842 IEEE Transactions on Energy Conversion, Vol. 3, No. 4, December 1988

S'iLDIES O B THE USE OF COiJVZNTIONAI, I i 6 U C T I O N MOTORS AS

SEW-EXCITED IiJDUCTION GETJEPATORS - S . S . W r t h y , B . P . Singh C .Nagamani K . V . V . S a t y an a r ay ana, Department of E l e c t r i c a l Engineer ing, Cent ra l Power Research I n s t i t u t e Indian Railways Indian Ins t i t u t e of Techno logy, New Delhi-110016 ( I n d i a ) .

Bangalore. Eombay

ABSTRACT: The paper i l l u s t r a t e s t he s u i t a b i l i t y of u s i n g a normal three-phase induc t ion motor a s a capac- i t o r s e l f - exc i t ed induc t ion gene ra to r (SEIG). The thermal l i m i t of t h e s t a t o r windings being t h e l i m i t i n g f a c t o r , t he c a p a c i t y of t h e SEIG i s de te rmined . The s t eady- s t a t e performance of such induc t ion gene ra to r s , ma in ta in ing a cons t an t t e rmina l v o l t a g e i s ana lysed under r e s i s t i v e and r e a c t i v e loads . Typica l exper i - mental r e s u l t s a r e a l s o p re sen ted . An a n a l y t i c a l method employing Newton-Raphson technique i s used t o o b t a i n the d e s i r e d performance. C e r t a i n performance i n d i c e s a r e de f ined which would p rov ide g u i d e l i n e s i n t h e development of i nduc t ion gene ra to r systems inc lud - i n g t h e v o l t a g e r e g u l a t o r . It has been f cu rd t h a t f o r normal low power motors , t he m a x i r " power t h a t c a n be ex t r ac t ed as gene ra to r s i s 148% t o 160% of t h e motor r a t i n g f o r r e s i s t i v e loads and 118% t o 128% of t h e motor r a t i n g f o r 0.8 lagging power f a c t o r (PF) loads . Capac i t i ve r e a c t i v e volt-ampere(var) r equ i r ed t o ma in ta in cons t an t v o l t a g e a t 1 .0 p.u. speed i s i n t h e range 85% t o 140% of t h e power r a t i n g of t h e motor w i th r e s i s t i v e loads and 100% t o 140% wi th l agg ing r e a c t i v e loads .

INTRODUCTION

A three-phase i r d u c t i o n machine can be made t o work a s a s e l f - exc i t ed gene ra to r when i t s r o t o r i s d r i v e n a t s u i t a b l e speeds by a n e x t e r n a l prime mover a d i t s e x c i t a t i o n i s provided by connec t ing a three-phase c a p a c i t o r bank a t t h e s t a t o r t e r m i n a l s . The irduced emf a d c u r r e n t i n the s t a t o r windings w i l l con t inue t o r i s e u n t i l a n equ i l ib r ium i s a t t a i n e d due t o t h e magnet 1 c s a t u r a t i o n i n t h e machine. This t o p i c has r ece ived cons ide rab le a t t e n t i o n i n r e c e n t y e a r s c1-81 i n v iew of t h e s u i t a b i l i t y of i nduc t ion gene ra to r s f o r i s o l a t e d power gene ra t ion us ing convent iona l and renewable energy sources .

Such a n induc t ion gene ra to r compares f avcurably i n c o s t , ea se of o p e r a t i o n and maintenance wi th a convent iona l a l t e r n a t o r [7,81. emphasis on energy problems, t h e development of s u i t a b l e low c o s t i s o l a t e d power g e n e r a t o r s , d r i v e n by energy sources such as wind, b iogas e t c . , i s indeed a promis ing a l t e r n a t i v e [ 4 1. The a c c e p t a b i l i t y of t hese gene ra to r s a s v i a b l e gene ra t ing u n i t s would be decided by t h e i r a b i l i t y t o p rov ide des i r ed v o l t a g e and frequency a t a l l loads and speeds . The development of s t a t i c power conve r t e r s f a c i l i t a t e s c o n t r o l of t h e generated power t o t h e r equ i r ed v o l t a g e o r frequency l e v e l s C2-43.

