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6 OPERATING CHARACTERISTICS OF INDUCTION MOTORS This chapter is concerned with how the induction motor behaves when connectedtoaconstantfrequencysupply.Thisisbyfarthemostwidely used and important mode of operation, the motor running directly connected to a constant voltage mains supply. 3-phase motors are the most important, so they are dealt with first. METHODS OF STARTING CAGE MOTORS Direct Starting – Problems Our everyday domestic experience is likely to lead us to believe that there is nothing more to starting a motor than closing a switch, and indeedformostlow-powermachines(sayuptoafewkW)–ofwhatever type – that is indeed the case. By simply connecting the motor to the supply we set in train a sequence of events which sees the motor draw power from the supply while it accelerates to its target speed. When it has absorbed and converted suYcient energy from electrical to kinetic form, the speed stabilises and the power drawn falls to a low level until themotorisrequiredtodousefulmechanicalwork.Intheselow-power applications acceleration to full speed may take less than a second, and we are seldom aware of the fact that the current drawn during the acceleration phase is often higher than the continuous rated current. FormotorsoverafewkW,however,itisnecessarytoassesstheeVect on the supply system before deciding whether or not the motor can be started simply by switching directly onto the supply. If supply systems wereideal(i.e.thesupplyvoltageremainedunaVectedregardlessofhow much current was drawn) there would be no problem starting anyOperating Characteristics of Induction Motors 199 induction motor, no matter how large. The problem is that the heavy currentdrawnwhilethemotorisrunninguptospeedmaycausealarge drop in the supply system voltage, annoying other customers on the same supply and perhaps taking it outside statutory limits. It is worthwhile reminding ourselves about the inXuence of supply impedance at this point, as this is at the root of the matter, so we begin by noting that any supply system, no matter how complicated, can be modelledbymeansofthedelightfullysimpleTheveninequivalentcircuit shown in Figure 6.1.(We here assumea balanced3-phaseoperation, so a 1-phase equivalent circuit will suYce.) Thesupplyisrepresentedbyanidealvoltagesource(V )inserieswith s thesupplyimpedanceZ .Whennoloadisconnectedtothesupply,and s the current is zero, the terminal voltage is V ; but as soon as a load is s connected the load current (I) Xowing through the source impedance results in a volt drop, and the output voltage falls from V to V, where s V ¼ V IZ (6:1) s s For most industrial supplies the source impedance is predominantly inductive,sothatZ issimplyaninductivereactance,X .Typicalphasor s s diagrams relating to a supply with a purely inductive reactance are shown in Figure 6.2: in (a) the load is also taken to be purely reactive, while the load current in (b) has the same magnitude as in (a) but the loadisresistive.Theoutput(terminal)voltageineachcaseisrepresented by the phasor labelled V. Fortheinductiveload(a)thecurrentlagstheterminalvoltageby908 while for the resistive load (b) the current is in phase with the terminal voltage. In both cases the volt drop across the supply reactance (IX ) s leads the current by 908. The Wrst point to note is that, for a given magnitude of load current, thevoltdropisinphasewithV whentheloadisinductive,whereaswith s Z I s V V Load s Supply system Figure 6.1 Equivalent circuit of supply system200 Electric Motors and Drives −IX s V V s s −IX s V V I I (a) Inductive load (b) Resistive load Figure6.2 PhasordiagramsshowingtheeVectofsupply-systemimpedanceontheoutput voltage with (a) inductive load and (b) resistive load aresistiveloadthevoltdropisalmostat908toV .Thisresultsinamuch s greater fall in the magnitude of the output voltage when the load is inductivethanwhenitisresistive.Thesecond,obvious,pointisthatthe larger the current, the more the drop in voltage. Unfortunately, when we try to start a large cage induction motor we faceadouble-whammybecausenotonlyisthestartingcurrenttypically Wveorsixtimesratedcurrent,butitisalsoatalow-powerfactor,i.e.the motorlookspredominantlyinductivewhentheslipishigh.