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8 INVERTER-FED INDUCTION MOTOR DRIVES INTRODUCTION We sawin Chapter 6 that theinductionmotorcanonly runeYciently at owslips,i.e.closetothesynchronousspeedoftherotatingWeld.Thebest method of speed control must therefore provide for continuous smooth variationofthesynchronousspeed,whichinturncallsforvariationofthe supply frequency. This is achieved using an inverter (as discussed in Chapter 2) to supply the motor. A complete speed control scheme which includes tacho (speed) feedback is shown in block diagram form n Figure 8.1. We should recall that the function of the converter (i.e. rectiWer and variable-frequency inverter) is to draw power from the Wxed-frequency constant-voltage mains, and convert it to variable frequency, variable voltage for driving the induction motor. Both the rectiWer and the inverter employ switching strategies (see Chapter 2), so the power conversions are accomplished eYciently and the converter can be compact. Variable frequency inverter-fed induction motor drives are used in ratings up to hundreds of kilowatts. Standard 50 Hz or 60 Hz motors are often used (though as we will see later this limits performance), and the inverter output frequency typically covers the range from around 5–10 Hz up to perhaps 120 Hz. This is suYcient to give at least a 10:1 speed range with a top speed of twice the normal (mains frequency) operatingspeed.Themajorityofinvertersare3-phaseinputand3-phase output, but single-phase input versions are available up to about 5 kW, and some very small inverters (usually less than 1 kW) are speciWcally intended for use with single-phase motors.280 Electric Motors and Drives 50/60 Hz supply Induction motor Speed Ref. Rectifier Inverter Control circuits Speed feedback Tachometer Figure 8.1 General arrangement of inverter-fed variable-frequency induction motor speed-controlled drive A fundamental aspect of any converter, which is often overlooked, is the instantaneous energy balance. In principle, for any balanced three-phase load, the total load power remains constant from instant to instant, so if it was possible to build an ideal 3-phase input, 3-phase output converter, there would be no need for the converter to include any energy storage elements. In practice, all converters require some energystorage(incapacitorsorinductors),butthesearerelativelysmall whentheinputis3-phasebecausetheenergybalanceisgood.However, as mentioned above, many small and medium power converters are supplied from single-phase mains. In this case, the instantaneous input power is zero at least twice per cycle of the mains (because the voltage and current go through zero every half-cycle). If the motor is 3-phase (and thus draws power at a constant rate), it is obviously necessary to store suYcient energy in the converter to supply the motor during the briefintervalswhentheloadpowerisgreaterthantheinputpower.This explains why the most bulky components in many small and medium power inverters are electrolytic capacitors. The majority of inverters used in motor drives are voltage source inverters(VSI),inwhichtheoutputvoltagetothemotoriscontrolledto suittheoperatingconditionsofthemotor.Currentsourceinverters(CSI) arestillused,particularlyforlargeapplications,butwillnotbediscussed here. Comparison with d.c. drive The initial success of the inverter-fed induction motor drive was due to the fact that a standard induction motor was much cheaper than aInverter-Fed Induction Motor Drives 281 Plate 8.1 Inverter-fed induction motor with inverter mounted directly onto motor. (Alternatively the inverter can be wall-mounted, as in the upper illustration, which also shows the user interface module.) (Photo courtesy of ABB) comparable d.c. motor, and this saving compensated for the relatively highcostoftheinvertercomparedwiththethyristord.c.converter.But whereasad.c.drivewasinvariablysuppliedwithamotorprovidedwith laminated Weld poles and through ventilation to allow it to operate continuouslyatlowspeedswithoutoverheating,thestandardinduction motor has no such provision, having been designed primarily for Wxed- frequencyfull-speedoperation.Thus,althoughtheinverteriscapableof driving the induction motor with full torque at low speeds, continuous operation is unlikely to be possible because the cooling fan will be ineVective and the motor will overheat.282 Electric Motors and Drives Now that inverter-fed drives dominate the market, two changes have become evident. Firstly, reputable suppliers now warn of the low-speed limitation of the standard induction motor, and encourage users to opt for a blower-cooled motor if necessary. And secondly, the fact that inverter-fed motors are not required to start direct-on-line at supply frequency means that the design need no longer be a compromise between starting and running performance. Motors can therefore be designed speciWcally for operation from an inverter, and have low- resistance cages giving very high steady-state eYciency and good open- loopspeedholding.Themajorityofdrivesdostillusestandardmotors, but inverter-speciWc motors with integral blowers are gradually gaining ground. Thesteady-stateperformanceofinverter-feddrivesisbroadlycompar- ablewiththatofd.c.drives(exceptforthelimitationhighlightedabove), withdrivesofthesameratinghavingsimilaroveralleYcienciesandoverall