Sub- and Super-Synchronous Induction Motor-Thyristor Cascade Control

Cop\'right © IFAC Control in Power Elec tron ics and Electrica l Drin' s. La usan n c , Switzerl and , 1983

SUB- AND SUPER-SYNCHRONOUS INDUCTION MOTOR-THYRISTOR CASCADE CONTROL A. I. Said* and Bingoto Mandoko na Mpeya** 'D epart ment of Electrica l Powe r & Ma chin es, Fa culty of E nginee ring, A in Shams University, Cairo, Egypt **I nstitut Sup erieu r de T echniqu es Apphqu ees, Unive rsit e Na tiona le du Zaire, KInshasa, Zaire

Abstract. Normally, thyristor controlled converter circuits are used on the rotor s i de of slip.ring induction motor for the purpose of sub-synchronous speed control. With possible reversibility of power flow in the rotor circuit by using reversible controlled converters, super-synchronous as well as subsynchronous speed control of induction motor drive is obtained. By proper design of such a system, it is possible to obtain the control and signal processing for current and speed feed-back over a very wide speed range with either driving or braking torque. This paper presents a modified speed control scheme of sub- and super-synchronous induction motor-static converter cascade using a current source converter on the slip-ring side and a modified bridge converter on the line side, thus the energy being returned or taken from the supply. A thorough analysis of the steady state performance between and during commutation of the current source converter is provided. The analysis also gives the three different modes of operation of the modified bridge converter taken into account the effect of commutation overlap. The control firing strategy for the two converters is formulated in order to reduce react i ve power requirements. Power factor and harmonic content are identified for the purpose of obtaining optimal power factor operation. The results are found by computer programming over a very wide range from standstill up to about twice synchronous speed and a comparat i ve discussion with other types of cascade is outlined. Keywords. Electric drives; a.c. motors; power converters; motor control; cascade c,) ntrol; feedback; speed control. INTROIlJCTION Conventional three-phase induction motor operation from a constant voltage, constant frequency supply suffers from reduced efficiency and higher losses at lower speeds. The use of induction motor-thyristor cascade systems for slip-energy recovery reduces these disadvantages and improves the operating characteristics. These cascades are widely used in many industrial applications to control the speed where the drive operation is intermittent, for example pumps, crane hoists, fans, compressors and l
*

£.1. Said, is now with the Arabic Fund of Development, Institut Superieur de Techniques Appliquees, UNAZA, Ambassade d'Egypte, B. p. 8838, Kinshasa, Zafre.

indicated that an improvement of power factor may be obtained by capacitive compensation on stator or on rotor or even on both sides. Further technique (Ohno and Akamatsu, 1968) by using voltage source inverters and (Smith, 1977) by using cycloconverter directly between the rotor side and the a.c. line side indicate that a reduct i on of reactive power requirement is obtained. Another strategy by the use of modified bridge converters or by asymmetrical firing of conventional }-phase bridge converter indicates an improvement of power factor (Said, 1980, 1982). Because of the advantages of simple firing control, slow turn-off thyristors and reliability in case of current-fed converters over voltage-fed converters (Phillips, 1971; Maag, 1971 ; Farrer, 1973), ourrent source converter operation of induction motor finds increasing application in industry. In an advanced work (Said, 1983) describes an investigation on analysis and speed control of induction motor-thyristor cascade using current source converter on the slip.ring side and conventional }-phase bridge converter on the &eC. line side. In this recent work, the command is carried-out by using a

-

Bingoto Mandoko na Mpeya. Prof••• eur • l'Univers ite du Kins has a et Di r ec CcuI' G en~r~l de l'ISTA, B. P . ( ~ ~3 , Xi ns hasa,)1.

345

A. I. Said and B. Mandeko na Mpe ya

346

signal generator synchronised to the rotor e. m.f. to obtain a stable operation. This paper describes a development into such a system using a position detector for control of the current source converter and a current phaseangle controller for the modified converter in order to improve the power factor in cloSed loop operation. Different modes of opera~ ion of each converter and the system as well as the control angle conditions for optimal power factor operation are treated. Sub- and supez-synchronous speed control firing str/r tegy is studied and compared with the case of using conventional 3-phase bridge converter. Harmonic content and a comparative discussion with other types of cascade systems are also given. The advantages of such improved system are reported in the conclusion.

for a very wide range from stand-still up to twice synchronous speed control operation. 3-,Us~

•. c..