Owing t o t h e changed

83 WN 027-5 A paper recommended and approved tby the I E E E Ro ta t ing Machinery Committee of t he I E E E Power Engineer ing Soc ie ty f o r p r e s e n t a t i o n a t the IEEE/PES 1988 Winter Meeting, New York, New York, January 31 - February 5 , 1988. Manuscript submi t ted August 18, 1987; made a v a i l a b l e f o r p r i n t i n g December 2 , 1987.

Tro p o s s i b l e a l t e r n a t i v e s are a v a i l a b l e i n deve lop ing such gene ra t ing systems. One i s t o r e d e s i g n t h e i r d u c t i o n machine t o o b t a i n t h e r equ i r ed gene ra to r performance an3 the o t h e r i s t o exp lo re t h e s u i t a b i l i t y of u s i n g a n a v a i l a b l e induc t ion motor a s a SEIG. While t h e published pape r s [5-81 re la te mainly t o a n a l y t i c a l t echniques , no work i s r epor t ed r ega rd ing t h e d e s i g n ard development of such gene ra to r s . I n p a r t i c u l a r , t h e a s p e c t r e l a t i n g t o t b c use of commercially a v a i l a b l e motors as gene ra to r s has not been r e p o r t e d . I f i t c a n be e s t ab l i shed by a proper s tudy t h a t t h e normal motors c a n be employed a s g e n e r a t o r s , cons lde rab le expend i tu re and e f f o r t towards a t a i l o r made d e s i g n of t h e genera- t o r c a l d be e l imina ted . Such a s tudy has been u rde r - t aken i n t h i s paper.

It i s d e s i r e d t h a t t h e i d u c t i o n gene ra to r provides a c o n s t a n t te rmina l v o l t a g e under va ry ing l aods . I n p r a c t i c e , a drop i n both t h e t e rmina l v o l t a g e and f requency wi th inc reas ing load i s an observed f e a t u r e . A cons tan t t e rmina l v o l t a g e a l o n e impl ies a n inc reas ing v a l u e of a i r gap f l u x f o r t h e induc t ion gene ra to r , which would r e s u l t i n a cont inuous ly va ry ing magnet i s ing r e a c t a n c e . A cons t an t 'air gap v o l t a g e t o f requency ' r a t i o ensures t h e ope ra t ion of t h e induc t ion gene ra to r a t a cons t an t a i r gap f l u x . Hence, i n t h i s a n a l y s i s t h e c r i t e r i o n of ma in ta in ing a cons t an t 'air gap v o l t a g e t o f requency ' r a t i o i s cons idered . However, because of t h e ease of measurement, t he exper imenta l r e s u l t s have been obta ined under a cons t an t ' t e rmina l v o l t a g e ' cond i t ion . S ince t h e d i f f e r e n c e between t h e air gap v o l t a g e and t h e t e rmina l v o l t a g e i s i n s i g n i f i c a n t , t h e consequent e r r o r s can be ignored . The a n a l y t i c a l method would be more involved i f r e s u l t s under cons t an t t e rmina l v o l t a g e had t o b e obta ined i n s t e a d of t hose under cons t an t f l u x .

For t h e case under s t u d y , i t i s d e s i r a b l e t h a t t he machine f u n c t i o n s e q u a l l y w e l l e i t h e r as a motor or as a g e n e r a t o r . I n the case of a s q u i r r e l cage induc t ion motor a c t i n g as a g e n e r a t o r , hea t ing of t he s t a t o r wi rd ings i s t h e l i m i t i n g f a c t o r on the c a p a c i t y of power gene ra t ion r a t h e r t h a n the r o t o r s i n c e t h e r o t o r cage i s capable of wi ths tanding cons ide rab le thermal overload . I n t h e case of a n induc t ion gene ra to r , t he s t a t o r windings c a r r y a c u r r e n t equa l t o t h e vec to r d i f f e r e n c e of t h e r o t o r c u r r e n t and t h e magnet i s ing c u r r e n t whereas i n t h e same machine a c t i n g a s a n induc t ion motor, t he s t a t o r windings c a r r y a c u r r e n t equa l t o t h e v e c t o r sum of t h e r o t o r c u r r e n t and the magnet i s ing c u r r e n t . Thus t h e a l lowab le range of i nduc t ion gene ra to r ope ra t ion with a n imposed l i m i t on the r o t o r c u r r e n t does no t c o n t a i n t h e e n t i r e a v a i l a b l e range of s t a t o r c u r r e n t . This imp l i e s t h a t power can be ex t r ac t ed from t h e gene ra to r even under the cond i t ion when t h e r o t o r c u r r e n t i s more than i t s r a t e d v a l u e and the s t a t o r c u r r e n t i s w i th in i t s maximum l i m i t . Therefore , i n t h i s s tudy t h e fu l l - load v a l u e of t h e s t a t o r cu r ren t has been t aken t o be the l i m i t i n g c o n d i t i o n f o r power gene ra t ion . The c a p a c i t i v e va r requi rement of t he machine t o ma in ta in a cons t an t t e rmina l v o l t a g e and t h e maximum power t h a t c a n be obta ined from t h e machine working as a gene ra to r a r e de te rmined . S ince most e l e c t r i c a l l oads a r e of l agg ing PF, t he performance of t h e gene ra to r w i th lagging PF loads i s a l s o s tud ied and t h e c a p a c i t i v e va r requi rement i s de termined .