torque–speed capabilities. Speed holding is likely to be less good in the inductionmotordrive,thoughiftachofeedbackisusedbothsystemswill beexcellent.Theinductionmotorisclearlymorerobustandbettersuited to hazardous environments, and can run at higher speeds than the d.c. motor,whichislimitedbytheperformanceofitscommutator. Some of the early inverters did not employ pulse width modulation (PWM),andproducedjerkyrotationatlowspeed.Theywerealsonotice- ablymorenoisythantheird.c.counterparts,butthewidespreadadoption ofPWMhasgreatlyimprovedtheseaspects.Mostlowandmediumpower invertersuseMOSFETorIGBTdevices,andmaymodulateatultrasonic frequencies,whichnaturallyresultinrelativelyquietoperation. The Achilles heel of the basic inverter-fed system has been the rela- tively poor transient performance. For fan and pump applications and high-inertia loads this is not a serious drawback, but where rapid re- sponsetochangesinspeedorloadiscalledfor (e.g.inmachinetoolsor rolling mills), the d.c. drive with its fast-acting current-control loop traditionally proved superior. However, it is now possible to achieve equivalent levels of dynamic performance from induction motors, but the complexity of the control naturally reXects in a higher price. Most manufacturersnowoVerthisso-called‘vector’or‘Weld-oriented’control (see Section 8.4) as an optional extra for high-performance drives. Inverter waveforms Whenwelookedattheconverter-fedd.c.motorwesawthatthebehav- iourwasgovernedprimarilybythemeand.c.voltage,andthatformost purposes we could safely ignore the ripple components. A similar ap-Inverter-Fed Induction Motor Drives 283 proximation is useful when looking at how the inverter-fed induction motor performs. We make use of the fact that although the actual voltage waveform supplied by the inverter will not be sinusoidal, the motor behaviour depends principally on the fundamental (sinusoidal) component of the applied voltage. This is a somewhat surprising but extremely welcome simpliWcation, because it allows us to make use of our knowledge of how the induction motor behaves with a sinusoidal supply to anticipate how it will behave when fed from an inverter. In essence, the reason why the harmonic components of the applied voltage are much less signiWcant than the fundamental is that the im- pedanceofthemotorattheharmonicfrequenciesismuchhigherthanat the fundamental frequency. This causes the current to be much more sinusoidal than the voltage, as shown in Figure 8.2, and this in turn means that we can expect a sinusoidal travelling Weld to be set up in much the same way as discussed in Chapter 5. Itwouldbewrongtopretendthattheharmoniccomponentshaveno eVects,ofcourse.Theycancreateunpleasantacousticnoise,andalways give rise to additional iron and copper losses. As a result it is common forastandardmotortohavetobede-rated(byuptoperhaps5or10%) for use on an inverter supply. Aswiththed.c.drivetheinverter-fedinductionmotordrivewilldraw non-sinusoidalcurrentsfromtheutilitysupply.Ifthesupplyimpedance is relatively high signiWcant distortion of the mains voltage waveform is inevitable unlessWlters areWtted on the a.c. input side, but with normal Voltage Current Figure 8.2 Typical voltage and current waveforms for PWM inverter-fed induction motor. (The fundamental-frequency component is shown by the dotted line.)284 Electric Motors and Drives industrial supplies there is no problem for small inverters of a few kW rating. Someinvertersnowinclude‘front-endconditioning’i.e.anextrahigh- frequencyswitchingstageandWlterwhichensurethatthecurrentdrawn from the mains is not only sinusoidal, but also at unity power factor. This feature will become widespread in medium and high power drives to meet the increasingly stringent conditions imposed by the supply authorities. Steady-state operation – Importance of achieving full flux Three simple relationships need to be borne in mind to simplify under- standing of how the inverter-fed induction motor behaves. Firstly, we established in Chapter 5 that for a given induction motor, the torque developeddependsonthestrengthoftherotatingXuxdensitywave,and on the slip speed of the rotor, i.e. on the relative velocity of the rotor withrespecttotheXuxwave.Secondly,thestrengthoramplitudeofthe Xux wavedependsdirectly on the supplyvoltageto thestator windings, and inversely on the supply frequency. And thirdly, the absolute speed of the Xux wave depends directly on the supply frequency. Recalling that the motor can only operate eYciently when the slip is small,weseethatthebasicmethodofspeedcontrolrestsonthecontrol ofthespeedofrotationoftheXuxwave(i.e.thesynchronousspeed),by control of the supply frequency. If the motor is a 4-pole one, for example, the synchronous speed will be 1500 rev/min when supplied at 50 Hz,1200 rev/minat40 Hz,750 rev/minat25 Hzandsoon.Theno- load speed will therefore be almost exactly proportional to the supply frequency,becausethetorqueatnoloadissmallandthecorresponding slip is also very small. Turning now to what happens on load, we know that when a load is appliedtherotorslowsdown,theslipincreases,morecurrentisinducedin therotor,andmoretorqueisproduced.Whenthespeedhasreducedtothe pointwherethemotortorqueequalstheloadtorque,thespeedbecomes steady. We normally want the drop in speed with load to be as small as possible, not only to minimise the drop in speed