induction mo-tor, proposed derating operation under waveform distortion[56]. In 1985 and 1993, Ortmeyer et al. and Wagner et al.,respectively, presented a summary of the state-of-knowledgeabout the effects on power system equipment and load underharmonics [57,58]. Lee and Lee in 1999, reported a paper on effects of non-sinusoidal voltage on the operating perfor-mance of a three-phase induction motor [59].There have been many studies on iron losses in induc-tion machines. The well-known equivalent circuit has beenmodified in various ways to improve the accuracy of the lossestimate for wide ranges of operating conditions such as inRef. [1]. In case of distorted voltage waveform supply, it is not possible to use, in general, such a model due to the ironnon-linear behavior and the complexity of the phenomenainvolved. One such modification of the standard equivalentcircuitrepresentationofthemotorforthe k  thharmonicofthevoltagewaveformproposedbyVamvakarietal.[60]isshownin Fig. 1. In this figure,  V  k   denotes the voltage harmonic of order  k  ,  R s  the stator winding resistance,  R rk   the correspond-ing rotor resistance,  X  ls ,  X  lr  and  X  m  the stator, rotor leakagereactances and magnetizing reactances at fundamental fre-quency, respectively,  R mk   the core loss resistance.  R lsk   and  R lrk   are resistors representing harmonic iron losses associ-ated with stator and rotor leakage fluxes, respectively, placedin parallel with corresponding leakage reactance terms. Ironloss models suitable for use in  dq -models of the inductionmachine have also been studied [61,62]. These lumped mod- els of iron loss are useful but do not allow to detail of ironloss to be studied. Some studies have specifically addressedlosses arising from inverter supply [63,64] but are limited in nature. There are models for iron loss in thin laminations[1,60,61,65]. These models provide loss density results for a Fig. 1. Modified equivalent circuit of induction motor for the voltage har-monic component of   k  th order.  G.K. Singh / Electric Power Systems Research 75 (2005) 200–213  203 localized flux density expressed as a function of time. Bogli-etti et al. [66] have reported the effect of inverter charac-teristics on the iron loss increment in induction motors fedby PWM-controlled converters. The inverter parameters likemodulation index, modulation waveform and switching fre-quency are considered in the study. In a study [67], Green et al. have examined the extent and nature of additional lossesin induction machine over those occurring with grid supplyfor a switching frequency representative of current practice.A comparative study of the losses in voltage and currentsource inverter-fed induction motor has been presented byVenkatesan and Lindsay [68]. In this study, the equivalent circuit that includes the effects of space harmonics and cor-rectedfortheskineffectinrotorbarshasbeenusedforcalcu-lation of main and stray copper loss. Boglietti [69] has givena method for evaluation of the steady state loss in mediumpower industrial induction motors supplied by PWM invert-ers.Themethodisbasedontheno-loadandshortcircuittestswithPWMsupplyandisquitesimpletorealize.GerlandoandPerini[70]havereportedamethodologyforthecalculationof the extra iron losses occurring in the core of the inverter-fedelectromagneticdevices.Inanotherstudy,Bogliettietal.[71]have presented a simple method based on no-load and shortcircuit tests in order to get the useful machine parameters toadopt in equivalent circuit model for the loss evaluation. Ina recent study [72], authors have presented a methodology for a convenient modification of induction motor equivalentcircuit parameters, taking into consideration switching fre-quency iron losses in case of inverter supply. The authorshave also presented a modified two axes equivalent circuitas shown in Fig. 2. The various studies [73–76] made on harmonic losses reveal that: ã  Presenceofharmoniccurrentsinthestatorwindingcausesan increased copper loss. When skin effect is negligible,the stator copper loss on a non-sinusoidal supply is pro-portional to the square of the total rms current. Fig. 2. Modified equivalent circuits for induction motor dynamic model: (a) d  -axis equivalent circuit and (b)  q -axis equivalent circuit. ã  Presence of harmonic contents also increases the funda-mental component of current slightly, due to an increasedmagnetizing current. ã  The assumption of a constant resistance at harmonic fre-quencies is reasonably justified for the stator windings of the wire-wound machines. For large ac motors, there is anincrease in stator resistance with frequency that dependson the shape, size and disposition of the conductor in thestator slots. ã  Theskineffectismuchmorepronouncedinthecagerotor,which exhibits a significant increase in resistance at har-monic frequencies, particularly in case of deep bar rotors.Since the rotor resistance is a function of harmonic fre-quency, the rotor copper loss is calculated independentlyfor each harmonic. ã  It is appropriate to use a reduced value of per unit reac-tance because the rotor leakage inductance is reduced sig-nificantly as a result of skin effect. ã  The core loss in the machine is also increased by the pres-ence of harmonics in the supply voltage and current. ã  The core loss due to space harmonic air gap flux is negli-gible, but the end-leakage and skew-leakage fluxes, whichnormally contribute to the stray load loss, may producean appreciable core loss at harmonic frequencies. Conse-quently, these effects must be taken into consideration formotor operation on non-sinusoidal supply. ã  The magnitude of harmonic loss obviously depends on theharmonic content of the motor voltage and current. Largeharmonic voltage at low-harmonic frequencies cause sig-nificantly increased machine loss and reduced efficiency. ã  Higherorderharmoniccurrentsusuallyhavesmallmagni-tudes.Forsuchwaveforms,thereductioninfullloadmotorefficiency is not excessive. 4. Harmonic reduction techniques Theincreasingapplicationofpowerelectronicequipment,especially adjustable-speed drives (ASDs) in the industrialenvironment has led to a growing concern for harmonic dis-tortionandtheresultingimpactsonsystemequipmentandop-erations.Possibleproblemsincludetransformeroverheating,motor failures, fuse blowing, capacitor failures and malfunc-tioning of control. Harmonic currents are generated by theoperation of non-linear loads and equipment on power sys-tem. Voltage distortion results from the interaction of thesecurrents with the system impedance versus frequency char-acteristics. The characteristics of the input current for ASDsdepend on the drive type, drive loading and characteristicsof the system supplying the drive. The harmonic distortionin these currents can vary over a wide range. In the lasttwo decades, major focus has been on harmonic reductiontechniques. Some summaries on three-phase harmonic re-duction technique can be found in Refs. [77–81]. The third harmonicinjectionschemesforthethree-phasedioderectifierfor reducing the harmonic currents has drawn some promis-

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