0885-8969/88/12OO-0842$01 .OOO 1988 IEEE

843

I n earlier papers C5,63, a n a l y t i c a l methods have been expla ined f o r s o l v i n g a s e t of two nonl inear equa- t i o n s encountered i n t h e i n i t i a l s t a g e of t h e a n a l y s i s . Th i s paper i n i t i a l l y e x p l a i n s a modified a n a l y t i c a l method f o r de te rmining t h e range of c a p a c i t i v e va r requi rements f o r ma in ta in ing a cons t an t f l u x and f o r ob ta in ing performance wi th a des i r ed l e v e l of vo l t age r e g u l a t i o n .

S tud ie s a r e made on fou r t y p i c a l machines of low power r a t i n g s a v a i l a b l e commercially i n o rde r t o o b t a i n t h e i r behavioura l p a t t e r n s . Relevant t h e o r e t i c a l and exper imenta l r e s u l t s a r e presented and d i scussed .

exper imenta l ly . The s a t u r a t e d p o r t i o n of c t e r i s t i c c a n be l i n e a r i s e d and expressed

t h i s ohexa- i n t h e form

V g /F = K1 - K2 xm

where R, a d IC2 depend upon t h e d e s i g n of t h e machine.

A cons t an t V /F of 1.0 p.u. w i l l approximate ly ensu re a

t e rmina l v o l t a g e Vt/F of 1.0 p.u. a t a cons t an t s p e d g

w= 1.0 p.u.

A p p l y i n g K i r c h o f f ’ s V o l t a g e Law t o t h e c i r c u i t Of F i g . 1 and r e a r r a n g i n g t h e t e r m s , w e g e t

ISZS = 0 (2)

where

ANALYTICAL METHOD

The p resen t a n a l y s i s fo l lows t h e normal assump- t i o n s a l r e a d y m e n t i o n d i n earlier papers C5-81, cons ide r ing t h e v a r i a t i o n of t h e magnet i s ing r e a c t a n c e wi th s a t u r a t i o n a s t h e b a s i s f o r c a l c u l a t i o n s . The s t eady- s t a t e equ iva len t c i r c u i t h a s been used t o p r e d i c t t h e performance of t h e gene ra to r . F ig .1 such a c i r c u i t of an induc t ion gene ra to r w i th a r e s i s t i v e load ,

shows

R JF j X l S JXlr Since Is # 0, Z s = 0 ( 3 )

Rr - F -U

J- -jx T-FZ’ V

F 9.

I

C

Fig .1 . Equiva len t c i r a i t of t h e induc t ion gene ra to r w i th load .

where,

R s , Rr = per phase s t a t o r and r o t o r r e s i s t a n c e

xlS,xlr= per phase s t a t o r and r o t o r leakage r e a c t a n c e s

r e s p e c t i v e l y .

r e s p e c t i v e l y .

X = magnet i s ing r eac t ance . x m (p.u.1

F ig .2 . V a r i a t i o n of V /F wi th x - a 9 m

per phase c a p a c i t i v e r e a c t a n c e of t h e termi- n a l c a p a c i t o r .

load r e s i s t a n c e per phase .

p.u. f requency and speed r e s p e c t i v e l y .

per phase s t a t o r and r o t o r c u r r e n t s .

load c u r r e n t per phase.

t e rmina l and a i r g a p v o l t a g e r e s p e c t i v e l y .

