I2E8 TRANSACTIONS ON INDUSTRIAL ELECTRONICS AND CONTROL INSTRUMENTATION, VOL. IECI-22" 1So 2, MAY 1975

[31 R. OldenbLirger and It. C. Boyer, Trans. ASME, J. Basic Eng.,84 559, 1962.

[4] A. G(elb and W. E. Vander Velde, IEEE Trans. on Automat.Contr., vol. 8, p. 142, 1963; Multiple-Input,Describing Functionsand Aonlinear System Desi ', New York: McGra*-Hill- 1968.

[51 J. E. Gibson and P. Sridhxar, IEEE Tr-ans. on Appl. and Ind.,667 65, 1963.

[6] D. P. Atherton and G. F. Turnbull, Proc. IEE, vol. 111, p. 157,

1964.[71 G. Jumarie, Annales des- Telecommunications, 24, 11, 1969;Int. J. Control, 11, 835, 1970.[81 C. A. Karybakas and E. C. Servetas, Int. J. Control, 15, 929,

1972.[9] E. C. Servetas and C. A. Karybakas, It. J. Control, 17, 635,

1973.[10] C. A. Karybakas Doctorate Thesis, Athens University, 1971.

ontrolied Braking of-Slip Energy Recovery Drive

tilizing Capacitor Excitation of Induction Motor

TONY C. BLAND AND WILLIAM SHEPHERD, SENIOR MEMBER, IEEE

Abstract-Capacitancre excitation of the induction motor resultsin considerable braking torque. With primary capacitance excitation;braking torque is controlled by using a rectifier-invertor combinationwhich acts as a variable secondary resistance. Braking torque isthen a linear function of dc link current.

f Braking torque is also produced by capacitance excitation due tosecondary side capacitors. Equal capacitance per phase can resultbalanced excitation and then high speed braking results. Also brakingis possible with unequal secondar side capacitors. All tIe circits

are suitable for incorporation in closed-loop systems as the torque atany Jspeed, provitde excitationl takes place, is a function of the firingangle of the thyristors in the:invertor bridge.

NOTVENCILATURECV Capacitor voltage, volts.f: Freqiuenrcy of excitation/frequency of supply.I Primary current, amps.

12 Secoindary current, amps.Im MV[agnetising current, amps.No0 Synchronous speed, radians/second.r, Per-phase resistance of primary winding, ohms.r2 Per-phase resistance of secondary winding, ohmns.S Slip

Sp Speed, radians/second.7T Torque, Newtonimetre.V Line volt-age, volts.xl Per-phase primary winding reactance, ohms.r2 Per-phase secondary winding reactance, ohms.xe Capacitive reactance, ohms.

Ingvertor firing angle, degrees.

Mlanuscript received November 8 1974.T. G. Bland is with the Irnperial Collee, London, England-.,W. Shepherd is with the Postgraduate School of Electrical and

Electronic Engirneering, University of Bradford, Bradford, England.

I. INTRODUCTIONT HE ACTION of capacitor-excitation of an induction

motor is analogous in its build-up to that of a dc,shungenerator [1]. The reactive current requirement of induc-tion generators has been supplied by terminal capacitors [2]and it has been found that the operation of such generatorsis similar to that of a dc generator in that as the load in-creases the voltage at the machine terminals -decreases.The use of, capacitors for power factor correction is

frequently applied:in practice. Usually it is very importantthat, self-excitation of the motor-capacitor combination isavoided. Investigations L3]-[6J, [15] have been made todetermine the maximnum value of capacitance that can beconnected at the motor terminals without risk of exclitat-'tion. In general the impedance of the relevant capacitor-bank must be greater than the gradient of the magnetiza-tion characteristic of the machine.

Series capacitance in the supply circuit to induction:motors has been used to compensate for line drop. Undercertain conditions the eapacitors' have- gven rise to in-stability [7], [8] by the action of excitation and henceeirculating lowu frequency currents in the supply.