with load, but also to maximiseeYciency:inshort,wewanttominimisetheslipforagivenload. We saw in Chapter 5 that the slip for a given torque depends on the amplitude of the rotating Xux wave: the higher the Xux, the smaller the slip needed for a given torque. It follows that having set the desired speedofrotationoftheXuxwavebycontrollingtheoutputfrequencyof the inverter we must also ensure that the magnitude of the Xux is adjusted so that it is at its full (rated) value, regardless of the speed ofInverter-Fed Induction Motor Drives 285 rotation. This is achieved by making the output voltage from the in- verter vary in the appropriate way in relation to the frequency. We recall that the amplitude of the Xux wave is proportional to the supply voltage and inversely proportional to the frequency, so if we arrange that the voltage supplied by the inverter vary in direct propor- tiontothefrequency,theXuxwavewillhaveaconstantamplitude.This philosophy is at the heart of most inverter-fed drive systems: there are variations,aswewillsee,butinthemajorityofcasestheinternalcontrol of the inverter will be designed so that the output voltage to frequency ratio (V/f) is automatically kept constant, at least up to the ‘base’ (50 Hz or 60 Hz) frequency. Many inverters are designed for direct connection to the mains sup- ply,withoutatransformer,andasaresultthemaximuminverteroutput voltage is limited to a value similar to that of the mains. With a 415 V supply, for example, the maximum inverter output voltage will be per- haps 450 V. Since the inverter will normally be used to supply a stand- ard induction motor designed for say 415 V, 50 Hz operation, it is obviousthatwhentheinverterissettodeliver50 Hz,thevoltageshould be 415 V, which is within the inverter’s voltage range. But when the frequency was raised to say 100 Hz, the voltage should – ideally – be increased to 830 V in order to obtain full Xux. The inverter cannot supply voltages above 450 V, and it follows that in this case full Xux canonlybemaintaineduptospeedsalittleabovebasespeed.(Itshould be noted that even if the inverter could provide higher voltages, they couldnotbeappliedtoastandardmotorbecausethewindinginsulation will have been designed to withstand not more than the rated voltage.) Established practice is for the inverter to be capable of maintaining the V/f ratio constant up to the base speed (50 Hz or 60 Hz), but to accept that at all higher frequencies the voltage will be constant at its maximum value. This means that the Xux is maintained constant at speeds up to base speed, but beyond that the Xux reduces inversely with frequency. Needless to say the performance above base speed is adversely aVected, as we will see. Users are sometimes alarmed to discover that both voltage and fre- quency change when a new speed is demanded. Particular concern is expressedwhenthevoltageisseentoreducewhenalowerspeediscalled for.Surely,itisargued,itcan’tberighttooperatesaya400 Vinduction motor at anything less than 400 V. The fallacy in this view should now be apparent: the Wgure of 400 V is simply the correct voltage for the motorwhenrundirectlyfromthemains,atsay50 Hz.Ifthisfullvoltage was applied when the frequency was reduced to say 25 Hz, the implica- tion would be that the Xux would have to rise to twice its rated value.286 Electric Motors and Drives This would greatly overload the magnetic circuit of the machine, giving risetoexcessivesaturationoftheiron,anenormousmagnetisingcurrent and wholly unacceptable iron and copper losses. To prevent this from happening, and keep the Xux at its rated value, it is essential to reduce the voltage in proportion to frequency. In the case above, for example, the correct voltage at 25 Hz would be 200 V. TORQUE–SPEED CHARACTERISTICS – CONSTANT V/F OPERATION When the voltage at each frequency is adjusted so that the ratio V/f is kept constant up to base speed, and full voltage is applied thereafter, a familyoftorque–speedcurvesasshowninFigure8.3isobtained.These curvesaretypicalforastandardinductionmotorofseveralkWoutput. As expected, the no-load speeds are directly proportional to the frequency, and if the frequency is held constant, e.g. at 25 Hz in Figure 8.3, the speed drops only modestly from no-load (point a) to full-load (point b). These are therefore good open-loop characteristics, because the speed is held fairly well from no-load to full-load. If the application callsforthespeedtobeheldprecisely,thiscanclearlybeachieved(with theaidofclosed-loopspeedcontrol)byraisingthefrequencysothatthe full-load operating point moves to point (c). Wealsonotethatthepull-outtorque andthetorquestiVness(i.e. the slopeofthetorque–speedcurveinthenormaloperatingregion)ismore orlessthesameatallpointsbelowbasespeed,exceptatlowfrequencies where the eVect of stator resistance in reducing the Xux becomes very pronounced. (The importance of stator resistance at low frequencies is explored quantitatively in Section 7.10.) It is clear from Figure 8.3 that Torque b c 50 Hz 37.5 Hz 25 Hz 10 Hz 5 Hz a Speed Figure 8.3 Torque–speed curves for inverter-fed induction motor with constant voltage–frequency ratioInverter-Fed Induction Motor Drives 287 thestartingtorqueattheminimumfrequencyismuchlessthanthepull- out torque at higher frequencies, and this could be a problem for loads which require a high starting torque. The