£;".

S''r-''''""

:,..,..,14w. .... '~ht&

Fig. 1

Single line diagram of the main circuit.

BASIC PRINCIPLES

The method of speed control for 3-phase slipring induction motor is based on the idea of slip-energy recovery incorporating static frequency changing cascade between the sli~ ring terminals and the 3-phase a.c. line terminals. A variety of circuits and switching systems can be devised to achieve this idea. Here, the control of power flow in the cascade circuit both in magnitude and direction enables super-synchronous as well as subsynchronous speed control and generating as well as motoring operation. The main circuit shown in Fig. 1 consists of a reversible indirect converter with some modifications referred to the work given before by the author (1983). Practically, current and speed feedback closed loop are used to realise the advantages of the modified system of better eff.iciency, good winding utilisation and better power factor. It is clear that the converters C1 and C have the same rating as the machine. The 2reactive power is maximum at zero slip and approximately as great as the synchronous power of the machine. The reduction of the reactive power can be achieved by control of firing of the current source converter from one side and by complex firing of main and auxiliary thyristors· of the modified converter from the other side. Figure 2 shows the entire power circui t diagram of the two converters of the indirect conversion cascade link. In addition to the control of both converters to reduce the reactive power demand, parallel capacitors may be used to compensate the reactive power due to the magnetising current of the machine. It has been found that the operation at twice

synchronous speed as rated speed gives the advantage of reactive power reduction because only one half of the maximal shaft power is fed into the rotor. If the switching sequence is reversed by inter-changing two phases on the stator a.C. supply side as explained by the author (1979) in a previous work, the direction of rotation of the machine is reversed and four-quadrant operation is obtained. Then the machine is either generating or motoring in both the two directions of rotation

c

c .. ,,.,.,.1

J"",."c.

,.",,~f(r

Fig. 2

Cl

....d:/;e
''''"tI''~rC.a

Basic power circuit diagram of the indirect converter cascade.

THE CURRENT SOURCE CONVERTER

The current source converter discussed by Phi11ips (1971) and also by Maag (1971) with blocking diodes is becoming increasingly favourable for reversible sub- and supez-synchronous speed control of induction motor-thyristor cascade drives. The converter must be reversible and having the possibility to work for the required frequency and voltage range on both a.c. and d.c. links. The performance and analysis of single phase current-fed converter with counter e.m.f. and inductive load has been considered before by McMurra,v (1978) which is based on an earlier work by Farrer (1973). Here a detailed analysis of the commutation process is studied. Figure 3a,b,c,d show the equivalent cu-cuits of commutation sequence of the current source converter, which represents the commutation from phase to phase 2 of the rotor e.m.f. of the induction machine. Fbr simplification, each phase of the rotor is represented by an inductance in series with rotor induced e.m.f. Consider, for example that T1 and T2 are conducting as shown in Fig. 3a, when T is fired, T1 is biased in the reverse directi~n by the

Sub- and Super-synchronous Induction

347

vol tage of the upper capacitor group and it is tunled-off. While T3 and D1 are conducting as shown by Fig. 3b, a constant current discharging of the upper commutation capacitors takes place. The 1 inear charging stops when the capacitor voltage reaches the rotor line voltage which is defined by first commutation time t. • At the end of charging,D conducts, which is illustrated by diode commatation and it is defined as second commutation time 1.2 a s shown in Fig. 3c. Finally, the current nas a.pletely changed from phase 1 to phase 2 as shown in Fig. 3d. The conduction sequence and r3tor phase currents are shown in Fig. 4 • The rotor e.m.f.'s are given by:

ISEo I sin IsEo I sin ISEo I sin

swt s( wt - 2Jf3)

(1)

s(wt - 411'/3)

where Eo is the open circuit rotor e.m.f. at stand-still, w .. 21rf, f is the supply frequency and s is the motor slip. There is no overlap between different stages of commutation in the operating frequency range of induction motor-thyristor cascade and six symmetrical commutations occur for each cycle. The rotor currents can be cos idered constants during the time of commutation Z • The rotor vol tages are also assumed cons~ants and the resistance is neglected during commutation. Waveforms of capacitor and thyristor voltages as well as the phase currents during the commutation period are shown in Fig. 5 • From the equivalent circuit of Fig. 3c, the following differential equations describe the evolution of voltages and currents during the second stage of commutation.