Disconnection of induction motors from the supply cangive rise to high transient torque on reswitching, if thedisconniection period: is relatively short [6], [9]. If capac-itor-excitationooccurred during the period of disconnectionit has been found that the transient torque on reswitchingcaIn be relatively much larger compared to the case wereno excitation took place.The more popular, methods of braking an induction

motor, iamely plugging and dc dynamic braking, havebeen discussed in many papers; at length, Capacitor brak-ing has received rather less attention presumawably because

208

BL3LAND AND SHEPHERD . SLIP ENERGY RECOVERY DRIVE

.1Of tx o principal disadvantages. One is that capacitor-excitation falls off rapidly with decrease in speed al-though it should be remembered that' of the drivekinetic energy has been dissipated by the time that halfspeed has been acheived. Secondly no easy method ofcontrolling the torque produced has been available al-though the use of resistances has been suggested [10] withsquirrel cage induction motors.There are two major advantages associated with capac-

itorexcitation braking of an induction motor, one, that-itis independent of supply voltage failure in its most simpleform and second, that it gives a- power factor correction tothe motor -when in normal motoringb use.

II. BRAKING UTILIZING PRIMARYCAPACITANCE EXCITATION

A. Descriptio of the System.

It has been shown theoretically elsew'here that thebraking torqiie produced by an induction motor withbalanced primary capacitor excitation cani be controled bythe addition of external secondary resistance [1]. Con-sider a conventional slip-ring induction motor, discon-nected from the eledrical supply, with equal primary sideeapacitance per phase, oprating at some forward speed.

With zero additional secondary resistance there existsthe familiar circuit for capacitor excitation of the inductionMotor and, With sufficient capacitance, a braking torqueis produced. For the condition of infinite additionalsecondary resistance the secondary circuit is open-cir-X0cuit;ed, the mlachine fails to excite and no electrical brakingtorque is then produced Between these two extremesofadditional secondary resistance, control of the brakingtorque produced by an induction motor with balancedprimary capacitor-excitation, at a given speed, is possible.Computed Ireults showed that an induction motor run-

ning at constant speed, with balanced primary capacitorsproviding excitation, wNvould give reduced braking torqueias the external secondary resistance is increased. Teenergy dissipated within the vhole circuit is mainly in theprimary, wV,indings for low values of additional secondaryresistance but, for larger values of secondary resistane, thevalues of dissipated energy in the primary and secondarycir uits become comparable.An adjustable seconldary "resistance" ca be inserted

into an induction motor secondary winding by use of therectifier-invertor combination. This conbination is used inthe .W ell-established static, slip-energy recovery system forinduction motor speed control [12], [13] shown in Fig. I.With a diode bridge rectifier at the iiotor secondary ter-M.minals, feedirng a naturally comutated thyristo-r invertor,:Fig. I, energy is extrated from the secondary windigsand returned to the supply. Control is thereby achievedfor increase: of speed over the subsynchronous motoringregion from zero to rated motor speed. The effect of thermectifier-invertor cor bination is equivalent to a form of-lip-f equen y secondary voltage injection, or an adjust

209

PRIMARY SECONDARY

-__ o _ ~~SL P RING FULEL-WAVE3 Phose INDUCTION DIODEsupply- MOTOR RECTIFIER. .. __ _ _ ~~~~~~BRtIDGE

Fig. 1. Arrangement of slip-e.ergy-recovery drive.

Fig. 2. Primnry balanced capacitor-excited induction motor withSER system in secondary circurV

able secondar resistance. Thequvln nrtd"-

sistance" is funcfl -u e-n

sistane" isa fucion of speed, secondary crreh andi'nvertor fir"ing anigle. With pr'iir ary, capacitance ex,citat'ionlthe system i.s show in Fig. 2. I:n the,experimental

equal cap'acitorts- were connected v'ia slip ring~ to, the rotor

- .~~~~~~~~~9-

of the induction- motor wh'ich was' the prmr smachine.' 1D.etails of -the induction mnotor are gvenAppendi-x I1. -'The capacitors pe'rform a double role sincethey 'operate as. power factor-:o'rrection dev'ice's in' thenormal,motorling, mode of the SEP "sy tem, Fig. r14T.'The secon-dary, stator windings,of the machine -were, con-anected, -to a standard SER circuit co isisting of a full-wavediode hridge, a- smoothing. ~hoke and a: full-w yecntrolle'd thyristor brildge., Current from ~the secondar wind-