low-frequency performance can be improved by increasing the V/f ratio at low frequencies in order to restore full Xux, a technique whichisreferredtoas‘low-speedvoltageboosting’.Mostdrivesincorp- orateprovisionforsomeformofvoltageboost,eitherbywayofasingle adjustment to allow the user to set the desired starting torque, or by meansofmorecomplexprovisionforvaryingtheV/fratiooverarange of frequencies. A typical set of torque–speed curves for a drive with the improved low-speed torque characteristics obtained with voltage boost is shown in Figure 8.4. ThecurvesinFigure8.4haveanobviousappealbecausetheyindicate that the motor is capable of producing practically the same maximum torque at all speeds from zero up to the base (50 Hz or 60 Hz) speed. This region of the characteristics is known as the ‘constant torque’ region,whichmeansthatforfrequenciesuptobasespeed,themaximum possible torque which the motor can deliver is independent of the set speed. Continuous operation at peak torque will not be allowable be- cause the motor will overheat, so an upper limit will be imposed by the controller, as discussed shortly. With this imposed limit, operation below base speed corresponds to the armature-voltage control region of a d.c. drive, as exempliWed in Figure 3.9. We should note that the availability of high torque at low speeds (especially at zero speed) means that we can avoid all the ‘starting’ problems associated with Wxed-frequency operation (see Chapter 6). By starting oV with a low frequency which is then gradually raised the Torque Voltage boost region 12.5Hz 25Hz 37.5Hz 50Hz 62.5Hz 75Hz 87.5Hz Speed Figure 8.4 Typical torque–speed curves for inverter-fed induction motor with low-speed voltage boost, constant voltage–frequency ratio from low speed up to base speed, and constant voltage above base speed288 Electric Motors and Drives slip speed of the rotor is always small, i.e. the rotor operates in the optimumconditionfortorqueproductionallthetime,therebyavoiding all the disadvantages of high-slip (low torque and high current) that are associated with mains-frequency starting. This means that not only can the inverter-fed motor provide rated torque at low speeds, but – perhaps more importantly – it does so without drawing any more current from the mains than under full-load conditions, which means that we can safely operate from a weak supply without causing excessive voltage dips. For some essentially Wxed-speed applications, the superior starting ability of the inverter-fed system alone may justify its cost. Beyond the base frequency, the V/f ratio reduces because V remains constant. The amplitude of the Xux wave therefore reduces inversely with the frequency. Now we saw in Chapter 5 that the pull-out torque alwaysoccursatthesameabsolutevalueofslipspeed,andthatthepeak torque is proportional to the square of the Xux density. Hence in the constant voltage region the peak torque reduces inversely with the square of the frequency and the torque–speed curve becomes less steep, as shown in Figure 8.4. Although the curves in Figure 8.4 show what torque the motor can produce for each frequency and speed, they give no indication of whether continuous operation is possible at each point, yet this matter is of course extremely important from the user’s viewpoint, and is discussed next. Limitations imposed by the inverter – constant power and constant torque regions Themainconcernintheinverteristolimitthecurrentstoasafevalueas farasthemainswitchingdevicesareconcerned.Thecurrentlimitwillbe atleastequaltotheratedcurrentofthemotor,andtheinvertercontrol circuitswillbearrangedsothatnomatterwhattheuserdoestheoutput current cannot exceed a safe value. The current limit feature imposes an upper limit on the permissible torque in the region below base speed. This will normally correspond to the rated torque of the motor, which is typically about half the pull-out torque, as indicated by the shaded region in Figure 8.5. In the region below base speed, the motor can therefore develop any torqueuptoratedvalueatanyspeed(butnotnecessarilyforprolonged periods, as discussed below). This region is therefore known as the ‘constant torque’ region, and it corresponds to the armature voltage control region of a d.c. drive.Inverter-Fed Induction Motor Drives 289 Torque Constant torque Constant region power High-speed region region Speed Figure 8.5 Constant torque, constant power and high-speed motoring regions Above base speed of theXux is reduced inversely with the frequency; because the stator (and therefore rotor) currents are limited, the max- imumpermissibletorquealsoreducesinverselywiththespeed,asshown in Figure 8.5. This region is therefore known as the ‘constant power’ region. There is of course a close parallel with the d.c. drive here, both systems operating with reduced or weak Weld in the constant power region. The region of constant power normally extends to somewhere around twice base speed, and because theXux is reduced the motor has to operate with higher slips than below base speed to develop the full rotor current and torque. At the upper limit of the constant power region, the current limit coincides with the pull-out torque limit. Operation at still higher speeds is sometimes provided, but constant power is no longer available be- cause the maximum torque is limited to the pull-out value, which