Slip Recovery

8/8/2019 Slip Recovery

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CHAPTER 7

Induction MotorSlip-PowerRecovery Drives

7.1 INTRODUCTIONInduction m otor drives w ith full-pow er control on the stator side, as discussed in Chapters 4. 5and 6, are w idely used in industrial applications. A lthough either a cage-type or wound-rotorm achine can be used in the drive, the form er is alw ays preferred because a w ound-rotor m achineis heavier, m ore expensive, has higher rotor inertia, a higher speed lim itation, and m aintenanceand reliability problems due to brushes and slip rings. However, it is interesting to note that aw ound-rotor m achine w ith a m echanically varying rotor circuit rheostat is possibly the sim plestand oldest method of ac motor speed control. One feature of this machine is that the slip powerbecom es easily available from the slip rings, w hich can be electronically controlled to controlspeed of the motor. For lim ited-range speed control applications, where the slip power is only afraction of the total pow er rating of the m achine, the converter cost reduction can be substantial.This advantage offsets the demerits of the wound-rotor machine to some extent. S lip-powerrecovery drives have been used in the follow ing applications:

L arge-capacity pum ps and fan drives V ariab le-sp eed w in d en erg y system s S hip bo ard VSCF (v aria ble -sp ee d/c on sta nt-fre qu en cy ) sy stems Va ria ble -s pe ed hyd ro pumps/g en era to rs U tility system flyw heel energy storage system sIn this chapter, w e w ill study the principles of slip-pow er control, particularly the popular

static K ram er and static Scherbius drives. It should be noted that the nomenclature in theseclasses o f d riv es is n ot co nsisten t.

307


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308 Chapter 7 Induction Motor Slip-Power Recovery Drives

7.2 DOUBLY-FED MACHINE SPEED CONTROL BY ROTOR RHEOSTATA simple and prim itive method of speed control of a wound-ro tor induction motor is by

m echanical variation of the rotor circuit resistance, as show n in Figure 7.1.The torque-slip curves of the motor for varying rotor resistance Rr, as calculated by

E quation (2.32), are show n in Figure 7 .2 . W ith external resistance R [ = 0, that is, w ith the sliprings shorted , the inherent torque-slip curve of the m achine gives a speed corresponding to poin tA at the rated load torque. A s the resistance is increased , the curve becom es flatter, giv ing lessspeed until the speed becomes zero at h igh resistance (> R4)' The maximum or breakdowntorque (see E quation (2.35)) rem ains constant, but the starting torque, given by Equation (2.33),increases w ith higher resistance. The m echanical variation of resistance has the inherent dis-advantage. In addition, this m ethod of speed contro l is very inefficien t because the slip energy isw asted in the ro tor circuit resistance. H ow ever, several advantages of this m ethod are: absence ofin-rush starting current, availability of full-rated torque at starting, high line power factor,absence of line current harmonics, and smooth and w ide range of speed contro l. The scheme ish ard ly u se d n ow -a-d ay s.

In stead of m echanically varying the resistan ce, the equiv alent resistance in th e roto r cir-cuit can be varied statically by using a diode bridge rectifier and chopper as show n in Figure 7.3.A s usual, the stator of the m achine is connected directly to the line pow er supply , but in the rotorcircuit, the slip voltage is rectified to de by the diode rectifier. The dc voltage is converted to cur-re nt s ou rc e I d by connecting a large series inductor L d . It is then fed to an IGBT shunt chopperw i th r es is ta nce R as shown. The chopper is pulse w idth modulated w ith duty cycle 8 = tOl/T,where lou = on -tim e an d T = tim e period . W hen the IGBT is off, the resistance is connected inthe circuit and the de link current I d flow s through it. On the other hand, if the device is on, theresistance is sh ort-circuited and th e current I d is bypassed through it. It can be shown that the

3~, 60 Hz supply

StatorRotor

R

Figure 7.1 Doubly-fed induction motor speed control by rotor rheostat


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Static Kramer Drive 309

Q)r-R 1=()Rated torque-~A .

Starting torque

0.75 0.5 0.25 oSlip S

Figure 7.2 Torque-slip curves of motor with variable rotor resistance3 < 1 > ,6 0H z su p p ly

mach ine

L .,=A

J RR_ _ ; j , . B

B ridge C hopperrectifier

Figure 7.3 Motor speed control with rotor circuit chopperduty cycle control of the chopper offers an equivalen t resistance Ro = (I - 5)R betw een points Aand B . Therefore, the developed torque and speed of the m achine can be controlled by the varia-tion of the duty cycle of the chopper. This electronic control of rotor resistance is definitelyadvantageous com pared to rheostatic control, but the problem of poor drive efficiency rem ainsthe same. This scheme has been used in interm ittent speed control applications in a lim itedspeed range, w here the efficiency penalty is not or great concern.7.3 STATIC KRAMER DRIVE