. .~~~~~~~~~~~~~~~~~~ii.e.oebi

ings of the-motor is reXid by th do big asupplied to, the hrist,orbridge whi ating is

invertor mode, transfers energy to the ac supply ata rate-fixed by the thyristor fring-angle, the direct voltage at:theinivertor termilnals and the su'pply voltage.B. Mlethod of Calculating Perfo -mancc Char-acteri'stiCs

Initially for each~po'int calculated ont the performancecharacteristics, the invertor dc side volta'ge and de linkcurrent were defined. The ipvertor voltage is fun tionfofthe su,ppliy voltage: andcthe@th ristor firing . It Limportantorirefer the. Witor p andy speedtaote itvetorS

emporali acto ref erte torque, ad i spee r'il:o theivrotor:

firing angle as this latter value is the-controlled parameter.Having defined the dc liik cmoditions it is$ possible to

evaluate the "equivalent resistance" on the secondary sideof fthe motor due to the rectifier-invertor combination. Thevalue is based on power flw considerations and sinusoidal

210 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS AND CONTROL INSTRUMENTATION, MAY 1975

currents are assumed to be flowing [16]. The theory forcapacitor excitation of an induction' motor is given inAppendix II Rewriting equation (At6) gives x

r2(x + fm)± fr1(x2 + x.n) - 0.

Let - m f(W)A = (xi + xr) 52

B rn(x2 + X.)

C = r2Xc

f2A + fBs + C = 0.-

then

Ua

CPcx

N4.

C

(1) a

Rewriting equation (A.5)-fx+)X

f28{( -X I1 X.) (X.'+ X2) + m Sa .S ip S

+ frlr2 + sXc,(x2 + X.) = O.

Let

thenI

D (- xi x) (xr + xc2) + xr2

E -= rIrRp = Xc (Xe2 + Xmr)

2sD+fE+sF=0. (2)

Combinaltion of equations (1) and (2) gives

LA CD]s

72[ A sIB .](Substitute back in equation (1) to eliminate f

S4(B2DF + S2 ( A -]2s4BDF) ([AF -CD]

-3E[AF + CD]) + ACE2 =. (4)

It is very convenient that the above equation contains no

quantities of order sI and hence will reake solution of theequation easy. It will also be noted lhat if all the circuitvat.es; are defined then the value of slip s can be obtained,and the frequency of excitation f has, been eliminated.

It has been stated 'that the total secondary resistancecan be calculated from the initially defined conditions. Theonly variable components involved in eqouation (4) are theslip s and xr the magnetizing reactance. Because themachine saturates, the value of XnM is variable; henceequation (4) could be restated as

=fi(cm) (5)

'From the initial conditions it is possible to calculate thevalue of Vr from equation (A.9) if the slip s is known. Apolynomial function was used in which Im is giveni forvalues of V,, [11]E , and hence the value-of magnetizingreactance xm can be calculated.

Thtis equation (A.9) allows one to calculate the value ofXr if the slip s is knowvn and hence can be restated as

Xm = f2 (8 (6)

Fig. 3. Approximate form of functions f' and f2.

The form of the two equations (5) and (6) is shown inFig. 3 for defined values of invertor firing angle and de linkcurrent.; The first method of calculation tried, namelytakirng any value' of -Xmr substituting in equation (4) toobtain a value for s, and using this latter value in equation(A.9) to obtain a new value -of xrn proved to be unusableas the method does not converge.The successful method involved using equation -(4) to

calculate two values of slip SA and B -for two close values ofmagnetizing reactance xr- and xn+i. The two values of slipSA and sB were substituted in equatio'n (A.9) to'give twovalues of magnetizing reactance xmrn and Xrn. From thes"esets of values, tangents to the two cu'rves are known andthe xr, value at their intersection can be calculated. Thisis shown in Fig. 3 and the new value xmr was used in thenext calculation. It was found that the-required solutionwas found in less than 6 iterations.Once the value of slip and magnetizing reactance are

known the frequency of excitation, primary current,torque, speed and capacitor voltage can be calculated fromequations (3) (A.8), (A.10), (A.11) and (A.12), re-spectively.