(Incontrast, when the machine is up to speedand fully loaded,its currentis perhaps only one Wfth of its starting current and it presents a predominantly resistive appearance as seen by the supply. Under these conditions the supply voltage is hardly any diVerent from at no-load.) Sincethedropinvoltageisattributabletothesupplyimpedance,ifwe want to be able to draw alarge starting currentwithout upsetting other consumersitwouldbeclearlybestforthesupplyimpedancetobeaslow as possible, and preferably zero. But from the supply authority view- point a very low supply impedance brings the problem of how to scope in the event of an accidental short-circuit across the terminals. The short-circuit current is inversely proportional to the supply impedance, and tends to inWnity as Z approaches zero. The cost of providing the s switch-geartoclearsuchalargefaultcurrentwouldbeprohibitive,soa compromisealwayshastobereached,withvaluesofsupplyimpedances being set by the supply authority to suit the anticipated demands. Systems with a low internal impedance are known as ‘stiV’ supplies, because the voltage is almost constant regardless of the current drawn.Operating Characteristics of Induction Motors 201 (Analternative wayof specifyingthe natureof thesupply is toconsider the fault current that would Xow if the terminals were short-circuited: asystemwithalowimpedancewouldhaveahighfaultcurrentor‘fault level’.) Starting on a stiV supply requires no special arrangements and thethreemotorleadsaresimplyswitcheddirectlyontothemains.Thisis known as ‘direct-on-line’ (DOL) or ‘direct-to-line’ (DTL) starting. The switchingwill usually bedoneby meansofarelay orcontactor,incorp- orating fuses and other overload protection devices, and operated manually by local or remote pushbuttons, or interfaced to permit oper- ation from a programmable controller or computer. In contrast, if the supply impedance is high (i.e. a low-fault level) an appreciablevoltdropwilloccureverytimethemotorisstarted,causing lightstodimandinterferingwithotherapparatusonthesamesupply.With this‘weak’supply,someformofstarteriscalledfortolimitthecurrentat startingandduringtherun-upphase,therebyreducingthemagnitudeof thevoltdropimposedonthesupplysystem.Asthemotorpicksupspeed, the current falls, so the starter is removed as the motor approaches full speed.Naturallyenoughthepricetobepaidforthereductionincurrentisa lowerstartingtorque,andalongerrun-uptime. Whether or not a starter is required depends on the size of the motor in relation to the capacity or fault level of the supply, the prevailing regulationsimposedbythesupplyauthority,andthenatureoftheload. Thereferencesaboveto‘low’and‘high’supplyimpedancesmustthere- fore be interpreted in relation to the impedance of the motor when it is stationary. A large (and therefore low impedance) motor could well be startedquitehappilyDOLinamajorindustrialplant,wherethesupplyis ‘stiV’,i.e.thesupplyimpedanceisverymuchlessthanthemotorimped- ance.Butthesamemotorwouldneedastarterwhenusedinaruralsetting remotefromthemainpowersystem,andfedbyarelativelyhighimped- ance or ‘weak’ supply. Needless to say, the stricter the rules governing permissiblevoltdrop,themorelikelyitisthatastarterwillbeneeded. Motors which start without signiWcant load torque or inertia can accelerate very quickly, so the high starting current is only drawn for a short period. A 10 kW motor would be up to speed in a second or so, and the volt drop may therefore be judged as acceptable. Clutches are sometimes Wtted to permit ‘oV-load’ starting, the load being applied after the motor has reached full speed. Conversely, if the load torque and/or inertia are high, the run-up may take many seconds, in which case a starter may prove essential. No strict rules can be laid down, but obviously the bigger the motor, the more likely it is to require a starter.202 Electric Motors and Drives Star/delta (wye/mesh) starter Thisisthesimplestandmostwidelyusedmethodofstarting.Itprovides for the windings of the motor to be connected in star (wye) to begin pffiffiffi with, thereby reducingthevoltageapplied toeach phaseto 58% (1= 3) of its DOL value. Then, when the motor speed approaches its running value, the windings are switched to delta (mesh) connection. The main advantage of the method is its simplicity, while its main drawbacks are thatthestartingtorqueisreduced(seebelow),andthesuddentransition fromstartodeltagivesrisetoasecondshock–albeitoflesserseverity– to the supply system and to the load. For star/delta switching to be possiblebothendsofeachphaseofthemotorwindingsmustbebrought out to the terminal box. This requirement is met in the majority of motors, except small ones which are usually permanently connected in delta. Withastar/deltastarterthecurrentdrawnfromthesupplyisapproxi- mately one third of that drawn in a DOL start, which is very welcome, butatthesametimethestartingtorqueisalsoreducedtoonethirdofits DOLvalue.Naturallyweneedtoensurethatthereducedtorquewillbe suYcienttoacceleratetheload,andbringituptoaspeedatwhichitcan be switched to delta without an excessive jump in the current. Variousmethodsareusedtodetectwhentoswitchfromstartodelta. Inmanualstarters,thechangeoverisdeterminedbytheoperatorwatch- ingtheammeteruntilthecurrenthasdroppedtoalowlevel,orlistening to the sound of the motor until the speed becomes steady. Automatic versions are similar in that they detect either falling current or speed rising to a threshold level, or else they operate after a preset time. Autotransformer starter A 3-phase autotransformer is usually used where star/delta starting pro- videsinsuYcientstartingtorque.Eachphaseofanautotransformerconsists of