= i1

+ i2

(2)

The saturation in the rotor circuit of the induction machine is neglected, this means that the flux is assumed as a linear function of current with constant coefficients L, M.

~1 - (L2+L1-2M21)i1 - (L1-M21+M23-M13)Id Differentiating both sides with respect to(3) t, then:

FAIui valent circuits of sequence of commutation.

I

Tt

i,

~

d. 21 / dt - e 21 - L di/ dt - Vc' , dVc/dt - i 1/C', Id

Fig. 3

1

i2

J-J

1

I

~

I Fig. 4

r

I

I

I

r I

I I

..,f

L:'t

Conduction sequence and rotor currents.

v.;.

L di 1/dt - d421/dt in which, C' _

3C/2 , ~ - 2 (L - M )

where L represents the equivalent leakage inductance of the machine referred to t he rotor side and M represents the equivalent lIIutual inductance between the rotor windings. From EXr. (2) and for star connected rotor windings. di/dt - -di!dt - dijdt , io - - C'dvcldt Substituting EXr. (6) into ing is obtained. 2 di/dt _ - C' d2v o/dt

(5)

__~__~*-~~________~~_t ~~----~~--------~--~

(6)

EXr. (5),

the follow-

(7)

Fig. 5 Waveformll of vol tages and currents during commutation.

348

A. I. Said and B. Mandeko na Mpeya

Substituting Eq. (7) into Eq. (2), the following is obtained. I

I

,,_ _

/

Vc," e 21 - L C d -V6 dt

2

( 8)

The initial conditions are considered t .. 0, at the end of the first commutation time

i.

(Vc') t..o .. E sin sW71 '

ronous operation.

E ..

V3"lsEo I

(dV 6/dt)t..o .. - Id/ C'

TABLE 1 s

1.0

0.8

0.6

0.4

0.2

0

V co

1}5

144

15}

16}

174

1B2

cos~2

0.95

0.96

0.97

0.98

0.99

1.0

Then the solution of the differential Eq. (8) is obtained as follows. V, .. (- Id sin w t/w 6)+ coo where w .. 1 / o

VUiC'

E

sin swZ 1

Results with Positive SliE

TABLE 2

Resul ts with NeB!!:tive SliE

(10) s

Substituting Eq. (10) into Eq. (6) and differentiating, the following is obtained. ic .. Id cos wot (11) When w t .. .."./2, the commutation is complete

V co

0

-0.2

-0.4

-0.6

-0.8

-0.9

182

195

214

239

280

34}

0.99

0.97

0.94

0.78

0.46

2 1.0

COS'f

o

and the capacitor vol tage Vc' is then given by: Vc,= - Vco .. (- Id/w0 C) + E sin swz. , then, Vco Id Vfr/c' - E sin sw21 (12) The time of second statge of commutation is given as: ~ = 7r

VL' C' /2

21 ..

During the first stage of commutation, using Eqs. (2) and (9), the capacitor voltage V I is given by: c

VL' C'-

2 C'

+

'Zi .. VL' '" v -

Vco"

E sm . SW2'1 C' ~

VL' C'(1 Id

sin swz, ,

d

't2 .. 7r /L' C'/2 , tc"

Power Factor of Rotor Current

+

/r;/c' -

+) E

2 C'

~d

sin

sw~

sin swz,

(17)

THE MODIFIED CONVERTER

(13)

V,=V c co -Idt/C'

Substituting Eq. (12) into Eq. (13), the following is obtained. Vc,m (I/woe) - E sin sw~ - Idt/C'

(14)

The diode D3 conducts at the end of the first stage of commutation

Finally the commutation process of the current source converter can be characterised by:

~1'

when

Vc" e 21 .. E sin sw~

(15)

Substituting Eq. (15) into Eq. (14), the following is obtained. 2 E sin sw~ +(Id~/C) - I/woC..o

(16)

The time of first stage of commutation 2'1 can be found by solving Eq. (16), and the phase angle 9 of rotor current at any slip swill 2 then be swt.. radians. The calculations are done for th~ induction machine and the system under study, which have the following data: 3-phase, 50 Hz, 2.95 kW, 4 poles, 220 V, 10.2 A, star connected, C .. 40 uF, L .. 10 mH, E .. 0 110 V. The following results are obtained from Eqs. (12) and (16), for a d.c. current Id .. 10 A. The maximum capacitor voltage and tne phase angle of rotor current are tabulated as a function of slip. Table 1 gives the results for sub-synohronous operation, while table 2 indicates the results in case of super-synch-

For the purpose of power factor improvement, a modified si~pulse phase commutated converter is used at the a.c. line side through a matching transformer as shown above in Fig. 2. This converter consists of a conventional 3phase controlled bridge and two auxiliary thyristors 57' 58. A substantially reduction of reactive power is achieved at lower d.c. voltages for both rectifying and inverting by the use of the modified converter. Its advantages over the conventional si~pulse bridge converter lie in lower requirement of reactive power and lower harmonic content on the d.c. link as described by the author (1980) in a previous work. The main problem lies in firing control to ensure commutation of the two auxiliary thyristors and the main thyristors for the lolhole range of operation, where & and oc are auxiliary and main firing angles respectively. The following relations are reported again for both rectifier and inverter operation, which is determined by the range of the main firing angle 0(. y'fVl Vd" 3 lI'k" I .. - Id ( re k"

r.

+

LCOS

+

(ac + T"") + coss]

G cc J. ---)~ 71

pft - VdId 13 Ire V1 V?1OOs(oc+1r/6) + cos r] .. ".(.2... ~ )t 6 + rr

Sub- and Super-synchronous Induction

349

.-et I.loe,.

1

I~.-------------------~~~----~ If lrr-~~---------r----------+---~~--~ ( 18) where V1 , Vd' Ire' Ir1 represent phase stator voltage, d.c. voltage, total and fundamental current reffered to the line side of the matching transformer; pf , pf are total t 1 and fundamental power displacement factors of the converter, kMis the transformation ratio of the match ing transformer. In the rectified mode, the power factor of the modified converter C may be opimized Qy 2 setting ~ equal to zero and adjusting 0( to control the power flow. In the inverting mode, the power factor is negative and is optimized by setting (I( to 5 /6 and by varying $ to control the power flow. Generally the converter operation can be then divided into the following categories: 1) Rectification, 0
(7 -

It is notable from the power diagram that an obvious reduction of the apparent S and the reactive Q... per 'lmit powers is obta~ed, specially at 'fower d.c. vol tages near synchronous speed. The optimal power factor control may be slightly affected by the commutation overlap of the converter, which is due to the leakage reactance of the matching transformer. In general, there are three representative modes with commutation overlap depending on the values of the firing angles 0<, $ related to the overlap angles.

',3 -~r-------------~~------'~'~--~~~~ -/r---------------~~~-----_~1r-~~----J main and auxiliary firing angles D(, ~ Fig. 6

per unit power

Optimal power factor control

To avoid commutation failure, the range of the main and auxiliary firing angles have t o be limited by taken the commutation overlap angle and turn-off thyristor times into consideration. The main and auxiliary firing angles 0<, E baTe to be smaller than the following practical maximum values.