= I n p u t , a d output power r e s p e c t i v e l y .

l i n e a r approximation

T h i s equa t ion , a f t e r s e p a r a t i o n i n t o r e a l and imaginary p a r t s , can be r ea r r anged i n t o two nonl inear equat ions . I n t h e earlier a n a l y s i s , t h e l o a d cha rac t e r - i s t i c s were obta ined f o r a S e t of v a l u e s of capac i t ance , speed and load such t h a t xm and F were i d e n t i f i e d a s

unknown q u a n t i t i e s and solved hy d i f f e r e n t methods desc r ibed i n r e f e r e n c e s C5-71. But h e r e , f o r a c o n s t a n t f l u x i . e . , V /F, t h e v a l u e s of c a p a c i t a n c e and p.u.

f requency have t o be obta ined f o r vary ing loads . Thus equa t ion ( 3 ) can be w r i t t e n i n te rms of R and F. The

r e l e v a n t non l inea r equat ions a re g iven i n t h e Appendix. These equa t ions can be solved us ing s tandard Newton- Raphson technique [5,61 assuming c e r t a i n i n i t i a l v a l u e s f o r xc and F. The performance of t he gene ra to r i s

determined us ing t h e fo l lowing equa t ions obta ined from the equ iva len t c i r c u i t of F ig .1 .

g

(Al l t hese q u a n t i t i e s a r e r e f e r r e d t o t h e s h a t o r and are a t base f r equency) .

AS a l r eady mentioned, t h e magnet i s ing Charac te r - i s t i c of t h e machine is of mime jmuortance i n t h e ana l - y s i s . F ig .2 shows such a c h a r a c t e r i s t i c f o r t h e s e machines, r e l a t i n g the a i r gap v o l t a g e (V /F) t o t h e magnet i s ing r e a c t a n c e (x ) as obtained

844

(V / F ) Is =

RS j xc RL - + j x -- Is 2 F F RL-jFx

vt = ; c a p a c i t i v e va r = vt ( I ~ - I ~ 1

(4)

(5)

The a n a l y s i s has been exterded f o r r e a c t i v e loads by r e p l a c i n g % w i t h an appropriate per phase load

imped ance ZL. Based on t h e above a n a l y t i c a l t echn i -

que, a computer program has been developed t o c a l c u l a t e t h e performance of t h e gene ra to r .

DETAILS OF THE EXPERIMENT

Power gene ra t ion was a c h i e v d by d r i v i n g t h e i r d u c t i o n gene ra to r a t t h e r a t e d speed by a d . c . motor. S u i t a b l e three-phase c a p a c i t o r bar,ks were connected to provide e x c i t a t i o n . c o n s t a n t by a d j u s t i n g the c a p a c i t a n c e a t a l l l oads . Various inpu t ard ou tpu t q u a n t i t i e s were monitored f o r each load s e t t i n g .

The t e rmina l v o l t a g e was maintained

RESULTS AMI DISCUSSION

The r e s u l t s of t h e load t e s t i n g a re expressed i n p.u. v a l u e s s o as t o a l low comparison of t h e performance of t h e s e machines a s g e n e r a t o r s .

(a) General Performance: Tab le s IV and V i l l u s t r a t e the gene ra l performance of t hese machines i n t e r m s of t h e maximum power t h a t c a n be generated without exceed- i n g t h e s t a t o r c u r r e n t l i m i t and t h e range of c a p a c i t - ance r equ i r ed t o ma in ta in a cons t an t t e rmina l v o l t a g e f o r r e s i s t i v e a d r e a c t i v e loads r e s p e c t i v e l y .

(b) Power ou tpu t . : AS an i d e x of gene ra to r performance, a f a c t o r K may be de f ined a s a r a t i o of

of t h e maxinu~li power t h a t can be ex t r ac t ed from t h e machine working as a gene ra to r (without exceeding t h e thermal l i m i t of t h e s t a t o r ) t o t h e r a t e d power ou tpu t

g

of t h e machine a s a motor.

where

VLl IL = l i n e v o l t a g e gene ra to r

COS 0 = power f a c t o r

ard c u r r e n t of t h e

(PF) of t h e load

- r a t e d power of t h e motor Pm

Relevant experimentat ion was c a r r i e d o u t t o check the v a l i d i t y of t h e method of a n a l y s i s . e a r l i e r , i n order t o provide a gene ra l b a s i s of inform- a t i o n , four t y p i c a l motors were chosen f o r i n v e s t i g a t i o n . The parameters of t h e s e motors, as obtained experiment- a l l y , a r e presented i n Tables I a d 11. the cons t an t s K1 and K2, of eqn . ( l ) f o r t h e s e machines

a long wi th t h e unsa tu ra t ed va lue of magnet is ing r e a c t - a c e s , xm.