reduces inversely with the square of the frequency. In this high-speed motoring region (Figure 8.5), the limiting torque–speed relationship is similar to that of a series d.c. motor. Limitations imposed by motor The standard practice in d.c. drives is to use a motor speciWcally designed for operation from a thyristor converter. The motor will have alaminatedframe,will probablycomecomplete with atachogenerator, and – most important of all – will have been designed for through ventilation and equipped with an auxiliary air blower. Adequate venti- lation is guaranteed at all speeds, and continuous operation with full torque (i.e. full current) at even the lowest speed is therefore in order.290 Electric Motors and Drives By contrast, it is still common for inverter-fed systems to use a standard industrial induction motor. These motors are totally enclosed, with an external shaft-mounted fan, which blows air over the Wnned outer case. They are designed Wrst and foremost for continuous oper- ation from theWxed frequency mains, and running at base speed. When such a motor is operated at a low frequency (e.g. 10 Hz), the speedismuchlowerthanbasespeedandtheeYciencyofthecoolingfan isgreatlyreduced.Atthelowerspeed,themotorwillbeabletoproduce as much torque as at base speed (see Figure 8.4) but in doing so the losses in both stator and rotor will also be more or less the same as at base speed. Since the fan was only just adequate to prevent overheating at base speed, it is inevitable that the motor will overheat if operated at full torque and low speed for any length of time. Some suppliers of inverter drives do not emphasise this limitation, so users need to raise the question of whether a non-standard motor will be needed. When through-ventilated motors with integral blowers become the accepted standard, the inverter-fed system will be freed of its low-speed limitations.Meanwhileusersshouldnotethatoneapproachdesignedto combatthedangerofmotoroverheatingatlowspeedsisforthecontrol circuits to be deliberately designed so that theXux and current limit are reduced at low speeds. The constant-torque facility is thus sacriWced in order to reduce copper and iron losses, but as a result the drive is only suitable for fan- or pump-type loads, which do not require high torque at low speed. These systems inevitably compare badly with d.c. drives, but manage to save face by being promoted as ‘energy-saving’ drives. CONTROL ARRANGEMENTS FOR INVERTER-FED DRIVES ForspeedcontrolmanufacturersoVeroptionsranginginsophistication from a basic open-loop scheme which is adequate when precise speed holding is not essential, through closed-loop schemes with tacho or encoder feedback, up to vector control schemes which are necessary when optimum dynamic performance is called for. The variety of schemes is much greater than for the fully matured d.c. drive, so we will look brieXy at some examples in the remainder of this section. Themajorityofdrivesnowprovideadigitalinterfacesothattheuser can input data such as maximum and minimum speeds, acceleration rates,maximumtorque,etc.Generalpurposeinvertersthatarenotsold with a speciWc motor may have provision for motor parameters such as base frequency, full-load slip and current, leakage reactance and rotor resistance to be entered so that the drive can self-optimise its controlInverter-Fed Induction Motor Drives 291 routines. Perhaps the ultimate are the self-commissioning drives that apply test signals to the motor when it is Wrst connected in order to determine the motor parameters, and then set themselves to deliver optimum performance: their detailed workings are well beyond our scope Open-loop speed control Inthesmallersizesthesimple‘constantV/f’controlisthemostpopular, andisshowninFigure8.6.Theoutputfrequency,andhencetheno-load speed of the motor, is set by the speed reference signal, which in an analogue scheme is either an analogue voltage (0–10 V) or current (4– 20 mA).Thisset-speedsignalmaybeobtainedfromapotentiometeron thefrontpanel,orremotelyfromelsewhere.Intheincreasinglycommon digital version the speed reference will be set on the keypad. Some adjustmentoftheV/fratioandlow-speedvoltageboostwillbeprovided. Typical steady-state operating torque–speed curves are shown in Figure 8.7. For each set speed (i.e. each frequency) the speed remains reasonablyconstant because of the stiV torque–slip characteristic of the cage motor. If the load is increased beyond rated torque, the internal current limit (not shown in Figure 8.6) comes into play to prevent the motor from reaching the unstable region beyond pull out. Instead, the frequencyandspeedarereduced,sothatthesystembehavesinthesame way as a d.c. drive. SuddenchangesinthespeedreferencearebuVeredbytheactionofan internal frequency ramp signal, which causes the frequency to be grad- ually increased or decreased. If the load inertia is low, the acceleration will be accomplished without the motor entering the current-limit re- gime. On the other hand if the inertia is large, the acceleration will take place along the torque–speed trajectory shown in Figure 8.7. 