Instead of wasting the slip power in the rotor circuit resistance, it can be converted to60 Hz ac and pumped back to the line. The slip power-controlled drive that perm its only a sub-synchronous range of speed control through a converter cascade is known as a static Kramer


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3~, 60 Hz supply

Powerinput Power ifeedback

Shaftpower

motor

+

, .Slip power

Dioderectifier

Inverter

Figure 7.4 Static Kramer drive systemdrive, and the scheme is shown in Figure 7.4. It is different from the original K ramer drive,where rotating m achines were used for slip energy recovery. The static K ram er drive has beenvery popular in large power pum p and fan-type drives, where the range of speed control is lim -ited near, but below the synchronous speed. The drive system is very efficient and the converterpower rating is low , as mentioned before, because it has to handle only the slip power. In fact,the power rating becom es low er w ith a m ore restricted range of speed control. The additionaladvantages, w hich w ill be explained later, are that the drive system has de m achine-like charac-teristics and the control is very sim ple. These advantages largely offset the disadvantages of thew ou nd -ro to r in du ctio n m ac hin e.

The m achine air gap flux is established by the stator supply, and it practically rem ainsconstant if stator drops and supply voltage fluctuation are neglected. Ideally, the m achine rotorcurrent is a six-stepped w ave in phase w ith the rotor phase voltage if the de link current (1 is c on -sidered harm onic-free, and the com mutation overlap angle of the diode rectifier is neglected.The machine fundamental frequency phasor diagram referred to the stator is shown in Figure7 .5 , w h ere V I = phase voltage, 1 ,/ = fundam ental frequency rotor current referred to the stator,I f IR = air gap flux, 1 m = magn etizin g cu rren t, an d < p = pow er factor angle. W ith constant air gapflux, m achine torque becom es directly proportional to current I , / - Since 1 1/ is d ire ctly p ro po r-tional to de link current I d ' the torque is also proportional to I d . Instead of static resistance con-trol as discussed in the previous section, the schem e here can be considered as CEM F control,w here a variable C EM F VI is being presented by a phase-controlled, line-commutated inverter tocontrol the de link current Id. In ste ady -state o peratio n, th e rectified slip v oltag e Vd a nd in ve rte r


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Figure 7.5 Machine phasor diagram referred to the stator

de voltage VI will balance, ignoring the resistive drop in the inductance Ld . The voltage Vd isproportional to slip S, whereas the current Id is proportional to developed torque. At a certainspeed, the inverter's firing angle can be decreased to decrease the voltage Vb which will increaseId to increase the corresponding developed torque. The simplified speed and torque expressionscan be derived as follows. Neglecting the stator and rotor drops, voltage Vd is given as Equation(3.21).

(7.1 )

where S = per-unit slip, VL = stator line voltage, and nI = stator-to-rotor turns ratio of themachine. Again, the inverter de voltage VI is given as Equation (3.57).

(7.2)

where n2 = transformer line side-to-inverter ac side turns ratio and a= inverter firing angle. Forinverter operation, the range of the firing angle is 1(/2 < a < 1(. Since in steady state Vd and VImust balance, Equations (7.1) - (7.2) give

S=~lcosaln2 (7.3)

Therefore, the speed expression (Dr can be given asto, = w e (1- S)

~ We { I - ~ ; I c o s a l }= We (I-Icosal) (7.4)


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where 1 1 I In 2 = 1 has been assum ed. E quation (7.4) indicates that ideally, speed can be controlledbetween zero and synchronous speed we by controlling inverter firing angle a. A t zero speed,voltage Vd is maxim um , which corresponds to angle a = I T ; at syn ch ro nou s sp eed, Vd = 0 whena = rr/2. In practice, the maxim um speed should be slightly less than synchronous speed so thatto rque (i.e ., Id) can be developed w ith a finite resistance drop (V d = Id Rd) of the de li nk inductorat VI = O.

A gain, neglecting losses, the follow ing pow er equations can be w ritten:(7.5)

Pm = (1- S)~f( = Tewm2= Tewe (1-S)-P

(7.6)

where P g = air gap pow er, Pill = m echanical output pow er, wm = m echanical speed, and P =num ber of poles. Substituting Equations (7.2), (7.3), and (7.5) in (2.23) givesP P "t,=(-)-~-2 we

= (p) Vlld2 SWe1.35 I I--VL cosa Id= (p ) _ 1 1 _ ; : 2 : . . . . _ _ _

2 ~Icosalwen2

= (p) 1.35VL ld2 wenl

(7.7)

This equation indicates that the torque is proportional to current ld. The drive system hasnearly the characteristics of a separately excited dc m otor, because the air gap flux is nearly con-stant and the torque is proportional to current Id . W ith higher load torque Tv the m achine tendsto slow down and current ld increases so that Te = TL. In other words, for a fixed firing angle ofth e in ve rter, th e v olta ge VI is fixed. Therefore, to balance the resistance drop of the de link induc-tor, V e l m ust slightly increase, giving speed drop characteristics like a de m achine. F igure 7.6g iv es to rq ue-sp eed cu rv es fo r d ifferen t firin g an gles a. More accu rate to rq ue-sp eed relatio ns w illb e d ev elo ped later.