"synchronous speed t e s t " method desc r ibed i n r e f e r e n c e s C5-61. machines a r e k n o m .

A s mentioned

I t can fur ther be shown tha t Table 111 g ives

K = g

Load PF of gene ra to r These va lues were obtained us ing t h e

Thus t h e magnet is ing c h a r a c t e r i s t i c s of t h e s e

( F u l l load motor e f f i c i e n c y ) x ( F u l l load motor PT) ('1)

The C m p ' J t d v a l u e s of K f o r t hese machines g a r e shown i n Tab les I V a d V from which i t is

T A B L E-I

E l e c t r i c a l D e t a i l s of t h e Machines (No.of po le s t 4 ) .

Machine Make Voltage per L ine c u r r e n t Ra t ing S t a t o r Power base Frequency Phase (v) ( A ) (kW) connec- (kW) (Hz) .

t i o n

I Mawdsley gene ra l i s ed Machine 23 0 8 .2 2.2 a 1.090 50

I1 Kir loska r E l e c t r i c ( I n d i a ) 415 4.9 2.2 n 1.175 50

111 Canadian General E l e c t r i c 23 0 14.2 3.7 Y 1.885 60

I V K i r lo ska r E l e c t r i c ( I d i a ) 41 5 7.6 3.7 n 1.820 50

(U.K.)

(Ca nad a)

Note : Vbase = Rated vo l t age /phase ;

Ibase = Rated a r r e n t phase, a d

'base = 'base 'base'

845

encouraging t o no te that i n a l l t h e machines considered, t he power ou tpu t a v a i l a b l e i s i n t h e r anbe of 148% t c 160% of t h e motor r a t i n g w i t h u n i t y power f a c t o r l oads With 0.8 l agg ing load , on t h e o t h e r hard , t h e a v a i l a b l e power i s i n the r ange of 118% t o 1 2 8 % . This r e d u c t i o n i n a v a i l a b l e power a t lagging r e a c t i v e loads i s t o be expected. It c a n be seen t h a t each motor, wh i l e working a s a gene ra to r , can provide a maximum power t h a t i s w e l l above the v a l u e of t h e motor r a t i n g , a t 1.0 p.u. speed.

(c) Capac i t i ve v a r requi rement : The c a p a c i t i v e v a r r equ i r ed t o ma in ta in a cons t an t V /F of 1.0 p.u. was

d e t e r m i n d f o r a l l t h e machines. The v a r i a t i o n was of c a p a c i t i v e v a r requi rements f o r each machine wi th r e s i s t i v e and l agg ing r e a c t i v e loads i s i l l u s t r a t e d i n F ig . 3 and 4 . t he va lues of t he capac i t ance r e q u i r e d f a l l i n t o an economically v i a b l e r ange .

g

It can b e seen from these f i g u r e s t h a t

TABLE - I1 Parameters of t h e Machines

I 0.062 0.07 0.093 48.58

I1 0.06 0.078 0.084 146.64

111 0.05 0.049 0 .092 9.35

IV 0.053 0 . 0 6 1 0.087 94.58

Another f a c t o r , Kc, may be de f ined as the r a t i o

The range of v a r i a t i o n of of t h e kVAR r a t i n g of t h e t e rmina l capac i t ance t o t h e r a t e d power of t h e motor.