a single winding on a laminated core. The mains supply is connected across the ends ofthecoils,and oneormore tapping points (ora sliding contact)provideareducedvoltageoutput,asshowninFigure6.3. ThemotorisWrstconnectedtothereducedvoltageoutput,andwhen thecurrenthasfallentotherunningvalue,themotorleadsareswitched over to the full voltage. Ifthereducedvoltageischosensothatafractionaofthelinevoltage is used to start the motor, the starting torque is reduced to approxi- 2 matelya timesitsDOLvalue,andthecurrentdrawnfromthemainsisOperating Characteristics of Induction Motors 203 Start Run Figure 6.3 Autotransformer starter for cage induction motor 2 also reduced to a times its direct value. As with the star/delta starter, thetorqueperampereofsupplycurrentisthesameasforadirectstart. The switchover from the starting tap to the full voltage inevitably resultsinmechanicalandelectricalshockstothemotor.Inlargemotors thetransientovervoltagescausedbyswitchingcanbeenoughtodamage the insulation, and where this is likely to pose a problem a modiWed procedure known as the Korndorfer method is used. A smoother changeover is achieved by leaving part of the winding of the autotrans- former in series with the motor winding all the time. Resistance or reactance starter By inserting three resistors or inductors of appropriate value in series with the motor, the starting current can be reduced by any desired extent,butonlyattheexpenseofadisproportionatereductioninstarting torque. Forexample,ifthecurrentisreducedtohalfitsDOLvalue,themotor voltagewillbehalved,sothetorque(whichisproportionaltothesquare ofthevoltage–seelater) will bereducedtoonly25%ofits DOLvalue. This approach is thus less attractive in terms of torque per ampere of supply current than the star/delta method. One attractive feature, how- ever, is that as the motor speed increases and its eVective impedance rises, the volt drop across the extra impedance reduces, so the motor voltage rises progressively with the speed, thereby giving more torque. When the motor is up to speed, the added impedance is shorted-out by means of a contactor. Variable-resistance starters (manually or motor204 Electric Motors and Drives operated) are sometimes used with small motors where a smooth jerk- free start is required, for example in Wlm or textile lines. Solid-state soft starting Thismethodisnowthemostwidelyused.Itprovidesasmoothbuild-up of current and torque, the maximum current and acceleration time are easily adjusted, and it is particularly valuable where the load must not be subjected to sudden jerks. The only real drawback over conven- tional starters is that the mains currents during run-up are not sinus- oidal, which can lead to interference with other equipment on the same supply. The most widely used arrangement comprises three pairs of back- to-back thyristors connected in series with three supply lines, as shown in Figure 6.4(a). Each thyristor is Wred once per half-cycle, the Wring being synchron- ised with the mains and theWring angle being variable so that each pair conductsforavaryingproportionofacycle.Typicalcurrentwaveforms areshowninFigure6.4(b):theyareclearlynotsinusoidalbutthemotor will tolerate them quite happily. A wide variety of control philosophies can be found, with the degree ofcomplexityandsophisticationbeingreXectedintheprice.Thecheap- est open-loop systems simply alter theWring angle linearly with time, so that the voltage applied to the motor increases as it accelerates. The ‘ramp-time’ can be set by trial and error to give an acceptable start, i.e. one in which the maximum allowable current from the supply is not exceededatanystage.Thisapproachisreasonablysatisfactorywhenthe loadremainsthesame,butrequiresresettingeachtimetheloadchanges. Loads with high static friction are a problem because nothing happens for the Wrst part of the ramp, during which time the motor torque is insuYcient to move the load. When the load Wnally moves, its acceler- ation is often too rapid. The more advanced open-loop versions allow the level of current at the start of the ramp to be chosen, and this is helpful with ‘sticky’ loads. More sophisticated systems – usually with on-board digital control- lers–providefortightercontrolovertheaccelerationproWlebyincorp- oratingclosed-loopcurrentfeedback.Afteran initial rampingupto the start level (over the Wrst few cycles), the current is held constant at the desired level throughout the accelerating period, the Wring angle of the thyristors being continually adjusted to compensate for the changing eVective impedance of the motor. By keeping the current at the max- imumvalue,whichthesupplycantoleratetherun-uptime,isminimised.Operating Characteristics of Induction Motors 205 (a) Start Synchronising, control and firing circuits Run High (b) Firing angle delay Low Figure 6.4 (a) Thyristor soft-starter, (b) typical motor current waveforms Alternatively, if a slow run-up is desirable, a lower accelerating