SUPERSATURATED SYNCHRONOUS MACHINE DESCRIPTION AND MODELISATION

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SUPERSATURATED SYNCHRONOUS MACHINE DESCRIPTION AND MODELISATION

A. Mailfert, A. Rezzoug, P. Manfe

To cite this version:

A. Mailfert, A. Rezzoug, P. Manfe. SUPERSATURATED SYNCHRONOUS MACHINE DESCRIP- TION AND MODELISATION. Journal de Physique Colloques, 1984, 45 (C1), pp.C1-725-C1-728.

�10.1051/jphyscol:19841148�. �jpa-00223620�

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JOURNAL DE PHYSIQUE

Colloque C1, supplkment a u n o i, T o m e 45, janvier 1984 p a g e C1-725

SUPERSATURATED SYNCHRONOUS MACHINE DESCRIPTION AND MODELISATION

A. M a i l f e r c , A. Rezzoug and P . Manfe

Groupe de Recherche en EZectrotechnique e t Ezectronique de Nancy (G.R.E.E.N.), E.N.S. E.M., 2 rue de Za CitadeZZe, 54040 Nancy Cedex, Prance

RESUME - L e s a u t e u r s d e c r i v e n t et analysent un nouveau t y p e d e m a c h i n e syn- c h r o n e supraconductrice dans laquelle la bobine s u p r a c o n d u c t r i c e e s t fixe. Aprks e n avoir evalu6 l e s p e r f o r m a n c e s en, couple volumique, les a u t e u r s indiquent I'Ctat d ' a v a n c e m e n t d e leur p r o g r a m m e experimental.

ABSTRACT

-

A new c o n c e p t of cryogenic synchronous m a c h i n e is described a n d analysed. In this t y p e of machine, t h e superconducting coil is motionless. In t h i s paper, a f t e r a n evaluation of t h e unit volume torque, a comparison with a conventionnal high power high number of poles machines is made. T h e l a s t p a r t i s d e v o t e d t o indications a b o u t t h e e x p e r i m e n t a l program .under development.

I - INTRODUCTION

T h e application of superconductors t o a.c machines with a low number of poles is now widely studied in many c o u n t r i e s /I/. O u r paper deals with a new c o n c e p t of superconduc- t i n g machine a d a p t e d t o t h e design of a high number of poles a.c machine. In t h i s concept, a l a r g e volume of r o o m - t e m p e r a t u r e f e r r o m a g n e t i c m a t e r i a l (such a s iron o r iron - c o b a l t alloy) i s conveniently shaped in o r d e r t o c r e a t e a multipole configuration of m a g n e t i c field when i t is polarised by t h e field of a superconducting soienoTd. T h e r o t a t i o n of t h e f e r r o - m a g n e t i c m a t e r i a l is used t o obtain e.m.f. a t t h e t e r m i n a l s of a room t e m p e r a t u r e multipole a r m a t u r e winding. T h e best p e r f o r m a n c e s a r e o b t a i n e d if t h e iron is deeply s a t u r a t e d (SUPERSAT u r a t e d )

In t h i s paper, will b e p r e s e n t e d :

-

The g e n e r a l c o n c e p t of SUPERSAT a.c. m a c h i n e / 2 / .

- T h e t h e o r e t i c a l evaluation of t h e t o r q u e p e r unit volume and a comparison with conventionnal high power, high number of poles a.c. machines.

- S o m e indications a b o u t p r o t o t y p e SUPERSAT 01 under construction.

I1 - THE GENERAL CONCEPT OF SUPERSAT A.C. MACHINES

In a c c o r d a n c e with t h e principle described in t h e preceding introduction, t h e main e l e m e n t s of SUPERSAT a.c. m a c h i n e a r e t h e following (Fig.1) :

(a) (b) (c)

Fig 1

-

Schematic diagram of SUPERSAT a.c. machine (a) Longitudinal c r o s s s e c t i o n (b) Inductor p i e c e (c) A r m a t u r e disc

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19841148

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C1-726 JOURNAL DE PHYSIQUE

- A superconducting solenoid (1) with a room t e m p e r a t u r e working zone.