Kc The range of Kc f o r r e s i s t i v e loads i s found t o be 85

t o 140%. F o r t h e case of lagging power f a c t o r l o a d s , t he r ange of Kc i s found t o be 100 t o 185%. Obviously,

t h e r e i s a n i n c r e a s e i n t h e capac i t ance r equ i r ed wi th l agg ing PF loads i n comparison wi th r e s i s t i v e loads .

f o r t hese machines i s i nd ica t ed i n Tables IV and V

(d) R e l a t i v e Magnitudes of Winding. Currents: F i g . 5 a d 6 show t h e r e l a t i v e magnitudes of s t a t o r and r o t o r c u r r e n t s i n t h e genera t ing mode. It i s i n t e r e s t i n g t o no te t h a t t h e magnitude of t h e r o t o r c u r r e n t i s always l e s s t han t h a t of t h e s t a t o r c u r r e n t , a phenomenon observed i n t h e motoring mode. This i s because t h e r o t o r c u r r e n t i s approximate ly i n quadra tu re wi th t h e magnet i s ing c u r r e n t i n both t h e

TABLE - 111 Constan ts of Magnet i s ing C h a r a c t e r i s t i c s

of; Hachines (Eon. 1) x unsa tu ra - K2 m Machine K

1 ted (p.u.1

I 1.714 0 .4 2 . 2 2

I1 1.437 0.334 1 . 5 2 4

111 1.338 0.219 2.70

IV 1.6275 0 .3419 2.35

T:A B L E - I V

Performance w i t h R e s i s t i v e Loads

* Machine var r equ i r ed (p.u.) Capac i tance Power l i m i t Max. Power K ( % ) Kc ( % )

g range ( UF)@ (p.u.1 ( kW)

I 0.59 - 0.645 37 - 47 3 .O 3 .27 1 4 9 87.7 - 96

I1 0.81 - 0.85 17 - 2 1 2.998 3 .52 1 6 0 13.0 - 135

, 1 0 5 . 0 - 115 111 0.69 - 0.75 185 - 224 3 .o 5.66 153

IV 0.58 - 0.67 18 - 25 3 .O 5.46 148 8 6 . 2 - 98.8

T A B L E - V

Performance w i t h Reactive Loads 0.8 PF Load

M a x . P a r e r K % ) Kc ( % ) e! Machine var* r equ i r ed (p .U .) Capaci tance Power l i m i t r ange ( PF)@ (p.u.1 (kW)

I 0.72 - 1.09 4 5 . 0 - 7 9 2.4 2.614 119 108 - 162

1 3 2 - 212 I1 0.95 - 1 . 3 2 19.6 - 3 2 2 .4 2.816 128

111 0.825- 1 .21 762.0 - 425 2.4 4.528 1 2 2 126 - 185

1 0 4 - 170 N 0.704- 1 .15 23.0 - 43 2 .4 4.37 1 1 8

* var Base = Rated Power of t h e machine @ UF = microfarads

846

3.5-

3.2-

2.9-

2.6-

2.3-

0 . a

Table - V (Contd.) 0 . 9 PF Load

Capaci tance range Power l i m i t Max.power K( "I) K&%) g Machine va r r equ i r ed

(P.U.) (1-I P) ( p a . ) (kW)

I 44 - 69 .5 2.697 2 .94 134 103 - 142

19 - 28 2 .697 3 .169 144 147 - 185

252 - 364 2 .7 5 .094 138 120 - 159

2 .7 4 . 9 1 4 133 99 - 142

0 . 6 9 - 0 .95

I1 0 . 9 2 - 1 . 1 6

XI1 0 . 7 9 - 1 . 0 4

IV 0 .67 - 0 . 9 6 22 - 35 -.

I I I C J 0.5 0.6 1.0 1 . 4 1.8 2.2

Power output(p.u.) Fig .3* V a r i a t i o n of c a p a c i t i v e v a r and

susceptance wi th ou tpu t f o r r e s i s t i v e load 5.

( : I , I I , I I I , I V r e f e r t o d i f f e r e n t machines -see TablesI-V)

Power ou tpu t (p .u . )

F i g .4 . V a r i a t i o n of c a p a c i t i v e v a r and capac i t ance wi th p w e r outplltt f o r lagging PF loads .

1.2

0.0 o-2L?d+-h 0.6

Power ou tpu t (P.u.) F ig . 5. * V a r i a t i o n of s t a t o r and r o t o r

1 .o

0.9

- 3

- 0.8 d, c, al !4

2 0.7

0.6

c u r r e n t s w i th power o u t p t f o r r e s i s t i v e loads .

- 0.8 PF

0 .9 PF -- --

/ . 0 /

0.4 0.8 1 . 2 1.6 2.0 Power o u t p u t ( P . u . )

F ig .6 . V a r i a t i o n of s t a t o r and r o t o r c u r r e n t s w i th power ou tpu t f o r lagging PF loads .