0<. • arccos

1 - k. cos t

S

k, COS:hl - 1.

m

= arccos

k~

11

j

)

-rr

- -6-'

) - :

(20)

:a {6 V/Xl I dki: k = 3 v/{2 Xlldk~ Ez wtoff' Xl is the equivalent leakag reac-

in which, k

tanoe of the matching transformer reffered to converter side· In the above treatment of the modified conv-

erter, the advantages of improved power factor, lower harmonic distortion, reduced reaotive power and maintaining a 6-pulse reaction on the a.c. system compared with the conventional type, have to be evaluated against the additive cost ot two auxiliary thyrietors and increased complexity of firing control. CONTROL SCHEME

The scheme for closed loop operation is considered as a double control system, the speed and current controllers. While the speed is controlled by variation of the firing angle ex, of the current source converter at the slip ring side, the current is controlled by variation of the main and auxiliary firing angles.. ~ of the modified converter at the a.c. line side. The block diagram of the control system for olosed loop operation is given in Fig. 7. The power and control circuits are adjusted to enable both converters to change automatically from rectifying to inverting operation and vice versa according to the operating conditions of load, speed and direction of power flow. For constant torque operation as an example, the amplified speed error is considered as the demand signal to a current servo amplifier. The output of the

A. I. Said and B. Mandeko na Mpeya

350

3 -pA~.st!.

".C. Sul'l":J

'~oke.

Po-;;f...... "~~dv

0

I

:{IDI

f---

~'''J

I . i'l.

C,*

Con\/,-

/';'.H·

~"t,,.

C'ol1f~{

r--

J

c~#J

c.," ... n~ t..-u/...,...,f"

I

fr~ •• "'j r. vo/"&J e.

-

""I

r-- ·11'4.;1 f---

t-4/LIF-oCf"

I--

r--

l'lw.

;i..i1l

+''rl-o

c.-w...,t:s f4- Co"l".,t

~;r"r:";

0(,

"'-

cwt't'f!:,d.

cx".s

II fA«.s~

del.. .;

c:: f:J 5ft'eJ

7$,J

Sflf~-

~ft!!e:J

_t

c.,,,f,,.,/

t.ry~

C-9"h-.{

"'I";;;'"

,.,~ ~

....J...i:

....:,..

~~

Fig. 7 Block diagram of the control scheme. TABLE machine

i

Range of Firing Angles for Different Modes of Operation firing control

converter C 1 rectifier

Of

6uper-synchronOUB motor

inverter

0<1 ~ 180

sub-synchronous generator

inverter

0\1 ~

super-synchronous generator

rectifier

0(

sub-synchronous motor

«0

~

firing control i.

~

inverter

0(= 0( m

0

rectifier

180 0

rectifier

2!:. ' ~ '

O·

inverter

0

1 .....

1 '"

converter C 2

current controller is used to adjust the firing angles of the modified converter. so that the desired current can be maintained constant for both rectifying and inverting modes. The polarity of speed error is detected to control the firing sequence of the current source converter to provide the required torque. 'r he operation of the two converters and the corresponding controlled range of the firing angles for different speed and power flow conditions are given in table 3. The trigger-

£ <.,'iO <~

<0<. <<>
S .. 0

<0«0(

~. 0 0

....

0

m

0<.0<

m

~ <. h <~ . .

The triggering pulses of the modified oonv.rter C2 for optimal power factor operation are genefated as given in table 3. where ~ • ~ and €. are given by Eq. (20). Practical'y ?or optimal power factor operation of C in the 2 angle rectifying mode. the auxiliary firing ~ is equal to zero and the aa.1n firing angle ~ is adjusted for power flow oontrol. In the inverting mode. the main firing angle D( 18 fixed at IX and the auxiliary firing angle & is varied ~etween E and S for machine contm rol.

;~ ~!:::t~~ !:eac~~;o:o~~~o~:~~!~~eC1 position of rotor flux vith respect to air gap flux of the induction machine. A special poai tion detector of di~i tal type may be used as given by the author (1979) in a previous work. Tbe firing angle ~1 and the sequence of conducting ~istors are determined from the above information. which is given by the poaition detector. This angle which repreaents the phase angle of rotor current is controlled. either delayed or advanced to reduce reactive pover demand by the commutation proceas.