- Several r o t a t i n g discs (2) locked o n t h e s h a f t (3) of t h e m a c h i n e ; e a c h of t h e m f i t t e d with p l a r g e iron plugs.

- Fixed a r m a t u r e (4) discs with 2 p poles number a n d q phases number interleaved with t h e r o t a t i n g discs. In order t o r e d u c e e d d y currents, t h e elenrer-iiary conductors a r e finely divided, a s t h o s e of l a r g e superconducting g e n e r a t o r s /3/

- An e l e c t r o m a g n e t i c s c r e e n ( 5 ) is provided by a conducting cylinder, just a t t h e periphery of t h e room t e m p e r a t u r e working zone. It p r o t e c t s t h e superconducting coil against t h e fringing fields of t h e c e n t r a l part.

Assuming t h a t :

- t h e plug m a t e r i a l is supersaturated, with a s a t u r a t i o n value of m a g n e t i z a t i o n p,M,

- t h e z- period 2 b of t h e discs and a r m a t u r e windings is much lower t h a n t h e pole pitch Cp - t h e length L of t h e machine is well a b o v e Zrp

i t is e a s y t o show t h a t t h e maximum peak t o peak variation of t h e axial induction is : ( A B ) m a x =

g

^~ ^o ^~ ^s ( 1 . 1 )

= a poMs

I t will be shown t h a t a n o p t i m a l v a l u e ~ o f power is obtained when 112 < a 4. The classical values p , ~ , ~ 2 , 2 T ( i r o n ) o r poM,w2,4T(Fe-Co) show t h a t t h e maximum (A8)values a r e limited in t h e r a n g e of 1.1-2.2T (or 1.2-2.4T) in t h e SUPERSAT concept. C o m p a r e d t o t h e corres- ponding values of 2T classically realized in t h e conventionnal multipole a.c machine, t h i s .result would s e e m t o show t h a t SUPERSAT c o n c e p t is n o t advantageous ! In s p i t e of this particularity, i t will b e shown in t h e n e x t p a r t t h a t t h e unit volume t o r q u e of SUPER- SAT c a n b e higher t h a n t h a t of conventionnal machines. T h e main reasons .being t h e following :

- T h e filling f a c t o r of t h e iron f r e e SUPERSAT a r m a t u r e is b e t t e r , t h e s h a p e of t h e design leads t o a n i m p o r t a n t volume of energy conversion.

- T h e iron plugs being s a t u r a t e d , t h e i r r e l a t i v e permeability is not f a r f r o m unity : t h e whole working z o n e h a s a n "iron f r e e " behaviour when s u b j e c t e d t o t h e field of a r m a t u r e windings.

T h e s e t w o c i r c u m s t a n c e s allow t h e a r m a t u r e c u r r e n t of SUPERSAT t o b e q u i t e higher t h a n t h a t of a conventionnal machine, leading t o a large value of t h e unit volume torque.

Moreover, o t h e r p a r t i c u l a r i t i e s of t h e c o n c e p t must b e noticed : - No moving coils, a l l t h e r o t a t i n g p a r t s a r e rigidly locked.

- Z e r o t o r q u e applied t o t h e s t a t i c superconducting coil.

111

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MODELISATION - UNIT VOLUME TORQUE EXPRESSION

With t h e hypothesis described in t h e previous c h a p t e r , a n d assumlng a n a r m a t u r e modeli- s a t l o n w h e r e all t h e winding s p a c e i s filled w ~ t h copper, with a m e a n c u r r e n t density K, 3 (0)

,

t h e v a r ~ a b l e flux density B(0) f o r R c p < R m a y b e r e p r e s e n t e d by a s q u a r e - function. T h e f ~ r s t h a r m o n i c : ₂

~ ~ ( 0 ) = 71 a p 0 M , cos p 0 (2.1)

is used t o c a l c u l a t e t h e t o r q u e when a sinuso'idal distribution is assumed for c u r r e n t density :

J,(B) = K, J M cos C p ( e +

k ) I

^(2.2)