C. ResultsA number of tests were made using the arrangement of

Fig. 2, maintaining a constant supply of 100 volts at 50Hz. M\Ieasurements of torque were obtained from the springbalance attached to a swinging framie dynamometer loadmachine. Variations of braking/torque/speed, at constantvalues of firing angle with equal capacitance of 100I E, areshown itlFig. 4. Measured and calculated v'alues were inclose agreement. It is seen fromn the characteristics that ata given speed the'braking torque is controlled by theinvertor firing-angle. Minimum speed for a given brakingtorque was obtained for a firing angle of 90' which cor-responds approximately to a short-circuited secondarywinding.

BLAND AND SHEPHERD: SLIP ENERGY RECOVERY DRIVE 211

as the motor rating. The capacitor current, at a fixed firing2 X \ X angle, varies approximately directly with motor speed.

z | \ \ Braking torque was found to be a linear function of delink current in the primary capacitor excited static SERI

o system. Theoretical characteristics of braking torqueversus de link current were identical for all firing angles

--00\ \- \ \0 and calculated and measured operationi were in close0 ~~~~~~~~~~07: 2 | oO9°<=?0 agreement. This linear characteristie of braking torque

suggests that this system can readily be extended for0 _ t£000 2000 3000 closed-loop control by utilizing the de link current, or the| Speed r.p.m. invertor ac line current, as a feedback signal for braking

I£00 £30torque control.

z 0

oX III. BRAKING UTILIZING SECONDARY0; C -£00 F/Ph\ A.CAPACITANCE EXCITATION

A. Primary Windings of Induction iMotor Short-Circuited) EAqual Capacitors: Consider now the standard SER

drive with switches, S, open, (Fig. 1) the primary motorFig. 4. Measured and calculated braking torque/speed perform- windings short-circuited and equal capacitors connected

ance witlh balanced primary excitation.across the secondary windings. iIeasured values of brakingtorque are slhown in Fig. 6, and are found to demonstratef

£2 0 0 0 symmetrical excitation of the motor.o(1°t=99. lt£0 £30 'soThe voltage appearing across the capacitors is limrited

£0. Cp£00 F/p. / // by the voltage in the dc link. The invertor "internalvoltage," in turn, depends on the supply voltage and thenivertor firing angle. The degree of saturation of the ma-chine depends mainly on the seconidary emf and the speed.This suggests that the machine was operating unsaturated

4- o / / / for low values of firing angle at most speeds and also for2] t / / / large firing angles at higher speeds.2 - For this mode of operation capacitance excitation oceurs

£400 ---initially at a speed determined by the magnetization0 :800o0go 2200 2600 3000 characteristic of the nachine and the value of theicapaciSpeed, r.p.m.* : :;Spee -rpm.. tance. For the system tested this particular speed cor-7Fig .5. Measit.ed and calculated capacitor current/speed per responded to that observed using the capacitor-excited

formance with balanced primary excitation.machine without the rectifier-invertor combination.