The static K ram er drive has one-quadrant speed control characteristics. The drive cannothave regenerative braking capability, and speed reversal is not possible. R egenerative braking inthe subsynchronous speed range w ill be discussed later. For reversal of speed, a circuit breaker


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Speed( c o r ) (pu)

o 0.5Torque (Te) pu

1.0(pu)

Figure 7.6 Typical torque-speed curves at different inverter firing anglescan be installed on the stator side, w hich should reverse the phase sequence of the line voltages.F or m ost pum p and fan drive applications, sim ple one-quadrant speed control is acceptable.

7.3.1 Phasor DiagramA fundamental frequency phasor diagram can be drawn to explain the performance of the

drive system . In practice, the rotor current displacem ent factor w ill slightly deviate from unitybecause of the commutation overlap angle shown in Figure 7.7. In fact, the overlap angle f . 1in tro du ces a lag gin g an gle C P r to the fundam ental current, as indicated in the figure. T his currentin creases as ld increases w ith the increase of slip S. N ear zero slip, w hen the rotor voltage is verysm all, a larg e cu rren t ld m ay cause overlap angle u to exceed the 1[/3 angle, causing a short cir-cuit betw een the upper and low er diodes.

F igure 7.8 shows the approximate phasor diagram of the drive system at the ratedtorque condition, where all the phasors are referred to the line or stator side. The stator draws a

Fundamentalcomponent

Irf

(0 t

Figure 7.7 Rotor phase voltage and current waves


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; 'u. = 0S = 1.0

constantslip lineT 0.5 ~ tI. S = 0\n)n1 = 1 l.cos a

Figure 7.8 Phaser diagram of static Kramer drive system at rated voltagemagnetiz in g cu rre nt 1 11 1 , w hich lags 7 [ 1 2 angle w ith respect to the stator phase voltage VI ' Theto ta l s ta to r c urr en t 1 \ lags the stator voltage by angle q J s as show n. O n the inverter side, altho ughthe active power is fed back to the line, it also demands lagging reactive current from the linebecause of p hase control. T his additional reactive current d raw n by the inverter reduces the over-all pow er factor of the system . A ssum ing continuous conduction of the inverter and ripple-freecurrent (" the inverter output power factor is [cos q J l =Icos a i , that is, its pow er factor varies lin-early w ith de voltag e VI' T his, of cou rse, neglects the inverter commutatio n overlap effect. C on-sider no transformer connection for the present and n I = I. The phasor diagram shows theinv er te r lin e c urr en t ha t slip S = 0.5. P hasors I T and 1 , / are nearly equal in m agnitude becauseof the nearly identical w aves of these currents. T he active com ponent hco s q J o pp oses th e stato ractive curren t, w hereas the reactiv e component I T si n q J adds to the stator m agnetizing current1/11' T he to tal lin e cu rren t I L is the phasor sum of IIan d I T and it lags at angle qJL ' w hich is largerthan the stator pow er factor angle q J . \ . W ith constant torque, the m agnitude of I r rem ains con-stan t, but as the slip varies between 0 and I, the phasor I T r ota te s fr om a = 90 to 160, as shownin the figure. A t zero speed (S = I), the m achine acts as a transform er, and ignoring losses, all theactive power is transferred back to the line through the inverter. The result is that both them achine and inverter consum e only reactive pow er. The inverter m argin angle ( f 3 ) of 20 for thein verter c ov ers b oth commutatio n u n a nd tu rn -o ff (y ) angles. From the phasor diagram , it is evi-dent that at S = 0, the system power factor is lagging at low value, w hich deteriorates as the slipincreases. T herefore, w ith restricted speed range close to synchronous speed, the pow er factor iscomp arativ ely b etter. F or red uced to rq ue co nd itio n, th e cu rren t I T is p ro po rtio nally less. T he co r-responding phasor diagram m odification is left as an exercise to the reader. If, for exam ple, the


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torque is reduced to 50 percent at S = 0 .5 , a ng le c p rem ains the sam e as shown and current I T isreduced to 50 percent, that is, both I T cos c p and I T si n c p a re a ls o p ro po rtio na te ly re du ce d.