50/60 Hz supply Variable frequency and voltage f Speed Speed−frequency reference Inverter Volts/Hz power I.M. V circuits Voltage boost Figure 8.6 Schematic diagram of open-loop inverter-fed induction motor speed controlled drive292 Electric Motors and Drives Torque b c g a d Speed f e Figure 8.7 Acceleration and deceleration trajectories in the torque–speed plane Suppose the motor is operating in the steady state with a constant load torque at point (a), when a new higher speed (corresponding to point (d)) is demanded. The frequency is increased, causing the motor torque to rise to point (b), where the current has reached the allowable limit.Therateofincreaseoffrequencyisthenautomaticallyreducedso that the motor accelerates under constant current conditions to point (c), where the current falls below the limit: the frequency then remains constant and the trajectory follows the curve from (c) to settleWnally at point(d). A typical deceleration trajectory is shown by the path aefg in Figure 8.7.Thetorqueisnegativeformuchofthetime,themotoroperatingin quadrant 2 and regenerating kinetic energy to the inverter. Most small inverters do not have the capability to return power to the a.c. supply, and the excess energy therefore has to be dissipated in a resistor inside the converter. The resistor is usually connected across the d.c. link, and controlledbyachopper.Whenthelinkvoltagetendstorise,becauseof the regenerated energy, the chopper switches the resistor on to absorb the energy. High inertia loads, which are subjected to frequent deceler- ation can therefore pose problems of excessive power dissipation in this ‘dump’ resistor. Speed reversal poses no problem, the inverter Wring sequence being reversed automatically at zero speed, thereby allowing the motor to proceed smoothly into quadrants 3 and 4.Inverter-Fed Induction Motor Drives 293 Someschemesincludeslipcompensation,wherebythedrivesensesthe activecomponent of the load current, which is a measure of the torque; deduces the slip (which at full Xux is proportional to the torque); and then increases the motor frequency to compensate for the slip speed of the rotor and thereby maintain the same speed as at no load. This is similar to the ‘IR’ compensation used in open-loop d.c. drives and discussed in Section 4.3.5. Closed-loop speed control Whereprecisionspeedholdingisrequiredaclosed-loopschememustbe used,withspeedfeedbackfromeitherad.c.ora.c.tachogenerator,ora digitalshaftencoder.ManydiVerentcontrolstrategiesareemployed,so we will consider the typical arrangement shown in Figure 8.8. This inverter has separate control of the a.c. output voltage (via phase- angle control in the input rectiWer) and frequency (via the switching in the inverter), and this makes understanding how the control system operateseasierthanwhenvoltageandfrequencyarecontrolledtogether, as in a PWM inverter. Figure8.8hasbeendrawntoemphasisethesimilaritywiththeclosed- loop d.c. drive that was discussed at length in Section 4.3. Experience suggests that an understanding of how the d.c. drive operates is very Slip speed, Inverter voltage ω slip Speed ω synch 50/60 Hz supply Rectifier Speed reference Voltage Variable frequency and voltage Speed error Inverter _ ω synch ω slip TG Frequency I.M. _ _ Speed controller actual speed, ω Speed feedback, ω Figure 8.8 Schematic diagram of closed-loop inverter-fed induction motor speed- controlled drive with tacho feedback _ _294 Electric Motors and Drives helpfulinthestudyoftheinductionmotordrive,soreadersmaywishto refresh their ideas about the 2-loop d.c. drive by revisiting Section 4.3 before coming to grips with this section. As in the previous discussion, we will assume that the control variables are continuous analogue signals, though of course the majority of implementations will involve digital hardware. The arrangement of the outer speed-control loop (see Figure 8.8) is identical with that of the d.c. drive (see Figure 4.11): the actual speed (represented by the voltage generated by the tachogenerator) is com- pared with the target or reference speed and the resulting speed error forms the input to the speed controller. The output of the speed con- troller provides the input or reference to the inner part of the control system, shown shaded in Figure 8.8. In both the d.c. drive and the induction motor drive, the output of the speed controller serves as a torque reference signal, and acts as the input to the inner (shaded) part ofthesystem.Wewillnowseethat,,theinnersystem of the inverter-fed drive is eVectively a torque-control loop that ensures that the motor torque is directly proportional to the torque reference signal under all conditions. We have seen that if the magnitude of the Xux wave in an induction motor is kept constant, the torque in the normal operating region is directly proportional to the slip speed. (We should recall that ‘normal operating region’ means low values of slip, typically a few per cent of synchronous speed.) So the parameter that must be controlled in order to control torque is the slip speed. But the only variable that we can directly vary is thestator frequency (and hencethe synchronousspeed); and the only variable we can measure externally is the actual rotor speed. These three quantities (see Figure 8.8) are represented by the following analogue voltages: Slip speed¼v slip Synchronous speed¼v synch Rotor speed¼v, where v ¼vþv (8:1) synch slip Equation(8.1) indicates how we must varythe statorfrequency(i.e. the synchronous speed) if we wish to obtain a given slip speed (and hence a given torque): we simply have to measure