current can be selected. As with the open-loop systems the velocity–time proWle is not neces- sarilyideal,sincewithconstantcurrentthemotortorqueexhibitsavery sharp rise as the pullout slip is reached, resulting in a sudden surge in speed. Prospectiveusersneedtobewaryofsomeofthepromotionalliterature, wherenaturallyenoughthevirtuesarehighlightedwhiletheshortcomings are played down. Claims are sometimes made that massive reductions in starting current can be achieved without corresponding reductions in startingtorque.Thisisnonsense:thecurrentcancertainlybelimited,but asfarastorqueperlineampisconcernedsoft-startsystemsarenobetter206 Electric Motors and Drives thanseriesreactorsystems,andnotasgoodastheautotransformerand star/deltamethods. Starting using a variable-frequency inverter Operation of induction motors from variable-frequency inverters is discussed in Chapter 8, but it is appropriate to mention here that one of the advantages of inverter-fed operation is that starting is not a problem because it is usually possible to obtain at least rated torque at zerospeedwithoutdrawinganexcessivecurrentfromthemainssupply. None of the other starting methods we have looked at have this ability, soinsomeapplicationsitmaybethatthecomparativelyhighcostofthe inverter is justiWed solely on the grounds of its starting and run-up potential. RUN-UP AND STABLE OPERATING REGIONS In addition to having suYcient torque to start the load it is obviously necessary for the motor to bring the load up to full speed. To predict how the speed will rise after switching on we need the torque–speed curves of the motor and the load, and the total inertia. By way of example, we can look at the case of a motor with two diVerentloads(seeFigure6.5).Thesolidlineisthetorque–speedcurve of the motor, while the dotted lines represent two diVerent load charac- teristics. Load (A) is typical of a simple hoist, which applies constant torque to the motor at all speeds, while load (B) might represent a fan. For the sake of simplicity, we will assume that the load inertias (as seen at the motor shaft) are the same. Torque T acc Load A Load B N 0 0 N Speed s Figure 6.5 Typical torque–speed curve showing two diVerent loads which have the same steady running speed(N)Operating Characteristics of Induction Motors 207 Speed N Load B Load A 0 Time Figure 6.6 Speed–time curves during run-up, for motor and loads shown in Figure 6.5 The speed–time curves for run-up are shown in Figure 6.6. Note that thegradientofthespeed–timecurve(i.e.theacceleration)isobtainedby dividingtheacceleratingtorqueT (whichisthediVerencebetweenthe acc torque developed by the motor and the torque required to run the load at that speed) by the total inertia. In this example, both loads ultimately reach the same steady speed, N(i.e.thespeedatwhichmotortorqueequalsloadtorque),butBreaches full speed much more quickly because the accelerating torque is higher during most of the run-up. Load A picks up speed slowly at Wrst, but then accelerates hard (often with a characteristic ‘whoosh’ produced by the ventilating fan) as it passes through the peak torque–speed and approaches equilibrium conditions. It should be clear that the higher the total inertia, the slower the acceleration and vice versa. The total inertia means the inertia as seen atthemotorshaft,soifgearboxesorbeltsareemployedtheinertiamust be ‘referred’ as discussed in Chapter 11. An important qualiWcation ought to be mentioned in the context of the motor torque–speed curves shown by the solid line in Figure 6.5. Thisisthatcurveslikethisrepresentthetorquedevelopedbythemotor when it has settled down at the speed in question, i.e. they are the true steady-statecurves.Inreality,amotorwillgenerallyonlybeinasteady- stateconditionwhenitsettlesatitsnormalrunningspeed,soformostof the speed range the motor will be accelerating. In particular, when the motorisWrstswitchedon,therewillbeatransientperiodofafewcycles as the three currents gradually move towards a balanced 3-phase pat- tern. During this period the torque can Xuctuate wildly and the motor canpick upsigniWcantspeed,sotheactualtorquemay beverydiVerent from that shown by the steady-state curve, and as a result the instant- aneous speeds can Xuctuate about the mean value. Fortunately, the average torque during run-up can be fairly reliably obtained from the208 Electric Motors and Drives steady-statecurves,particularlyiftheinertiaishighandthemotortakes many cycles to reach full speed, in which case we would consider the torque–speed curve as being ‘quasi-steady state’. Harmonic effects – skewing A further cautionary note in connection with the torque–speed curves showninthisandmostotherbooksrelatetotheeVectsofharmonicair- gap Welds. In Chapter 5, it was explained that despite the limitations imposedbyslotting,thestatorwindingmagneticXux(MMF)isremark- ablyclosetotheidealofapuresinusoid.Unfortunately,becauseitisnota perfectsinusoid,Fourieranalysisrevealsthatinadditiontothepredom- inant