For a restric ted speed range closer to synchronous speed, the system pow er factor canbe further im proved by using a step-dow n transform er. T he transform er prim ary-to-secondarytu rn s ra tio n2 can be adjusted so that at the desired maximum slip , angle c p = n. O f course. theinverter m argin angle should alw ays be m aintained. Substituting this condition in E quation (7.3)gives

(7.8)For exam ple, if Smax = 0.5 and n I = I, th en 1 1 2 should ideally be 2. In the phasor diagram of

Figure 7.8, th is condition corresponds to the transform er line current I; = 0.5IT, whic h c le arlyindicates the pow er factor im provem ent of line current h. As the speed is increased to changethe slip from 0.5 to 0, the phasor I; rotates anti-clockw ise, as show n, until c p = n12 . Equation(7.3) indicates that for constant slip , the variation of 1 1 2 1 1 1 1 lin early v aries co s a magn itu de. T heconstant slip line at S = 0.5 is indicated in F igure 7.8.

The step-dow n transform er has essentially tw o functions: besides im proving the linepow er factor, it a lso helps to reduce the converter pow er ratings. B oth the rectifier and invertershould be designed to handle the same current I d as dictated by the torque requirement. Therectifier should be designed for the slip voltage given by SV Lin l > w hereas the inverter should bedesigned for the line voltage VL in the absence of the transformer. The rectifier voltage andcorresponding power rating decrease w ith a smaller speed range, but the inverter must bedesigned for full pow er. Installation of the transform er reduces the voltage and correspondingpower rating of the inverter, and the criteria for the turns ratio 1 1 2 design is the same as that ofEquation (7.8). For the sam e exam ple (i.e ., Smux = 0.5, 1 1 I = I, and 1 1 2 = 2), both the rectifier andinverter have an equal pow er rating, w hich is 50 percent of the full pow er. It can be show n easilythat the converter power rating can be reduced proportionately as Sma.\" is reduced. This is anim portant advantage of the slip-pow er recovery drive. The discussion above assum es that them achine is not started w ith the converters in the circuit. O therw ise, the advantage of a reducedco nv erter ratin g is lo st.

A typical starting method of a Kramer drive w ith resistance sw itching is shown inFigure 7.9. The motor is started w ith sw itch I on and sw itches 2 and 3 off. As the speed buildsup , r es is tance s RI and R2 are shorted sequentially until at the desired Smar value, sw itch I isopened and the drive controller is brought into action.


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3~ ac supp IJ l---1- ....,

2 3Figure 7.9 Motor starting method

7.3.2 AC Equivalent CircuitThe drive system performance can be analyzed with the help of a de or ac equivalent cir-

cuit of the machine. We will attempt here an approximate ac equivalent circuit with respect tothe rotor. Neglecting drops in the semiconductor devices, the slip-power output is partly dissi-pated in the de link resistance Rd of the inductor and is partly fed back to the ac line through thetransformer.

The respective power components can be given as( 7 . 9 )

(7.10)

The equivalent rotor circuit power per phase is given as

(7.11 )

Therefore, the machine air gap power per phase, which includes the rotor copper loss, isgiven as

(7.12)

where I, . = rotor rms current per phase, R, . = rotor resistance, and Pn / = mechanical output powerper phase. The torque and corresponding mechanical power Pm ' are essentially contributed by


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the fundamental component of rotor current Irjonly. The expression for rotor circuit copper lossper phase is

, 2 1 2~'I = t, R; + -Id Rd3= 1/ (Rr +O .SRd )

where Ir t = J 6 Id has been substituted for a six-step wave. Therefore, the expression for P II/ is . T r

(7.13)

grven as, l-S

~II = (Fund.freq.slip power)--S

+ / ( R r+ O . 5 R d ) + 3~. L ~ V L l i f l c o s a l J C ~ S Jwhere the 11 = ~ Id relation has been used to replace Id in Equation (7.10). The air gap powerP g ' in Equation (7.12) can be written by substituting Equation (7.14) as follows:

(7.14)

(7.IS)

where

(7.16)

1 C 1.3SV L I IRA = tR , +O.SRd ) + r; . cosrz3 . . . ; 6 1 7 2 I d= (R ; +O .S Rd ) +~ Icosal17211

where the I,= ~ 11 relation has been used in Equation (7.16) to eliminate II " Note that the airgap power P g' consists of two components: one is the fundamental frequency slip power and theother is the ripple power loss. Equation (7.1S) indicates that the rotor circuit, which absorbs theactive power, can be represented by a per-phase passive ac equivalent circuit where RA is theequivalent resistance given by Equation (7.17). The resistance Rx represents an additional resis-

(7.17)


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Stator side .----+ ....-- :--+ Pg 'Rotor side --+>Figure 7.10 Per-phase passive equivalent circuit of the machine (with respect to rotor

tance that consumes harmonic power. The equivalent circuit is shown in Figure 7.10, where RAis a function of V s' Ir!' and cos a.