In polar coordinates, t h e e l e m e n t a r y t o r q u e o n volume :

d 2 v = 2b ( I - a) p d p d 8 (2.3) is given by t h e relation :

d2i? ( p 8) = pB1 (8) x $ I 1 (€0 X dp (2.4) w h e r e :

d I (8) = zb (1 - a) R ~(0) d e J ~

1 (2.5)

BY i n t e g r a t i o n of t h e relation (2.4), w e obtain ?he unit volume t o r q u e

2 L

K~ c ~ ~ M c o s ~ R@

t )

~ J ~

v

^(2.6)

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w i t h :

1 2

K = - a ( 1 - a ) ( I - E l ⁾K r

T 71 R 2 (2.7)

In relations (2.6) e t (2.7)

-

a ( I - a ) i s o p t i m a l f o r a e q u a l t o 0.5

-

F a c t o r [I - ($)'I is l i m i t e d by m e c h a n i c a l c o n s t r a i n t s and is smoothly varying f o r low values of

2

r a t i o

.

A r e a l i s t i c value of t h i s r a t i o should b e f o r e x a m p l e R 1

-

^0.5.

K 2

R -

-

T h e s a t u r a t i o n induction OM,) value lies, a s known, b e t w e e n 2 a n d 2.4 Tesla.

- Maximum a r m a t u r e c u r r e n t density J M , is mainly depending on t h e cooling process.

-

C o p p e r filling r a t e K r is function of phase t o phase insulation a n d d i r e c t l y depending o n t h e voltage level. For lowest voltages, a v a l u e K r g r e a t e r t h a n 0.3 c a n b e obtained.

- T h e a n g l e is r e l a t e d t o t h e v o l t a g e and t h e power f a c t o r . T h e maximum.of

2

is obtained

when = 0 v

Assuming [ = 0, t h e a r m a t u r e field c a n b e w r i t t e n : H = ( I - a ) - 1 R ~ K , J ~

P (2.8)

We c a n t h e n d e f i n e r a t i o b e t w e e n t h e inductive d r o p v o l t a g e modulus and t h e e.m.f.

F r o m (2.1) a n d (2.8), w e obtain :

6 ^=!![I-a]& R I J M

Z C 1 p M (2.9)

A t t h i s s t e p , t w o t y p e s of l i m i t a t i o n a p p e a r , t h 2 f i r s t o n e is d u e t o t h e r m a l c o n s t r a i n t s which limit t h e c u r r e n t density t o JI

,

t h e second o n e is r e l a t i v e t o B r a t i o which c a n n o t e x c e e d limit v a l u e 8,

F r o m t h e relation (2.9) w i t h B ⁼BI ,a particular v a l u e of R l J M could b e deduced :

2 M

R l 0 J l = P

P

^B, ^(2.10)

F o r R I J l < R ~ ~t h e on1 c o n s t r a i n t is a t h e r m a l one. T h e a b s o l u t e maximum unit volume J ~ t o r q u e (given by (2.6) with

{

⁼0) is linearly increasing w i t h R J I product a n d d o e s n o t de- pend on t h e number of pole pairs, a being c o n s t a n t ( N 0 . 5 ) .

If R > R 0, t h e condition imposed o n B ( 6 = 6)) l e a d s t o a n o p t i m a l value of a t h a t will b e c a l c u l a t e d f r o m (2.9)

a = --1 ^(2.11)

Thus, t h e o p t i m a l value of a is now ,great& 'than 0.5 meaning t h a t t h e thickness of t h e r o t a t i n g discs is higher t h a n t h a t of t h e a r m a t u r e discs. C o r r e l a t i v e l y _1'

-

( A B ),,,,

,

increases.

T h e a b s o l u t e maximum of given by (2.6) b e c o m e s :

t r ~ v ) , . , = 3p0 (K, R ~ J ~[ 8 ) B~ ~ ( 1 + TIK ( R ~ J , ) / ( 2 8 ) P M ~ ) (2.12) A s a n example, by taking BI

7

0.5, p,M, = 2.2T aLd K K , = 0.3, t h e c u r v e s of

vmax

i n t e r m s of R 1 3 1 0 r p a r e r e p o r t e d in f ~ g u r e s 2 a n d 3.