fundamental component, there are always additional unwanted ‘space harmonic’Welds. These harmonicWelds have synchronous speeds that are inversely proportional to their order. For example a 4-pole, 50 Hz motor will have a main Weld rotating at 1500 rev/min, but in addition there may be a Wfth harmonic (20-pole) Weld rotating in the reverse direction at 300 rev/min, a seventh harmonic (28-pole) Weld ro- tatingforwardsat214 rev/min,etc.Thesespaceharmonicsareminimised bystatorwindingdesign,butcanseldombeeliminated. If the rotor has a very large number of bars it will react to the harmonicWeld in much the same way as to the fundamental, producing additionalinductionmotortorquescentredonthesynchronousspeedof the harmonic, and leading to unwanted dips in the torque speed, typic- ally as shown in Figure 6.7. Users should not be too alarmed as in most cases the motor will ride throughtheharmonicduringacceleration,butinextremecasesamotor might, for example, stabilise on the seventh harmonic, and ‘crawl’ at about 214 rev/min, rather than running up to 4-pole speed (1500 rev/ min at 50 Hz), as shown by the dot in Figure 6.7. Torque Load torque −300 0 214 1500 rev/min Figure6.7 Torque–speedcurveshowingtheeVectofspaceharmonics,andillustratingthe possibility of a motor ‘crawling’ on the seventh harmonicOperating Characteristics of Induction Motors 209 TominimisetheundesirableeVectsofspaceharmonicstherotorbars in the majority of induction motors are not parallel to the axis of rotation, but instead they are skewed (typically by around one or two slotpitches)alongtherotorlength.ThishasverylittleeVectasfarasthe fundamental Weld is concerned, but can greatly reduce the response of the rotor to harmonicWelds. Because the overall inXuence of the harmonics on the steady-state curveisbarelynoticeable,andtheirpresencemightworryusers,theyare rarely shown, the accepted custom being that ‘the’ torque–speed curve represents the behaviour due to the fundamental component only. High inertia loads – overheating Apart from accelerating slowly, high inertia loads pose a particular problemofrotorheating,whichcaneasilybeoverlookedbytheunwary user.Everytimeaninductionmotorisstartedfromrestandbroughtup tospeed,thetotalenergydissipatedasheatinthemotorwindingsisequal to the stored kinetic energy of the motor plus load. (This matter is explored further via the equivalent circuit in Chapter 7.) Hence with high inertia loads, very large amounts of energy are released as heat in thewindingsduringrun-up,eveniftheloadtorqueisnegligiblewhenthe motorisuptospeed.Withtotallyenclosedmotorstheheatultimatelyhas toWnditswaytotheWnnedoutercasingofthemotor,whichiscooledby airfromtheshaft-mountedexternalfan.Coolingoftherotoristherefore usually much worse than the stator, and the rotor is thus most likely to overheatduringhighinertiarun-ups. No hard and fast rules can be laid down, but manufacturers usually worktostandardswhichspecifyhowmanystartsperhourcanbetoler- ated.Actually,thisinformationisuselessunlesscoupledwithreferenceto the total inertia, since doubling the inertia makes the problem twice as bad.However,itisusuallyassumedthatthetotalinertiaisnotlikelytobe morethantwicethemotorinertia,andthisiscertainlythecaseformost loads. If in doubt, the user should consult the manufacturer who may recommend a larger motor than might seem necessary simply to supply thefull-loadpowerrequirements. Steady-state rotor losses and efficiency The discussion above is a special case, which highlights one of the less attractivefeaturesofinductionmachines.Thisisthatitisneverpossible for allthepower crossingtheair-gapfrom thestator tobe convertedto mechanical output, because some is always lost as heat in the rotor210 Electric Motors and Drives circuit resistance. In fact, it turns out that at slip s the total power (P ) r crossing the air-gap always divides so that a fraction sP is lost as heat, r while the remainder (1s)P is converted to useful mechanical output r (see also Chapter 7.). Hence, when the motor is operating in the steady state the energy conversion eYciency of the rotor is given by Mechanical output power h ¼ ¼ (1s) (6:2) r Rated power input to rotor This result is very important, and shows us immediately why operating at small values of slip is desirable. With a slip of 5% (or 0.05), for example, 95% of the air-gap power is put to good use. But if the motor was run at half the synchronous speed (s¼ 0.5), 50% of the air- gap power would be wasted as heat in the rotor. WecanalsoseethattheoveralleYciencyofthemotormustalwaysbe signiWcantly less than (1s), because in addition to the rotor copper lossestherearestatorcopperlosses,ironlossesandwindageandfriction losses. This fact is sometimes forgotten, leading to conXicting claims such as ‘full-load slip ¼ 5%, overall eYciency ¼ 96%’, which is clearly impossible. Steady-state stability – pullout torque and stalling We can check stability by asking what