Note that all the stator circuit parameters and the supply voltage are multiplied by S torefer to the rotor circuit. The symbol'(prime) indicates rotor-referred parameters with turns ration I; in other words,

(7.18)

(7.19)

(7.20)

(7.21 )

(7.22)

It is more convenient to represent the equivalent circuit in terms of the CEMF presented bythe inverter. Equation (7.15) can also be written in the form

(7.23)


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where

(7.24 )

(7.25)

Figure 7.11 shows part of the rotor referred equivalent circuit with the CEMF Vc' wheretorque can be increased by increasing Iif, that is, by decreasing Vc (with the help of S and cos aparameters).

7.3.3 Torque ExpressionThe average torque developed by the machine is given by the total fundamental air gap

power divided by the synchronous speed w e - The expression in terms of a passive ac equivalentcircuit is

(7.26)

where Pd = fundamental frequency per-phase air gap power, and the expression of RA is givenin Equation (7.17). The equation can be solved in terms of circuit parameters as

(7.27)

1 VV c = S n ; I cosc I

"_____'p: 9."Figure 7.11 Part of rotor referred per-phase equivalent circuit with CEMF V c


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where

(7.28)

has been substituted. Equation (7.27) relates torque as a function of slip S, rotor current I r f " andin ve rte r firin g a ng le a. A n approxim ate torque expression relating slip and the a angle can bederived m ore conveniently from the equivalent circuit of F igure 7.11. T he torque in term s of fun-dam ental air gap pow er PJ is given from Equation (7.23) as

(7.29)

A n approxim ate expression of Ir l can be w ritten from the equivalent circuit by neglectingthe reactances and stator resistance, w hich are sm all at sm all values of slip . T herefore,

(7.30)

S ub stituting E quatio ns (7 .30 ) and (7.2 5) in (7 .2 9) yield s

( 7.3 1 )

where RB = RrlS has been substituted, neglecting the resistance Rd' E qu atio n (7 .31 ) relatestorque as a function of both the slip S and a angle approxim ately. A more accurate torqueexpression can be derived by a com puter program using the equivalent circuit. The results areplotted in Figure 7.12. The shaded area in the figure indicates the normal zone of operation,which can be com pared w ith the approxim ate curves show n in Figure 7.6.


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S'-9;(J):::J~or - = - 1.0 t--~:---......lI~";T.~ob77.:i"*---t~----

Normal operation zone

Load torque

rr/2 < o. < r r

o0 .5 1.0

Speed (pu)Figure 7.12 Torque-speed curves at different firing angles of inverter

7.3.4 HarmonicsT he rectification of slip pow er causes harm onic currents in the rotor, and these harm onicsare reflected to the stator by the transformer action of the machine. The harmonic currents are

also injected to the ac line by the inverter. As a result, the m achine losses are increased and som eam ount of harm onic torque is produced. The rotor current wave is ideally six-stepped, which isg iven b y th e F ourier series

(7.. 3 2 )

w here the fundam ental com ponent contributes the useful torque, but the low er order harm onics,(such as 5 th an d 7th) have dom inating harm ful effects. Each harm onic current in the rotor w illcreate a ro tating m agnetic field and its direction of rotation w ill depend on the order of the har-monic. The 5 th h arm on ic, fo r ex am ple, at freq uen cy Sw s/' rotates opposite to the direction of thero to r, w hereas th e 7th h armonic, at fre qu en cy 7 ws/' rotates in the sam e direction. T he interactionof different harm onics w ith the air gap flux creates pulsating torque. For exam ple, the 5 th an d 7thh arm on ics, in teractin g w ith th e fu nd am en tal lJ Ig wave, contribute to the 6 th harmon ic puls atin gtorque, which is d iscussed in Chapter 2 . However, it can be shown that the harmonic torque issm all com pared to the average torque and can be neglected in a practical drive.


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+(Or-+

Figure 7.13 Speed control of static Kramer drive

7.3.5 Speed Control of a Kramer DriveA speed control system of a Kramer drive is shown in Figure 7.13, and Figure 7.14 shows

its typical perform ance. As explained before, the drive has the characteristics of a separatelyexcited de m otor, and therefore, the control strategy is sim ilar to a phase-controlled rectifier dedrive. W ith essentially constant air gap flux, the torque is proportional to de link current Id .which is controlled by an inner feedback loop. If the com mand speed O J , . " is increased by a step.as shown in Figure 7.14, the motor accelerates at a constant developed torque corresponding toth e Idt lim it set by the speed control loop. The inverter firing angle (X in itially d ecreases w ithh igh slo pe to estab lish Id and then gradually decreases as speed increases. As the actual speedapproaches the command speed, the de link current is reduced to balance the load torque at acertain (X angle in steady state. As the speed comm and is decreased by a step, Id ap pro ac he s z eroand the m achine slow s dow n by the inherent load torque braking effect. D uring deceleration. the(X angle increases continuously so that the inverter voltage VI balan ces th e rectifier v oltage Vd .Then, as the speed error tends to be zero in the steady state, I i i is restored so that the developedtorque balances w ith the load torque. The air gap flux during the whole operation remainsapproxim ately constant, as dictated by the stator voltage and frequency. As m entioned before.the maxim um speed should be slightly less than the synchronous speed so that the current It ! ca nb e estab lished w ith fin ite Yd'