Variation of invertor power w-ith speed, for the sameThe lowest speed at which braking torque could be constant values of invertor firing angle, results in curves

achieved occurred with firing angle 0 900 and was de- similar to those of Fig. 6. Much of the braking energy ispendent on the value of the primary capacitance. If the extracted from the drive by the invertor and returned tocapacitance Was increased, braking was achieved at a the three phase supply. The braking torque, at a givenlower machine speed. The use of firing angles smaller thani90ccaused the thyristor bridge to operate as a rectifier Speed, r,p.m.without further contribution to the braking performance. i4oofi80 2200 2600 3000The speed range for which electrical braking is possible 'isdependent on the current rating of the semiconductors and -1\the maximum dc side voltage of the invertor. This voltage £10is given by 1.35 V cos 0, where V is the rms supply voltage iand 0 the firing angle. For a given dc link current, capacitor ,31:value and maximum value of firing angle the range ofcontrol is increased if the supply voltage is raised. ,4

Variation of capacitor current with speed, at constant '- 0invertor firing angles, is shown in FIig. 5. Characteristics for 120 n Primarysehorcircuitthe variation of capacitor voltage with speed (not shown) -6 £50 £300are of the saien form. A knowledge of these two sets of -14:characteristies is sufficient to determine the rating of thed p y ce w h is of te ssFig. 6. eoastred brakin dtrque/spxt ptrinance with.balerequired pr'imary capa¢litance wbich 'IS of the samne order, secondary excitation.

212 'ErETANSACTIONS ON IINDUSTRIAL ELECTRONICS AND CONTROLNSUNTIO,IMY 17

Speed r-pm. Speed., r.P.m.1400 6002200 2600 3000 ~~~~~ ~~~~~~~20002500~ 3000 01400 1800 2200 2600 22.~~~~~s"10Fn2

0~~~~~~~~~~~~~~~~~~~~~~3

Cs~~~~~'100 Fin2phses~~ ~ s 00,iin2 hae

120"~~~~~~5

130 ~ ~~ ~ ~ ~ ~ ~ ~ ~ ~~~3 2

150P 1406

i.7. Measured, braking torque/speed, performance vwith uin- Fig. 8'. Mea aured 'brking torqu /,spee peWoaIc witmains

balanced s odr xiain ary ryecitation ndunbalanc~ed seondary capacitoexiaon

speed,is d ety controlled by the firin anle of the-i. o stehg s eer gion conmpare4w4th,uncnpnvertor. vhich le'ads: to the poss'ibility of closed-loop con- sated, operat'ion.troL. The poe factor -of'the system is that of the in'vertor Staystate. hraking is psilwthAthis circi't, with:w,ihich is,a- functiont'of- hArng ange [14j, seontry compensation p'roviddtathspe,hy.-The dispolac-em- n-t of the brak'inog tor'que/speed charac-, ristor firing angie erI apacitor ae- ofsutbevleteristics (ig. 6) anb hagdosiderably by utilizing- The reetifier-invro miation acts 'as a variable rdifferent. values of balanced K eoondaryv. capacitan . For" sistanc inprlel' with the .'econdar caaitance.lower; values -of ap'acitance the 'ini'tial "e'xcitatfoocusa Cpcitanceeecittion of, 'the m-achine -gives, rkse. to, the-r~aelatively h-ige speed, ,the gnrlshape of the cha'rac-, braking -torqe prdcd. The braking ehar 'eteristic oteitCs hem utagd. this cruit hiave bee gvn elsewhere [17]2)Unquest Caacithr:Wt unequal secondary capac- z)Ueual, Cpap to':-Brakigcarcei isc be

itors: the. braking torque/spe.ed.charactritisver fund obained with capacitors ofueuap uei hseeondrte~~~~~~~~~~~~~~~~~~rtqaicut.A t,o,Na bof th'e ~same form as 'those obta'ined wit eua cicis Anivestgto sismd ithi one, ad two, of-

.seconda-ry~capacitors~as shown in Fig. 7.- With two'ca,pa - the capacitors remnoved from the. normAl delIt conetionit ahin e tto ul pin a balanced manne Uing tw aaitors only the.yvrnation of brakin oqinthat allsecondary voltages are equal inmgnitude wihpe,frcntant inverto ri g anigles is showin.