the rotor speed and add to it the appropriate slip speed to obtain the frequency to be supplied to the stator.Thisoperationisperformedatthesummingjunctionattheinput to the shaded inner section in Figure 8.8: the output from the summingInverter-Fed Induction Motor Drives 295 junction directly controls the inverter output frequency (i.e. the syn- chronous speed), and, via a shaping function, the amplitude of the inverter output voltage. The shaping function, shown in the call-out in Figure 8.8, provides a constant voltage–frequency ratio over the majority of the range up to basespeed,with‘voltage-boost’atlowfrequencies.Theseconditionsare necessary to guarantee the ‘constant Xux’ condition that is an essential requirementforustobeabletoclaimthattorqueisproportionaltoslip speed. (We must also accept that as soon as the speed rises above base speed, and the voltage–frequency ratio is no longer maintained, a given slipspeedreferencetotheinnersystemwill yieldless torquethanbelow base speed, because theXux will be lower.) Wehavenotedthesimilaritiesbetweenthestructuresoftheinduction motorandd.c.drives,butatthispointwemightwishtopauseandreXect onthediVerencesbetweentheinnerloops.Inthed.c.drivetheinnerloopis a conventional (negative feedback) current control where the output (motor current) is measured directly; the torque is directly proportional to current and is therefore directly controlled by the inner loop. In con- trast, the inner loop in the induction scheme provides torque control indirectly, via the regulation of slip speed, and it involves a positive feedbackloop.Itreliesforits successonthelinearrelationshipbetween torqueandslip,andthusisonlyvalidwhentheXuxismaintainedatfull valueandtheslipspeedislow;andbecauseitinvolvespositivefeedback there is the potential for instability if the loop gain is greater than one, whichmeansthatthetachogeneratorconstantmustbejudgedwithcare. Returningnowtotheouterspeedloopandassumingforthemoment that the speed controller is simply a high-gain ampliWer, understanding the operation of the speed-control loop is straightforward. When the speed error increases (because the load has increased a little and caused the speed to begin to fall, or the target speed has been raised modestly) the output of the speed controller increases in proportion, signalling to theinnerloopthatmoretorqueisrequiredtocombattheincreasedload, ortoacceleratetothenewspeed.Asthetargetspeedisapproached,the speederrorreduces,thetorquetapersoVandthetargetspeedisreached very smoothly. If thegain of the speederror ampliWer is high, the speed error under steady-state conditions will always be low, i.e. the actual speed will be very close to the reference speed. In the discussion above, it was assumed that the speed controller remained in its linear region, i.e. the speed error was always small. But we know that in practice there are many situations where there will be very large speed errors. For instance, when the motor is at rest and the speed reference is suddenly raised to 100%, the speed error will296 Electric Motors and Drives immediatelybecome100%.Suchalargeinputsignalwillcausethespeed error ampliWer output to saturate at maximum value, as shown by the sketch of the ampliWer characteristic in Figure 8.8. In this case the slip referencewillbeatmaximumvalueandthetorqueandaccelerationwill alsobeatmaximum,whichiswhatwewantinordertoreachthetarget speed in the minimum time. As the speed increases the motor terminal voltage and frequency will both rise in order to maintain maximum slip until the speed error falls to a low value and the speed error ampliWer comes out of saturation. Control then enters the linear regime in which the torque becomes proportional to the speed error, giving a smooth approach to theWnal steady-state speed. In relatively long-term transients of the type just discussed, where changes in motor frequency occur relatively slowly (e.g. the frequency increases at perhaps a few per cent per cycle) the behaviour of the standard inverter-fed drive is very similar to that of the two-loop d.c. drive, which as we have already seen has long been regarded as the yardstickbywhichothersarejudged.Analoguecontrolusingapropor- tionalandintegralspeederrorampliWer(seeAppendix)cangiveagood transientresponseandsteady-statespeedholdingofbetterthan1%fora speed range of 20:1 or more. For higher precision, a shaft encoder together with a phase-locked loop is used. The need to Wt a tacho or encodercanbeaproblemifastandardinductionmotorisused,because there isnormallynoshaft extensionatthenon-driveend.Theuserthen faces the prospect of paying a great deal more for what amounts to a relatively minor modiWcation, simply because the motor then ceases to be standard. VECTOR (FIELD-ORIENTED) CONTROL Whereveryrapidchangesinspeedarecalledfor,however,thestandard inverter-fed drive compares unfavourably with d.c. drive. The superior- ity of the d.c. drive stems Wrstly from the relatively good transient response of the d.c. motor, and secondly from the fact that the torque canbedirectlycontrolledevenundertransientconditionsbycontrolling the armature current. In contrast, the induction motor has inherently poor transient performance. For example, when we start an unloaded induction motor direct-on- line we know that it runs up to speed, but if we were to look in detail at what happens immediately after switching on we might be very surprised. We would see that the instantaneous torqueXuctuates wildly fortheWrstfewcyclesofthesupply,untiltheXuxwavehasbuiltupand allthreephaseshavesettledintoaquasi-steady-stateconditionwhiletheInverter-Fed Induction Motor Drives 297 motorcompletesitsrun-up.