7.3.6 Power Factor ImprovementAs discussed above, the static Kramer drive is characterized by poor line power factorbecause of a phase-controlled inverter. The power factor can be improved by a scheme called


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SUpply_ ......power Air gappower S h a ft in p u t

S h aft o ut pu t

In du ctio n m o to rs ta to r In pu t

S l/n e m o to rs ta to r In pu tSta torco p p e r

lossRotor COIT'ielterco p p e r IIJSS

I O~3SFigure 7.16 Power flow diagram in commutatorless Kramer drive system

input power to constitute the total m echanical pow er. The synchronous m otor field is suppliedfrom the line through a contro lled rectifier. The speed and torque of the drive system are con-tro lled b y th e field cu rren t Ifwith the inverter tiring angle ex set to an optim um value for load com -m utation of the inverter. A t any speed, a higher value of If w ill increase the m achine C EM F, thatis. the inv erter de v oltage VI, which w ill decrease the developed torque. A s the m achine speeddecreases from syn ch ron ous speed, Vd in cr ea se s lin ea rly . b u t I rin cr ea se s vr: K(Vj/w r , reach-ing saturation soon at a low er speed. A gain , as is characteristic to the load-com m utated inverterdrive, speed co ntrol is not po ssible at lo w v alu es because of insufficien t C EMF. B esides havin g anim proved pow er factor, the system w ill operate reliably w ith short-tim e pow er failure. w hich isno t po ssible in a static K ram er d rive. T he d rive, as usu al, h as one-quadran t characteristics.

7.4 STATIC SCHERIUS DRIVEAs explained above and indicated by the phasor diagram of Figure 7.5, the K ram er drive

has only a forward motoring mode (one quadrant) of operation. For regenerative mode opera-tion, rotor current w ave should be reversed and the corresponding phasor I r F sh ou ld b e n eg ativ e.as in dicated in F igu re 7 .1 7.

This feature requires that the slip power in the rotor flow in the reverse direction. If thediode rectifier on the m achine side is replaced by a thyristor bridge. as show n in Figure 7.18 , theslip pow er can be controlled to flow in either direction . W ith reverse slip-pow er flow at subsyn-chronous speed . the power corresponding to shaft input m echanical pow er can be pum ped out ofthe stator. It can be shown that such a drive system , w ith bidirectional slip-power flow . can becontro lled for m otoring and regenerating in both the subsynchronous and supersynchronousranges of speed. This schem e is often defined as a static Scherbius drive system . The line com -m utation of the m achine-side converter becom es difficult near synchronous speed (excessivecommutation overlap tim e), w hen the ac voltage is very sm all.


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Static Scherius Drive 32 5

(a )

t V g(b )Figure 7.17 (a) Waveforms for regenerative operation of Kramer drive, (b) Phasor diagram

3~, 60 Hz supply

(1-S)Pg

Figure 7.18 Static Scherbius drive system using de-link thyristor convertersThe dual-bridge converter system in Figure 7.18 can be replaced by a single phase-

controlled line-commutated cycloconverter, as shown in Figure 7.19. The use of a cycloconvertermeans additional cost and complexity of control, but the resulting advantages are obvious. Theproblem of commutation near synchronous speed disappears, and the cycloconverter can easilyoperate as a phase-controlled rectifier, supplying de current in the rotor and permitting true syn-chronous machine operation. The additional advantages are near-sinusoidal current waves in therotor, which reduce harmonic loss, and a machine over-excitation capability that permits leadingpower factor operation on the stator side. In fact, the cycloconverter's input lagging power factorcan be cancelled by the leading machine's power factor so that the line's power factor is unity.The cycloconverter should be controlled so that its output frequency and phase track preciselywith those of the rotor slip frequency voltages. Like a Kramer drive, a Scherbius drive also


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32 6 Chapter 7 Induction Motor Slip-Power Recovery Drives

Transformer

Inductma

J1f'y ~ t J IW. t:~"t\t ~ ~ n ~ ; . .I

~' ,~, ~, ~ ,f, ~, , J ',f, ~,~.)r.) J " ' " ~)~,,') J ~) r. ~"~;-- + J - + - + -Cycloconverter

ABC

3


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Static Scherius Drive 327

1(1-S)Pg~ lI'

Figure 7.20 Modes of operation of static Scherbius drive(cycloconverter not shown):