'Br'akin.g torque is produce'd initially at 'a h'igher:spee'd than Fig.S8, Symmletrie~al'and u,nsymmetrical modes of operation.that obtained with: equal capacitors 'of -the same value. aebtinvidence. for invertor fin g nge of, 150, 140

With o l one secondaryr capa itor 'n the circuit,te ad10egthe th'rniino ring withhageo.f-:machine exhibited a ymtrical bu'dup of- excitation sed obaigtru a b&idblwoehlgiving rise to br'akn toqecharacteristic'similar in~ sn oous speed A reuton. in capa itor va re-form to~those of Fig. 7 The speed, at which exitain sle nasito h n' ohge ed.initilallyv occuorred was- furthetr increas8d, and the braki-ng The uns'm mictrical -excitation.,chara trsti s occu.r nertorque produed- was in geealde ed hut remained a to one-halfspeanarofgetr adnthstefunction- of" theinverto :firing angle for aer ngiv -n, machine synunietri al xcitatio c'harateristcsvhich a iprespee over the higher speed range.

For operation, xv4th short-circnited pri'mary windings With a single cap'acito inthe,'secondar ici htherefore a, redn tion in, the nui iber of capacitors or a -torque/spdcuvswrilatohsefFg.8Tereduction in the, capacitanice value resulted 'in a-higher unsmme iamoefopration was much]lesincise04-at wlich the initi I e citation occurred but, motor deuce thnadtecurves for s meralxitoni

excitation waps-always synmmetric~ai. gee`,wr islcdt ih .rsedcompared withIorsonding results obandsthtoo hee capac-~,

B.Mai~ns~kSupPly to Pr ayof Jfaladne itor banks.,1)EatSecadar Gapacitaiwe : Consider operation of VCO LUIN

,the stanidard, SEU drive (Fig, I) 4vth' equlcpctne Several-methods- of bakin tesaislpenergy- re-;-connected' across the seodary. wndi g at, the diode covery drive hay 'been eci tlzn io xterminal. OneVW -'Of the authors has shown previonsly [14] citation & the iinduction mtor Th a.in hVthat this seeodary compensated SER ceircuit,gives, some, exc-ited by 'placing, capacito'rs. in 'the prinmr rseodrnsea$nrefp e factor corr etiont at, low speeds. Also the windings of th a e or prmry eapa ito exiaionaddition: of-se odary capacitancee resuIts ingetrtqu thbakgtoueialn ar futtion of the-de link crrbetteIr spe euainaddisplaces the toru rvsad hence is, suitable for cilosed-loOO,Contrl

BLAND AND SHEPHERD: SLIP ENERGY RECOVERY DRIVE

For secondary capacitor excitation braking torque isproduced with or without primary supply and also withbalanced or unbalanced values of capacitor banks in thedelta connection. In all the circuits the braking torque at agiven speed is a function of the thyristor firing angle andcan be controlled by variation of that parameter.

APPENDIX I

DETAILS OF THE MOTOR TESTED

Three-phase, 50 Hz, 240 V, two-pole, wound rotor induc-tion motor, nominally rated at 2 HP.

Per-phase equivalent circuit constants, referred to theprimary (rotor), established by standard tests:

r= 3.75Q x1 = 4.82Q rm = 378Q

r2 2.330 x2 = 3.222 xm = 1600.The turns ratio of primary to secondary was 0.76. At

reduced suppDl voltage of 100 V, the motoring pull-outtorque was measured at 2.8 N.m. Equivalent full-loadtorque at this supply voltage would be approximately 1.3Nem.

APPENDIX IIA per-phase equivalent circuit for an induction motor

with primary capacitor excitation is given in Fig. Al. Thisis derived by standard methods and all component valuesare those measured by established tests at a frequency of50 Hz and referred to the primary side.From a consideration of the equivalent circuit and the

defined current flow:

Il lr/f + jx -j(x6/fl) } + Imjxm = 0 (A. 1)12fr2/s + jX2} Imjxm 0 (A.2)

I1-I = inm. (A.3)By combining the above three equations to eliminate bothIm and I2.

rlr2/fs- {XI + Xm- x/If2} (X2 + X) ± J(r2/s){Xi+ X x /f2} +j(rlf) (x2+x) +X.2 O.