EQUIVALENT CIRCUIT MODEL The closed loop control scheme ensures that the rotor current is controlled in magnitude and phase by the indirect modified oonverter rather than by the circuit and machine para.eters. If the rotor current 12 is oontrolled to be at an angle ~ vi th respect to the atator reference vOI~e V by using the position detector. then the ~upply pover. poyer into the machine stator and the total pover

Sub- and Super-synchr onous Induc tion

35 1

crossing the air gap are given by. Ps - 3 I s V, COS",

~

P, - 3 I, V, cos -;"

~

Pg = P, - Pc, - Pi1

=3

(21 )

(I/It) V 1oos 4>2

The rotor power is given by: (22) P2 - BPg - P02 - Pi2 where It is the transformation ratio of the llachine windinga, I and I represent suppl,. and stator currentsSrespectivel,.. It is well known that the above expressions of power can be either positive or negative according to power flow conditions. The useful torque is calculated from Eq. (2') by considering only the fundaaental component of rotor current, where the ideal waveform is shown in Fig. 8. The per unit rotor, atator and total power as a function of slip for full load torque operation is shown in Fig. 9. It ia noted that rotor and total power approximately represent a linear funotion of slip. 12 -

2(1" Id(sin wt - t sin 5wt + t Bin

Fig. 8

Rotor current.

10.-/,,(

_0'" _•.

I 2e -

if Id

-I·.

_ ... 2. b _"1 Dr---------~~~~~~--~----~--~

I' I I

/.D

3If

I I

7wt - ••• ) which gives an effeotive value of.

Fig.,O Equivalent vector diagram.

(23)

The total r.m.s. value ot rotor ournnt is given bys I

2r ••• s.

•

if v'3 I d

The power faotor 1& oaloulated troll the equivalent vector diagram of the syatem whioh ia shown in Fig. 10. Efteots of oommutation of the curnnt aource oonverter C and overlap ot the 1I0dified converter C2 d~ing different modes ot operation are taken into account during oalculations. Figure 11 represents the results with optimal power factor operation of converter C and oompenaation ot lagging power factor b,.2 ..ans of phase angle oontrol ~1 of oonverter The reaul ts are expressed lA per unit values. It 1& noted froll Fig. 11 that the rotor ourrent increases tor driving torque above synchronous speed and tor braking torque below ~oua speed. In fact thi. ia due to mechanical and iron losses rapidl,. increased above synohronous apeed. A f\1rther factor is due to co-utation. a greater lagging power faotor reeulte as the d.o. voltage increases. In order to improve the reeul te of constant torque operation. the firing anglee are adjusted &s given in table 3 to ainillise the reactive power require..nt by bringing the rotor current and vol tage in phaee. The iaproved results atter power faotor oOllpenaatioD are shown b7 the dotted lines in F~. 11. The ~c behaviour of the qatell oan be eeen b,. referenoe to Fig. 12, which re,re..nts the aachine running from etand-still up to twice B7DChronOUB apeed b7 digital sillulation on cOllputer. It 1& Doted b7 adjueteaent of firing angles. the phase angle between stator current and voltage is lIinimised. The

C,.

I I ~

___6 "s",. _____

Fig. 11

...,

I

- - - - - f'.ulU &-tJe1

"Jncli .....-..' - - - - -

sr,eJ

Cm"r"f!C ~ t .. ",

(.I ... (.~#J .

S14,,"' -

Load characteristics for conetant torque operation.

..

t-

o~~~----~----------~----~----~

.,."

~.

Fig. 12 n,na..uc behaviour running froll stand-still up to twice ns'