(a) Mode 1: Subsynchronous motoring,(b) Mode 3: Subsynchronous regeneration,(c) Mode 2: Supersynchronous motoring,(d) Mode 4: Supersynchronous regeneration

range, the slip S is positive and the air gap power P g is negative; correspondingly, negative slippower SP g is fed to the rotor from the cycloconverter so that the total air gap power is constant.The rotor current has positive phase sequence as before. At synchronous speed, the cyclocon-


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verter supplies de excitation current to the rotor and the machine behaves as a synchronous gen-erator. The drive can have sustained operation in mode 3. The typical application in this is avariable-speed wind generation system.Mode 2: Supersynchronous Motoring

In this mode, as shown in Figure 7.20(c), the shaft speed increases beyond the synchro-nous speed, the slip becomes negative, and the slip power is absorbed by the rotor. The slippower supplements the air gap power for the total mechanical power output (l + S)p z : The linetherefore supplies slip power in addition to stator input power. At this condition, the phasesequence of slip frequency is reversed so that the slip current-induced rotating magnetic field isopposite to that of the stator.Mode 4: Supersynchronous Regeneration

In this mode, indicated in Figure 7.20(d), the stator output power P g remains constant, butthe additional mechanical power input is reflected as slip-power output. The cycloconverterphase sequence is now reversed so that the rotor field rotates in the opposite direction. Thevariable-speed wind generation mentioned for mode 3 can also be used in this mode.

Power distribution as a function of slip in subsynchronous and supersynchronous speedranges is summarized for all four modes in Figure 7.21, where the operating speed range of 50percent about the synchronous speed is indicated. The control of the Scherbius drive is some-what complex. It will be discussed in Chapter 8 with the help of vector or field-oriented control(see Figure 8.45).

Bidirectional slip-power flow with a cycloconverter, as discussed above, is also possible ifthe cycloconverter is replaced by a double-sided, PWM, voltage-fed converter system, as shownin Figure 7.22. For a high power rating, IGBTs can be replaced by GTOs. The dc link voltage Vdshould be sufficiently higher than the inverter line voltage to permit PWM operation in thelinear or undermodulation region. Both the rectifier and inverter can be operated at a program-mable input power factor so that the effective line power factor can be maintained at unity. Therectifier operates satisfactorily at variable voltage and variable slip frequency on the ac side,including the ideal de condition at synchronous speed.

7.4.2 Modified Scherbius Drive for VSCF Power GenerationA modified Scherbius drive, which has a somewhat similar topology to Figure 7.15, has

been used for stand-alone shipboard VSCF power generation. The scheme, shown in Figure7.23, has some interesting features. Induction generator output power is fed to a stand-alone, 60Hz, constant voltage bus, which supplies the active and reactive load power as shown. The distri-bution of active and reactive powers in the supersynchronous and subsynchronous ranges isshown in the figure. The stator active power output Pm of the generator is equal to the turbineshaft power and the slip power fed to the rotor by the cycloconverter. The stator reactive poweroutput QL is reflected to the rotor as SQL , which is added with the machine magnetizing power


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Static Scherius Drive 329

Mechanicaloutput power

o _SlipS=1 S=D

I Operating __jrspeed rangeI IS= -1

Speed (pu)-

S=1 S=DSpeed (pu) _

S= -1o _Slip

Slip-poweroutput SPg

Mechanicalinput power

Figure 7.21 Power distribution vs. slip power in sub/supersynchronousspeed ranges:

(a) Motoring at constant torque,(b) Generation at constant torque

Slip-powerinput, -SP~

req uirem ent to co nstitute th e total reactive po wer QL' of the cycloconverter. T he pow er QL' isfu rth er in creased to QL" at the cyclocon verter in pu t, w hich is su pp lied b y the sh aft-m ou nted syn-chronous exciter. T he slip frequency and its phase sequence are adjusted for varying shaft speedso that the resultant air gap flux rotates at synchronous speed, as explained before. I n subsyn-chronous speed range, the slip pow er SPm is supplied to the rotor by the exciter, and therefore,the rem aining output power (1 - S)Pm is su pplied b y the shaft. I n su persyn ch ro no us sp eed ran ge.the rotor output power tlow s in the opposite d irection and runs the excitor as a synchronousm oto r. T herefo re, th e to tal shaft p ow er in creases to (I + S)Pm. R otor voltage and frequency varylinearly w ith deviation from synchronous speed. For example, if the shaft speed varies in therange of 800 to 1600 rpm w ith 1200 rpm as the synchronous speed (S = 0.3 3). th e c orre sp on d-ing range of slip frequency is 0 to 20 Hz for 60 Hz supply frequency.