(Thetorque–speedcurvesfoundinthisand most other textbooks ignore this phenomenon, and present only the averagesteady-statecurve.)WemightalsoWndthatthespeedoscillated around synchronous before Wnally settling with a small slip. For the majority of applications the standard inverter-fed induction motorisperfectlyadequate,butforsomeverydemandingtasks,suchas high-speed machine tool spindle drives, the dynamic performance is extremelyimportantand‘vector’or‘Weld-oriented’controliswarranted. Understanding all the ins and outs of vector control is well beyond our scope,butitisworthwhileoutlininghowitworks,ifonlytodispelsome of the mystique surrounding the matter. Some recent textbooks on electrical machines now cover the theory of vector control (which is stillconsidereddiYculttounderstand,evenforexperts)butthemajority concentrate on the control theory and very few explain what actually happens inside a motor when operated under vector control. Transient torque control We have seen previously that in both the induction motor and the d.c. motor, torque is produced by the interaction of currents on the rotor with the radial Xux density produced by the stator. Thus to change the torque, we must either change the magnitude of the Xux, or the rotor current, or both; and if we want a sudden (step) increase in torque, we must make the change (or changes) instantaneously. Since every magnetic Weld has stored energy associated with it, it shouldbeclearthatitisnotpossibletochangeamagneticWeld instant- aneously,asthiswouldrequiretheenergytochangeinzerotime,which calls for a pulse of inWnite power. In the case of the main Weld of a motor,wecouldnothopetomakechangesfastenougheventoapproxi- mate thestep change in torque we are seeking, so theonly alternative is to make the rotor current change as quickly as possible. In the d.c. motor it is relatively easy to make very rapid changes in the armature (rotor) current because we have direct access to the armature current via the brushes. The armature circuit inductance is relatively low, so as long as we have plenty of voltage available, we can apply a large voltage (for a very short time) whenever we want to make a sudden change in the armature current and torque. This is done automatically by the inner (current-control) loop in the d.c. drive (see Chapter 4). In the induction motor, matters are less straightforward because we havenodirectaccesstotherotorcurrents,whichhavetobeinducedfrom the stator side. Nevertheless, because the stator and rotor windings are298 Electric Motors and Drives tightlycoupledviatheair-gapWeld(seeChapter5),itispossibletomake moreorlessinstantaneouschangestotheinducedcurrentsintherotor,by makinginstantaneouschangestothestatorcurrents.Anysuddenchange inthestatorMMFpattern(resultingfromachangeinthestatorcurrents) is immediately countered by an opposing rotor MMF set up by the additional rotor currents which suddenly spring up. All tightly coupled circuitsbehaveinthisway,theclassicexamplebeingthetransformer,in which any sudden change in say the secondary current is immediately accompaniedbyacorrespondingchangeintheprimarycurrent.Organ- isingthesesuddenstepchangesintherotorcurrentsrepresentsboththe essenceandthechallengeofthevector-controlmethod. Wehavealreadysaidthatwehavetomakesuddenstepchangesinthe statorcurrents,andthisisachievedbyprovidingeachphasewithafast- actingclosed-loopcurrentcontroller.Fortunately,undertransientcondi- tions the eVective inductance looking in at the stator is quite small (it is equal to the leakage inductance), so it is possible to obtain very rapid changesinthestatorcurrentsbyapplyinghigh,short-durationimpulsive voltagestothestatorwindings.Inthisrespecteachstatorcurrentcontrol- When a step change in torque is required, the magnitude, frequency and phase of the three stator currents are changed (almost) instantan- eously in such a way that the frequency, magnitude and phase of the rotorcurrentwave(seeChapter5)jumpsuddenlyfromonesteadystate to another. This change is done without altering the amplitude or position of the resultant rotor Xux linkage relative to the rotor, i.e. without altering the stored energy signiWcantly. The Xux density term (B)inequation(5.8)thereforeremainsthesamewhilethetermsI andw r r change instantaneously to their new steady-state values, corresponding to the new steady-state slip and torque. We can picture what happens by asking what we would see if we were able to observe the stator MMF wave at the instant that a step increase in torque was demanded. For the sake of simplicity, we will assume that the rotor speed remains constant, in which case we would Wnd that: (a) the stator MMF wave suddenly increases its amplitude; (b) it suddenly accelerates to a new synchronous speed; (c) it jumps forward to retain its correct relative phase with respect to the rotor Xux and current waves. Thereafter the stator MMF retains its new amplitude, and rotates at its new speed. The rotor experiences a sudden increase in its current and

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