847

motoring and gene ra t ing mcdes, and t h e r e s u l t i n g s t a t o r c u r r e n t , s h a m i n F i g s . 5 a d 6 , i s of t he same o rde r of magnitude i n both t h e modes. The re fo re , a t c o n s t a n t r a t ed s t a t o r c u r r e n t , t h e r o t o r c u r r e n t i n t h e genera t - i n g m c d e i s of t h e same order of magnitude a s t h a t . i n t h e motoring mcde. Thus wi th a s t a t o r thermal l i m i t a s t h e b a s i s , t h e r o t o r h e a t i n g a s a gene ra to r would be of t h e same order a s t h a t of t h e motor. Added t o t h i s , t h e r o t o r cage can wi ths tand cons ide rab le thermal a v e r l o d s . The c a l c u l a t i o n of t h e maximum power r a t i n g wi th r a t e d s t a t o r c u r r e n t a s t h e t h e r e f o r e m o r e app ropr i a t e t h a n t h e case where r o t o r c u r r e n t i s main ta ined cons t an t .

c r i t e r i o n i s

(e ) C o r r e l a t i o n between t h e o r e t i c a l and exper imenta l r e s u l t s : 5__

Fig .7 shows a c a p a r i s o n between t h e t h e o r e t i c a l and exper imenta l r e s u l t s i n terms of t h e v a r i a t i o n of s t a t o r c u r r e n t , load c u r r e n t and c a p a c i t i v e va r requi rements f o r a r e s i s t i v e load on machine IV. A c l o s e agreement between t h e t h e o r e t i c a l and expe r i - mental r e s u l t s i s observed, v a l i d a t i n g t h e p red ic t ed r e s u l t s .

C . 6

c .4 ? (4

P

v

0

C' . 2

0 - T h e o r e t i c a l 1 I I

0 . J - 0.J .U 1.0 1 . 4 1.; 2 .2 ' c * o Power c u t p u t ( P . u . )

P ig .7 . Comparison of exper imenta l and t h e o r e t i c a l r e s u l t s ( f o r machine IV) wi th r e s i s t i v e loads . ( a ) gc, ( b ) Is and ( c ) IL .

CONCLUSIONS

The s tudy has confirmed t h a t a normally designed induc t ion motor can be s u c c e s s f u l l y used a s a t h ree - phase s e l f - e x c i t e d gene ra to r f o r low power a p p l i c a t i o n s . For each of t he fou r machines cons idered i n t h i s i n v e s t i g a t i o n , i t has been shown t h a t t h e maximum available power, as a generator, is in the range of 118 percent to 160 percent of' the respective motor rating.

In order to maintain the constancy of the gener- ator terminal voltage, i t has been shown that the value of the capacitance varies over a wide range. machines considered, the desired range of capacitive kVAR variation has been found to be 85 to 185% of the machine rating. The criterion of limiting the stator current in the determination of maximum generated power, has been found t o be appropriate. Test results confirm the validity of the analytical method employed.

The study was extended to cover a range of standard motors up to 100 k W and the results seem to confirm the general trend presented here. induction motors can be employed as self-excited generators, with constant speed prime movers.

For the

Thus normal

ACKNOWLEDGEMENT

Acknowledgements a r e due t o Department of Science and Technology, Government of I n d i a f o r sponsor ing t h i s p r o j e c t . Thanks a r e a l s o due t o P ro fes so r C.S.Jha f 3 r h i s encouragement and t o Dr.A.K.Tandon f o r h i s use- f u l sugges t ions .

REFERENCE S

D.W.Novotny, D .J. G r i t t e r a d G. E. Studtmann , "Self - e x c i t a t i o n i n I n v e r t e r d r i v e r Induc t ion Machines," IEEE Trans.on P.A.S. , Vol.PAS-96, p .1117 -112 5, July/August 1977.

M.B.BreMen a d A.Abbodant i " S t a t i c E x c i t e r s for I d u c t i o n Genera tors , " IEEE Trans . on I . A . , vo l . I ~ - 1 3 , pp. 422-42b, Sept./Oct.1977.

J. A r i l l a g a a d D.B. Watson " S t a t i c Power Con- v e r s i o n from se l f -exc i ted Induc t ion Genera tors ," Proc.IEE, Vo1.25, pp. 743-746, Aug.1978.