A. I . Sa id and B. Mand eko na Mpeya

352

rotor current has a low frequency region when the machine passes through synchronous speed. The torque pulsations are due to six-pulse reaction on the feeding line, its amplitude may be decreased by a proper design of the choke f11 ter. In general, by using Fourier analysis, it is found that the harmonics of the d. c. vol tage are the sixth, the 12th and multiples of harmonics. B.y using the modified converter with two auxiliary th7ristors, a reduction of these harmonics is obtained. The rotor current as shown in Fig. 8 and by Eq. (23) contains odd harmonics of the order 6q+1, where q is an integer. For the a.c. line-currents, while the modified converter does not inject evenorder harmonics as does the asymmetrical fired converter, there is a generation of triple harmonics on the a.c. line side, which can be prevented from entering the a.c. system by a delta-star transformer. The limitation of available speed range caused by cirouit and machine parameters in case of conventional types of cascades is overcame by using the current source converter from one side with its firing control ~ and the modified converter convert.~ with its double firing control 01., S • By using computer simulation, a favourable size of commutating and smoothing circuits as well as a suitable design of matching transformer and converters for a given induction motor can be reached. CONCLUSION The analysis and speed control of an induction motor-static converter cascade for industrial applications is pres.nted. Co~utation of the current source converter and different modes of operation of the modified six-pulse bridge are studied in order to find an exact equiTalent 1I0del of the system. This IIOdel is very useful for the study of power flow considerations, power factor and harmonic content. The proposed control scheme described here with its good dynamic responce, its stable operation and constant torque capability over a wide speed range from stand-still up to twice speed and for both motoring as well as generating operations ensure its advantages. The posaibility of four-quadrant operation by interchanging two of the three phases of the stator anticipate that this technique possibly find place in industry. where the quick responce is of prillary interest. The scheae provides continuous and contactless adjustement of the extended speed range for slip-ring induction motors. A reduction of reactive power requirellent is obtained by using a position detector to control the firing of the current source conTerter from one side and a modified six-pulse bridge conTerter with two auxiliary thyristors froll the ether side. However, other factors on effect of circuit and IIachine paraaeters as well as en dynamic modelling and control have to be worthy for further investigations.

ACKNOWLEWEMENTS The author greatly acknowledge the facilities placed at his disposal by the "Insti tut Superieur de Techniques Appliquees, Universite Nationale du Zalre~ Kinshasa and the useful suggestions discussed with Prof. Dr. Eng. M. S. Morsy, Faculty of Engineering, Ain Shams University, Cairo, Egypt. REFERENCES

Dubey, G.K., Pillai, S.K., and P.P. Reddy (1975). Analy s is and design of a doublyfed chopper for speed control of slip-ring induction motors. Part I, 11, IEEE Trans. rnd. Electron. & Control Instrum. IECI-21, 522-538. Farrer, W. (1913). Quasi-sine-wave fully regenerative inverter. Proc. lEE, Vol.120,9. Maag, R.B. (1971). Characteristics and applications of current source/slip regulated a.c. induction motor drives. IEEE IGA Conf. Record, 411-416. McMurray, w. ( 1978). The performance and analysis of a single-phase current-fed inverter with counter emf-inductive load. IEEE Trans. Ind. APplt IA-14, i, 319-329. Ohno, M. and M. Akama tau 1:9 68). Secondary excitation of an induction motor using a self-controlled inTerter. Electr. Ens. Jap. 88. 16-86. Pareah, C.S. and K.H.J. MA (1975). Rotor chopper control for induction motor drive: TRC strategy. IEEE Trans. Ind. Appl. IA-'1. 1. 43-49. Phillipe, K.P. (1911). Current source conTerter for a.c. IIOtor driTes. IEEE IGA ConI. Record, 385-,92. Said;A:'I.' (1979). A variable speed induction 1I0tor using an autopiloted static frequency converter. 5th ConI. on Automatic Control, EHCAC-Caire, 130-140. Said, A.I. (1980). Performance and analysis of improved power faotor induction motorthyristor cascade using modified phasecontrolled converter. 4th Int. Conf. of Eleo, Machines, ICEM-II, Greece, 876-885. Said, A.I. (1982). On asymmetrical operation of slip energy recovery drives. 5th Int. ConI. of Elec. Machines, ICEK-II, Hungary, 501-510. Said, A.I. (1983). On analysis and speed control of i~duction motor-thyristor cascade using current source converter. IASTli:D Int. SY!lposium on Applied InIormatics, France, 251. Shepeered, W. and A. Q. Khalil (1910). Capacitive compensation of a thyristor controlled slip energy recovery system. Proe. lEE, Vol. 117, ~, 948-956. Smith, G.A. (1977). Static scherbius syst.. of induction 1I0tor speed control. Proo. ~, Vol. 124, .2" 557-560. -Wan1. N.S. and M. Rallamoorty (1977). Chopper controlled slip-ring induction motor. IEEE Trans. Ind. Eleotron. & Control Instrua. IECI-24.£, 153-161.