happens if the load torque sud- denlychangesforsomereason.Theloadtorqueshownbythedottedline inFigure6.8isstableatspeedX,forexample:iftheloadtorqueincreased fromT toT ,theloadtorquewouldbegreaterthanthemotortorque,so a b the motor torque would decelerate. As the speed dropped, the motor torque would rise, until a new equilibrium was reached, at the slightly Torque Z Y X T Stable b T a region O 0 0 N Speed s Figure 6.8 Torque–speed curve illustrating stable operating region (0XYZ)Operating Characteristics of Induction Motors 211 lower speed (Y). The converse would happen if the load torque were reduced,leadingtoahigherstablerunningspeed. Butwhat happens if theload torque is increased more and more? We can see that as the load torque increases, beginning at point X, we eventually reach point Z, at which the motor develops its maximum torque. Quite apart from the fact that the motor is now well into its overloadregion,andwillbeindangerofoverheating,ithasalsoreached the limit of stable operation. If the load torque is further increased, the speedfalls(becausetheloadtorqueismorethanthemotortorque),and as it does so the shortfall between motor torque and load torque be- comes greater and greater. The speed therefore falls faster and faster, and the motor is said to be ‘stalling’. With loads such as machine tools (a drilling machine, for example), as soon as the maximum or ‘pullout’ torque is exceeded, the motor rapidly comes to a halt, making an angry hummingsound.Withahoist,however,theexcessloadwouldcausethe rotor to be accelerated in the reverse direction, unless it was prevented from doing so by a mechanical brake. TORQUE–SPEED CURVES – INFLUENCE OF ROTOR PARAMETERS WesawearlierthattherotorresistanceandreactanceinXuencedtheshape of the torque–speed curve. The designer can vary both of these param- eters,andwewillexploretheprosandconsofthevariousalternatives.To limit the mathematics the discussion will be mainly qualitative, but it is worthmentioningthatthewholemattercanbedealtrigorouslyusingthe equivalentcircuitapproach,asdiscussedinChapter7. WewilldealwiththecagerotorWrstbecauseitisthemostimportant, but the wound rotor allows a wider variation of resistance to be obtained, so it is discussed later. Cage rotor For small values of slip, i.e. in the normal running region, the lower we maketherotorresistancethesteepertheslopeofthetorque–speedcurve becomes, as shown in Figure 6.9. We can see that at the rated torque (shown by the horizontal dotted line in Figure 6.9) the full-load slip of the low-resistance cage is much lower than that of the high-resistance cage. But we saw earlier that the rotor eYciency is equal to (1s), wheresistheslip.So,weconcludethatthelow-resistancerotornotonly gives better speed holding, but is also much more eYcient. There is of course a limit to how low we can make the resistance: copper allows us212 Electric Motors and Drives Torque Low rotor resistance High rotor resistance Full-load torque 0 1 0 Slip Figure 6.9 InXuence of rotor resistance on torque–speed curve of cage motor. The full-load running speeds are indicated by the vertical dotted lines to achieve a lower resistance than aluminium, but we can’t do anything better thanWll the slots with solid copper bars. As we might expect there are drawbacks with a low-resistance rotor. The starting torque is reduced (see Figure 6.9), and worse still the starting current is increased. The lower starting torque may prove insuYcient to accelerate the load, while increased starting current may lead to unacceptable volt drops in the supply. Altering the rotor resistance has little or no eVect on the value of the peak (pullout) torque, but the slip at which the peak torque occurs is directly proportional to the rotor resistance. By opting for a high enough resistance (by making the cage from bronze, brass or other relatively high resistivity material) we can if we wish to arrange for the peaktorquetooccuratorclosetostarting,asshowninFigure6.9.The snagindoingthisisthatthefull-loadeYciencyisinevitablylowbecause the full-load slip will be high (see Figure 6.9). Therearesomeapplicationsforwhichhigh-resistancemotorsarewell suited, an example being for metal punching presses, where the motor accelerates a Xywheel, which is used to store energy. To release a signiWcant amount of energy, the Xywheel slows down appreciably during impact, and the motor then has to accelerate it back up to full speed. The motor needs a high torque over a comparatively wide speed range, and does most of its work during acceleration. Once up to speed the motor is eVectively running light, so its low eYciency is of little consequence. High-resistance motors are also used for speed control of fan-type loads, and this is taken up again in Section 6.6, where speed control is explored. To sum up, a high-rotor resistance is desirable when starting and at low speeds, while a low resistance is preferred under normal runningOperating Characteristics