(A.4)

By equating real parts of the above equation:

r1r2/fS - (X1 + Xm-x/f2) (X2 + Xm) + Xm2 = 0. (A.5)By equating imaginary parts of equation (A.4):

(r2/s) (Xi + Xm -X//f) + (ri/f) (x2 + Xm) = 0. (A 6)By combination of equation (A.5) with (A.6), xm can beeliminated:

s2 (r1X22f3) + s(-2r2xlf2xc + r2xj2f4 + r2X,2

+ ri2rf) + r22rlf3 = 0. (A.7)Equations (A.1) and (A.2) are in terms of the vectorquantities of the currents and can be converted to quan-tities involving only the magnritudes of the current:

rI/f j xi jX2

Fig. A-1.

{1 (r If) I + [X1- xGr22 /= +I x x/f2]2 }1/2

ImxmI2 = Im

[ (r2/S) 2 + X22]112

Also it is obvious that:

T = I22r2/Nos

sp (f-s)NoCV= I1(xlf).

(A.8A)

(A.9)

(A.10)

(A.11)

(A.12)

REFERENCES[1] E. 1). Bassett & F. M. Potter, "iCapacitive excitation for induc-

tion generators," Trans. AIEE, pp. 540-545, May 1935.[2] J. E. Barkle & RI. W. Ferguson, "Induction generator theory

and application," Trans. AIEE, pp. 12-19, Feb. 1954.[3] C. F. Wagner, "Self-excitation of induction motors," Trans.

AIEE, vol. 58, pp. 47-51, 1939.[4] W. C. Blomquist & W. K. Boice, "Application of capacitors for

power factor improvement of induction motors," Trans. AIEE,vol. 64, pp. 274-278, May 1945.

[5] C. E. de Sieno & B. J. Beaudoin, "A guide to the application ofcapacitors without induiction motor -self-excitation," Trans.IEEE, vol. PAS-84, pp. 8-15, Jan. 1965.

[6].I. R. Smith & S. Sriharan, "Transients in induction machineswith terminal capacitors," Proc. IEE, vol. 115, pp. -519-527,April 1968.

[7] J. W. Butler & C. Concordia, "Analysis of series capacitorapplication problems," Trans. AIEE, pp. 975-988, Aug. 1937.

[81 C. F. Wagner, "Self-excitation of induction motors with seriescapacitors," Trans. AIEE, vol. 60, pp. 1241-1247, 1941.

[9] P. L. Alger & Y. H. Ku, "S3witching transients in wound rotorinduction motors," Trans. AJEE, pp. 19-27, Feb. 1954.

[101 A. Srinivasan & M. A. Thomas, "Dynamic braking by selfexcitation of squirrel cage motor," Trans. AIEE, vol. 66, pp.145-148, 1947.

[111 T. G. Bland, "Speed control of an induction motor drive in-corporating a slip-energy recovery system," Phi) Thesis,University of Bradford, 1973.

[12] M. Meyer, "Uber di untersynchrone Stroinrichterkaskade,"Elektrotech. Z, (A), 82, pp. .589596, 1961.X

[131 A. Lavi & R. J. Polge, "Induction motor speed control withstatic invertor in the rotor," IEEE Trans. Power A pp. Syst.,vol. PAS-8+) pp. 76-84, 1966.

[14] W. Shepherd & A. Q. Khalil, "Capacitive compensation ofthyristor controlled slip-energy recovery system," Proc. IEE,vol. 117, pp. 948-956, 1970.

[151 D. Robb & P. C. Krause, "The self-excitation of inductionmachines with application to motor starting," Trans.: IEEEPower App. Syst., vol. PAS-90, pp. 579-58)86, March/April 1971.

[16] B. M. Bird & P. Mehta, "Regenerative braking in slip-powerrecovery systems," Proc. IEE, vol. 119, pp. 1343-1344,: 1972.

[171 T. G. Bland and W. Shepherd, "Electrical braking of staticslip power recovery drive," Proc. IEE, vol. 121, pp. 701-702,1974.

213