-

_I'

F o r a comparison, in f i g u r e 3, a t y p i c a l

($

of classical a.c synchronous machine is p l o t t e d / 4 /

( r / v , )

( r / r )

5 0 0 ; ( k ~ / m ~ ) Bl = . 5 ~ 3 7

502

= 6

4 0 0 . = 4

4 0 0 ,

300..

200..

1 0 0

R I J ~ x I O - ~

2 4 6 8 1 0 ( ~ / m ) *

( ~ N / K J ' ) B I = . 5 x 7 0 - 6 = 1 2

, l o 8

/---

⁶

.--

4

-.. . - . .--....-.-....-..---. - - - 2

P

2 6 1 0 1 4 1 8 2 2 2 6

Fig. 2 - Unit volume t o r q u e versus F i g 3 - Unit volume t o r q u e versus

R l J l product n u m b e r pole pairs p ( d o t t e d

line f o r conventional salient p o l e s a.c. m a c h i n e s

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Cl-728 JOURNAL DE PHYSIQUE

R e a l i s t i c values o f R = 0.35m a n d J , = 0.20 A / m m z should give a

0

value of 275 k ~ / m ' fo r

p 7 4.

As a n example, t a b l e 1 gives t h e c o m p a r e d dimensions of a p a r t i c u l a r 44 MVA SUPERSAT design a n d t h e dimensions / 5 / of a conventionnal m a c h i n e :

Conventionnal salient poles machines

Appparent power S M ⁼ 44 MVA Speed r o t a t i o n N = 500 r-p.m

Pole pairs p = 6

R o t o r d i a m e t e r DI = 3.70 m R o t o r l e n g t h L, =

.

^{78 m}

Unit volume t o r q u e

7 r

= 100 k ~ / m '

SUPERSAT structure (10 armature discs)

M ^: 44 MVA

N = 500 r.p.m

TABLE 1

IV

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EXPERIMENTAL PROTOTYPE SUPERSAT 01

An e x p e r i m e n t a l p r o g r a m is now under development in G.R.E.E.N. Laboratory in association with C.E.A. SACLAY. A f i r s t p r o t o t y p e using a single a r m a t u r e disc of d i a m e t e r 3 0 c m a n d t w o polar wheels with p = 8 i s under construction.

T h e e x p e r i m e n t s will d e a l with field distribution and m e a s u r e m e n t s of t h e e l e c t r i c a l parame- t e r s of t h e machine. T h e maximum p e r f o r m a n c e being d i r e c t l y dependent o n t h e a r m a t u r e c u r r e n t density J,

,

f u r t h e r d e v e l o p m e n t s will include high p e r f o r m a n c e cooling of t h e a r m a t u r e disc.

V - CONCLUSION

T h e SUPERSAT c o n c e p t applied t o a.c machines with a high number of poles, p r e s e n t s s e v e r a l i n t e r e s t i n g f e a t u r e s :

- A solid iron r o t o r without windings ; - A t o r q u e f r e e superconducting fixed coil ; - An iron f r e e , e a s y t o cool a r m a t u r e winding.

T h e e x p e c t e d high values of unit volume t o r q u e would allow SUPERSAT t o c o m p e t e favou- rably with t h e classical salient poles machines, i n t h e r a n g e of high power, low speed applications.

REFERENCES / I / J.L. SMITH

IEEE Transactions o n m a g n e t i c s - Vol Mag 19 - N0.3 - May 8 3 ( P a r t 1) /2/ A. MAILFERT

F r e n c h p a t e n t ANVAR 81-19620 - O c t o b e r 1981 /3/ M.R. PATEL a n d a l l

Designing P a n c a k e Coils of a L a r g e Superconducting G e n e r a t o r f o r E l e c t r o m a g n e t i c a n d T h e r m a l Loads - IEEE o n PAS - Vol PAS.102 - no 8

-

August 1983

141 J.H. WALKER

L a r g e Synchronous machines - Oxford S c i e n c e Publications

-

1981 / 5 / Alsthom A t l a n t i q u e d o c u m e n t