of Induction Motors 213 conditions.Togetthebestofbothworlds,weneedtobeabletoalterthe resistance from a high value at starting to a lower value at full speed. Obviouslywecannotchangetheactualresistanceofthecageonceithas been manufactured, but it is possible to achieve the desired eVect with either a ‘double cage’ or a ‘deep bar’ rotor. Manufacturers normally oVerarangeofdesigns,whichreXect thesetrade-oVs,andtheuserthen selects the one which best meets his particular requirements. Double cage rotors Double cage rotors have an outer cage made up of relatively high resistivity material such as bronze, and an inner cage of low resistivity, usually copper, as shown in Figure 6.10. The inner cage is sunk deep into the rotor, so that it is almost completely surrounded by iron. This causes the inner bars to have a muchhigherleakageinductancethaniftheywereneartherotorsurface, so that under starting conditions (when the induced rotor frequency is high) their inductive reactance is very high and little current Xows in them. In contrast, the bars of the outer cage are placed so that their leakage Xuxes face a much higher reluctance path, leading to a low-leakageinductance.Hence,understartingconditions,rotorcurrent is concentrated in the outer cage, which, because of its high resistance, produces a high starting torque. At the normal running speed the roles are reversed. The rotor fre- quencyislow,sobothcageshavelowreactanceandmostofthecurrent thereforeXowsinthelow-resistanceinnercage.Thetorque–speedcurve is therefore steep, and the eYciency is high. Considerable variation in detailed design is possible to shape the torque–speed curve to particular requirements. In comparison with a single-cage rotor, the double cage gives much higher starting torque, substantially less starting current, and marginally worse running performance. Figure 6.10 Alternative arrangements of double cage rotors. The outer cage has a high resistance (e.g. bronze) while the inner cage has a low resistance (e.g. copper)214 Electric Motors and Drives Deep bar rotors The deep bar rotor has a single cage, usually of copper, formed in slots which are deeper and narrower than in a conventional single-cage design. Construction is simpler and therefore cheaper than in a double cage rotor, as shown in Figure 6.11. The deep bar approach ingeniously exploits the fact that the eVective resistanceofaconductorishigherundera.c.conditionsthanunderd.c. conditions. With a typical copper bar of the size used in an induction motor rotor, the diVerence in eVective resistance between d.c. and say 50 or 60 Hz (the so-called ‘skin-eVect’) would be negligible if the con- ductor wasentirely surroundedby air. Butwhenit isalmostcompletely surroundedbyiron,asintherotorslots,itseVectiveresistanceatmains frequency may be two or three times its d.c. value. Under starting conditions, when the rotor frequency is equal to the supply frequency, the skin eVect is very pronounced, and the rotor current is concentrated towards the top of the slots. The eVective resist- ance is therefore increased, resulting in a high-starting torque from a low-starting current. When the speed rises and the rotor frequency falls, the eVective resistance reduces towards its d.c. value, and the current distributes itself more uniformly across the cross section of the bars. The normal running performance thus approaches that of a low-resistancesingle-cagerotor,givingahigheYciencyandstiVtorque– speed curve. The pullout torque is, however, somewhat lower than for an equivalent single-cage motor because of the rather higher leakage reactance. Most small and medium motors are designed to exploit the deep bar eVect to some extent, reXecting the view that for most applications the slightly inferior running performance is more than outweighed by the much better starting behaviour. A typical torque–speed curve for a general-purpose medium-size (55 kW) motor is shown in Figure 6.12. Such motors are unlikely to be described by the maker speciWcally as ‘deep-bar’buttheyneverthelessincorporateameasureoftheskineVect Figure 6.11 Typical deep-bar rotor constructionOperating Characteristics of Induction Motors 215 Torque, p.u. Current, p.u. Torque 3 6 2 4 Current 1 2 N 0 0 N Speed s Figure 6.12 Typical torque–speed and current–speed curves for a general-purpose industrial cage motor and consequently achieve the ‘good’ torque–speed characteristic shown by the solid line in Figure 6.12. The current–speed relationship is shown by the dotted line in Figure 6.12, both torque and current scales being expressed in per unit (p.u.). This notation is widely used as a shorthand, with 1 p.u. (or 100%) representing rated value. For example, a torque of 1.5 p.u. simply means one and a half times rated value, while a current of 400% means acurrentoffourtimesratedvalue. Starting and run-up of slipring motors By adding external resistance in series with the rotor windings the