D.B. Watson, J. A r i l l a g a and T . Densem, "ContrO- l l a b l e D.C. power supply from w i d - d r i v e r self- exc i t ed I d u c t i o n Machines," Proc . I E E , vo l . 126, pp. 1245-1248, 1979.

S.S. Murthy, O . P . Malik a d A.K. Tandon, "Analy- s is of Se l f -Exci ted I r d u d i o n Genera tors , " Proc . I E E , ~ 0 1 . 1 2 9 , p t .C . , pp. 260-265, 1982.

A.K. T a d o n , S.S. Murthy a d G . J . Berg, "Steady- s t a t e Ana lys i s of Capac i to r s Se l f - exc i t ed Induc- t i o n Genera tors , " IEEE Trans. on PAS, Vol. PAS 103, pp. 612 618, March 1984.

S.S."lurthy, 0 .P .Ya l ik and P . IJalsh, "Capac i t ive V A r requi rements of Se l f - exc i t ed Induct ion Genera tors t o Achieve Des i red Voltage Regulation," presented a t t h e I E E E I n d u s t r i a l and Comrrercial Power Systems Conference, Yilwaukee, 1983.

S . S . Murthy, O.P.Malik, D.Diwan & T.Grant , "A Sol id S t a t e Voltage Regula tor f o r Se l f - exc i t ed Induc t ion Genera tors , "presented a t t h e IEEE I n d u s t r i a l and Commercial Power Systems Conference, Yilwaukee, 1983.

APPENDIX

Equating r e a l and imaginary p a r t s of Z

z e ro a s per Eqn. (3) , and assuming x ls=xl r=xl , we

o b t a i n two non l inea r equa t ions wi th unknoms x and F a s fo l lows:

f ( x c , F ) = CIF3 + C2F2 + (C x +C ) F+C5Xc = 0;

s e p a r a t e l y t o

(A-1) 3 c 4

g ( x c , F ) = (D x +D )F2 + (D3xc+D4) F+D5x = 0 (A-2) I C 2

wherein :

( A - 3 )

848

D, = - D1

Dq = - RLRrC

D5 = - Rr(RL+Rs)

and

c = x + x

3

m 1’

(A-3)

S.Sreenivasa Murthy was born in Karnataka,India on December 6,1946. He received the B.E.Degree

cal engineering from the Indian Institute of Technology (IIT), New Delhi, in 1974.

After teaching a year at the Birla Institute of Technology and Science, Pilani, he joined IIT,Delhi in 1970 as Associate Lecturer and was promoted to the post of ?f.cKurer in 1 9 7 3 . Assistant Professor in 1975, Associate Professor in 1980, and Professor in 1983.

;wing 1975-76 he was at the Department of Electrical Engineering, University of Newcastle upon Tyne(Eng1and) as Visiting staff. Using his sabbatical leave he worked as a Visiting Scientist/Fellow at the University of Calgary (Canada) from November 1980 to Yay 1982. He worked at the R&D department of Kirloskar Electric Co., Bangalore as a visiting in-house Consultant during 1985- 86 and executed several projects relevant to the Industry He was also an adjunct Professor of the Indian Institute of Science,Bangalore, during this year

He has published a number of papers and has edited and published two laboratory manuals. He has completed many Industrially sponsored projects. His current interest area5 include electrical machines, electric drives, thyristor applications, efficient electric energy utilisation, isolated power generators, wind and micro hydro power generation,and engineering education.

He is a Fellow of the Institution of Engineers (India) and a Life Member of the Indian Society for Technical Education. In 1976 he received the President of India Award for the best research paper published i n the Journals of the I.F.(I).

B.P.Singh(SM) was born in Singhiya,India, in 1940. He received the B.Sc.(Engg.) degree in 1963 from BIT, Sindri, Y.E. in Electrical Engrg.in 1966, from Calcutta University, and Ph.D. in 1974, from I I T Delhi.

He was a Senior Fellow at B.E.Colleee,Howrah(l963- 66) and after serving M . I . T . Nuzaffarpur as a faculty member for over a decade (1966-78), he joined I I T Delhi in 1978 as Assistant Professor of Electrical Engrg.and became a Professor in the year 1985. His research interests are in design, analysis and control of electrical machines. He is a life member of Indian Society for Technical Education.