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3 < 1 > ,6 0 H z supply

PII\IMrectifier

PI/\/Minverter

Figure 7.22 Static Scherbius drive using double-sided PWM voltage-fed converter

ac exciter

(1S)Pm3 (1 1 ,6 0 H z busat constantvoltageTurbine shaft(variable-speed)

+SP~ SUB Rotor

L..-----....Cycloconverter ......-----'excitation

+-- SUPER-SPm

Figure 7.23 Variable-speed, constant frequency generation using modified Scherbius driveThe m odified Scherbius system as a VSCF generator has several advantages over the con-

ventional Scherbius system . O ne principal difference is that the w rap-around, or circulating,KVA dem anded by the rotor is supplied from a separate exciter instead of being supplied fromthe m achine's stator term inals. A s a result, the m ain m achine is m uch sm aller in size, although inthis case, the power is distributed between the two machines. The VSCF bus is much cleanerw ith regard to harmonics, because the cycloconverter input harmonics are reflected to theexciter. The rotor excitation circuit can be designed w ith a higher voltage, and the necessity of aninput transform er is elim inated. In the case of a supply brow n-out or tem porary short-circuitfault, the system has im proved controllability and reliability of pow er supply over the standardScherbius system . A gain, the cycloconverter can be replaced by a double-sided, PWM voltage-


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Summary 331

fed converter system , w hich w ill relieve the additional reactive and harm onic pow er loadings ofthe exci te r.

7.5 SUMMARYT his chap ter gives a broad review of different types of slip po wer-contro lled drives. U nlike

a standard cage-type induction m otor, these drives req uire a dou bly-fed w ound-rotor indu ctionmotor, which is more expensive and has the disadvantages of slip rings and brushes. In theb eginnin g, the prim itive rotor rheostat-type sp eed contro l w as discussed . T hen, the m ore im por-tant slip-pow er reco very-type drives, such as the static K ram er and static S cherbius drives. w erediscussed in detail for lim ited speed range applications. The important advantages of thesedrives are reduced power rating of the converter (at the expense of a 60 Hz transform er) and afast de m achine-like transient response. The additional disadvantages of these drives are theneed of a separate starting m ethod, low line pow er factor, and non-reversible speed control. ForS cherbius drives w ith cycloconv erters or dou ble-sid ed voltage-fed PWM converters. the pow erfactor problem does not arise. For large pow er pum p and com pressor-type applications w ithin alim ited speed range, these drives have been w idely used. Scherbius drives have also been usedIII variable-speed w ind generation, hydro/pum p storage and utility system s. and flyw heele nerg y sto ra ge sy stems.

REFERENCES1. A. Lavi and R . L. Polge, "Induction m otor speed control w ith static inverter in the rotor", IL 'EE Trans. Powc:

A ppar. S ys t .. vol. 85. pp . 76-84, Jan. 1966.2. T. Hori, H. Nagase, and M . Hornbu, "Induction M otor Control Systems", In dus tria l E lec tro n ic s Han dbook . J . D .

Irw in, pp. 310-315, CR C Press, 1997.3. T. Wakabayashi, T. Hori, K. Shimzu, an d T. Yoshioka , "Cornmutatorless K ram er control system for large capacity

induction m otors for driving w ater service pum ps", ILEE/IAS Annu. M eet. Con ]. Rec .. pp . 822-828. I1.J76.4. H. W. W eiss. "A djustable speed ac drive system s for pum p and com pressor applications", IL U:' T ra ns. Oil Ind.

A pp l .. vol. 10. pp . 162-157. Jan.lFeb. 1975.S. P . Z im merm ann. "Super synchronous static converter cascade". Co n / Rec. IFAC S\'IIII) Oil Control ill P(III'('/" l.lcc,

an d Electrical Drives , pp . SS9-S74, 1977 .6. G. A. Smith. "Static Scherbius system of induction m otor speed control", Proc . IEL , vol. 124. pp, SS7-S6S. I 1.J77 .7. S. Mori et al., "Com missioning of 400 MW adjustable speed pumped storage system for Ohkawachi h yd ro p ow er

plant", Pmc. Cigre Svntp., No. 520-04. 1995.8. T. Nohara, H. Scnaha, T. K ag cy arn a, and T. Tsukada. "Successful commercial o peratio n o f do ub ly-fed adju stab le-

sp eed fly wh eel gen eratin g statio n." Proc . ()j'c /C Rt/IEE Japan Colloquium 1 1 1 1 Rotating Elec tric M uchin crv L iicE xt n .. pp. 1-6, 19I.J7.

9. R . Pcana, J . C. Clare, and G. M . Asher. "Doubly fed induction generator using back-to-buck PW M converters andits application to varriablc speed w ind energy generation." I ! : 'E P ro t . Oil E le c . P ow er A pp .. \01. 14.1. pp . 231-2--1.May 1996.

10. R . Dalla and V . T. R angunathan, "D ecou pled control of active and reactive pow er for a grid-connected doubly-fedw ound rotor induction m achine w ithout position sensors:" II:'!:!: lAS AIIIIU. M eet. CO llI Rcc .. pp . 262.\-'::630. 19 l)l).


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Slip Recovery

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