startingcurrentcanbekeptlowbutatthesametimethestartingtorque is high. This is the major advantage of the wound-rotor or slipring motor, and makes it well suited for loads with heavy starting duties such as stone-crushers, cranes and conveyor drives. The inXuence of rotor resistance is shown by the set of torque–speed curves in Figure 6.13. The curve on the right corresponds to no added rotor resistance, with the other six curves showing the inXuence of progressively increasing the external resistance. A high-rotor resistance is used when the motor is Wrst switched on, and depending on the value chosen any torque up to the pullout value (perhaps twice full load) can be obtained. Typically, the resistance will be selected to give full-load torque at starting, together with rated current from the mains. The starting torque is then as indicated by point A in Figure 6.13. As the speed rises, the torque would fall more or less linearly if the resistance remained constant, so to keep close to full-load torque the resistance is gradually reduced, either in steps, in which case thee 216 Electric Motors and Drives Torque R=0 C B A 0 0 Speed Figure 6.13 Torque–speed curves for a wound-rotor (slipring) motor showing how the external rotor-circuit resistance (R) can be varied in steps to provide an approximately constant torque during acceleration trajectory ABC etc. is followed (see Figure 6.13), or continuously so that maximum torque is obtained throughout. Ultimately the external resistance is made zero by shorting-out the sliprings, and thereafter the motor behaves like a low-resistance cage motor, with a high running eYciency. As mentioned earlier, the total energy dissipated in the rotor circuit duringrun-upisequaltotheWnalstoredkineticenergyofthemotorand load. In a cage motor this energy ends up in the rotor, and can cause overheating. In the slipring motor, however, most of the energy goes intotheexternalresistance.Thisisagoodthingfromthemotorpointof view, but means that the external resistance has to absorb the thermal energy without overheating. Fan-cooled grid resistors are often used, with tappings at various resistance values. These are progressively shorted-out during run-up, either by a manual or motor-driven drum-type controller, or with a series of timed contactors. Alternatively, where stepless variation of resistance is required, a liquid resistance controller is often employed. It consists of a tank of electrolyte (typically caustic soda) into which three electrodes can be raised or lowered. The resistance between the electrodes depends on how far they are immersed in the liquid. The electrolyte acts as an excellent short-term reservoir for the heat released, and by arranging for convection to take place via a cooling radiator,theequipmentcanalsobeusedcontinuouslyforspeedcontrol (see later). Attempts havebeen madetovarytheeVectiverotorcircuit resistance by means of a Wxed external resistance and a set of series connected thyristors, but this approach has not gained wide acceptance. c Low n a t s i s e r r o t o High rOperating Characteristics of Induction Motors 217 INFLUENCE OF SUPPLY VOLTAGE ON TORQUE–SPEED CURVE We established earlier that at any given slip, the air-gap Xux density is proportionaltotheappliedvoltage,andtheinducedcurrentintherotor is proportional to the Xux density. The torque, which depends on the product of the Xux and the rotor current, therefore depends on the square of the applied voltage. This means that a comparatively modest fall in the voltage will result in a much larger reduction in torque capability, with adverse eVects which may not be apparent to the un- wary until too late. Toillustratetheproblem,considerthetorque–speedcurvesforacage motor shown in Figure 6.14. The curves (which have been expanded to focusattentiononthelow-slipregion)aredrawnforfullvoltage(100%), and for a modestly reduced voltage of 90%. With full voltage and full- load torque the motor will run at point X, with a slip of say 5%. Since this is the normal full-load condition, the rotor and stator currents will be at their rated values. Now suppose that the voltage falls to 90%. The load torque is assumed to be constant so the new operating point will be at Y. Since the air-gap Xux density is now only 0.9 of its rated value, the rotor current will have to be about 1.1 times rated value to develop the same torque, so the rotor e.m.f. is required to increase by 10%. But the Xux densityhasfallenby10%,soanincreaseinslipof20%iscalledfor.The new slip is therefore 6%. The drop in speed from 95% of synchronous to 94% may well not be noticed, and the motor will apparently continue to operate quite hap- pily.Buttherotorcurrentisnow10%aboveitsratedvalue,sotherotor heating will be 21% more than is allowable for continuous running. Torque 100% Voltage 90% Voltage X Y 0 6 5 0 Slip, % Figure 6.14 InXuence of stator supply voltage on torque–speed curves

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