This paper has presented some algorithms for quantitatively evaluating the effect of failures in auxiliary electrical sps- tem on the reliability of a generating unit.. We would like t
Trang 1IEEE T r a n s a c t i o n s o n P o w e r A p p a r a t u s a n d S y s t e m s , Vol PAS-96, no 5 , Septe&er/October 1977
RELIABILITY EVALLIATICN OF THE AUXILIARY ELECTRICAL SYSTFMS C f POWER STATIONS
Manchester Saskatocn
M.F D e f l l i v e i r a
M I S T Manchester
E n v l a n d
ABSTRACT
T h i s p a p e r p r e s e n t s a n o v e l a p p r o a c h t o t h e re-
l i a b i l i t y assessment o f d i f f e r e n t d e s i g n s o f power
s t a t i o n a u x i l i a r y e l e c t r i c a l s y s t e m s T h i s assessment
e v a l u a t e s th e im p a c t o f th e a u x i l i a r y s y s t e m on t h e
a v a i l a b i l i t y o f t h e u n i t i n t e n s o f d e r a t e d s t a t e s o f
t h e u n i t T h i s t e c h n i q u e p e r m i t s t h e r e l i a b i l i t y c o s t
t o be c a l c u l a t e d e a s i l y f o r d i f f e r e n t s y s t e m d e s i g n s
Alr e a l i s t i c f a i l u r e modes were t a k e n in t o a c c o u n t
An e f f i c i e n t c o m p u t e r p r o g r a m u s i n g t h e s e t e c h n i q u e s
has been developed and was used t o o b t a i n t h e r e s u l t s
p r e s e n t e d in t b i s p a p e r
INTROOUCTTON
T h e r e h a s b e e n c o n s i d e r a b l e i n t e r e s t i n r e c e l t
y e a r s t o q u a n t i f y t h e e f f e c t o f g e n e r a t i n g c a p a c i t y on
t h e r e l i a b i l i t y a n d l o n g t e n a v a i l a b i l i t y o f power
systems The e v a i l a b i l i t y o f t h e g e n e r a t i n g u n i t i s a
f u n d a m e n t a l e l e m e n t i n s u c h a n a n a l y s i s However i t
i s w e l l known t h a t t h e g e n e r a t i n g u n i t a v a i l a b i l i t y
b a s d e c r e a s e d a s th e u n i t r a t i n g h a s b e e n in c r e a s e p ;
l a r g e I J n i t s h a v i n g u n a v a i l a ! J i , l i t i e s a s h i g h a s 20%
T h e r e f o r e a r e a l i s t i c q u a n t i t a t i v e a p p r a i s a l o f t h e
r e l i a b i l i t y o f t h e u n i t and t h e components o f i t s sub-
systems i s n e c e s s a r y i n t h e d e s i g n phase from which
t h e i r i m p a c t o n t h e o u t p u t a v a i l a b i l i t y can he e v a l u -
a t e d One component c o n t r i b u t i n g t o t h i s u n a v a i l a b i l -
i t y i s t h e e l e c t r i c a l a u x i l i a r y system and i t s d e s i g n
A l t h o u g h t h i s c o n t r i b u t i o n i s o n l y one f a c t o r o f t h e
o v e r a l l u n a v a i l a b i l i t y i t i s n e v e r t h e l e s s one o f t h e
most d i f f i c u l t t o assess due t o t h e c o m p l e x i t y o f t h e
s y s t e m a n d t h e c o n s e q u e n c e s o f l o s i n g p a r t s o f it
The p r e z e n t s t u d i e s have t h e r e f o r e been c e n t r e d on
a s s e s s i n g t h e i m p a c t o f s u c h a u x i l i a r y s y s t e m s o n t h e
a v a i l a b i l i t y o f t h e u n i t
B a s i c a l l y t h e s e s y s t e m s do n o t d i f f e r g r e a t l y
f r o m a l a r g e s u b s t a t i o n R e f e r e n c e 1 p r e s e n t s a com-
p u t e r i s e d a p p r o a c h fo r a s s e s s i n g th e re l i a b i l i t y o f
s u b s t a t i o n s a n d s w i t c h i n g s t a t i o n s The b a s i c c n n -
c e p t s c o n t a i r , e d i n t h i s r e f e r e n - e werE u t i l i z e d i n t h e
p r o s e n t s t u d y w i t h c e r t a i n i m p r o v e m e n t s and n o d i f i z a -
t i o n s b e l n g made
One o f tk,e assumptions i n r e f e r e n c e 1 i s t i l a t
t n a a v e r a g e o u t a g e t i m e o f a m i n i m a l c u t sex which i s
e l k n i n a t e d by c l o s i n g a n c r m a l l y c p e n o a t h i s t n e t i m e
tab.en t o c l o s e t h e n o r m a l l y open p a t h T t l i s i s e q u i v -
a l e n t t o a s s u m i n g t h a t r;he system does n o t f a i l w h i l e
t h e r e p a i r i s b e i n g c a r r i e d o u t and s e r v i c e i s r e t u r n -
ed t a normal ty r e s t o r l n g a t l e a s t one component o f
t h e m i n i m a l s l i t s e t T h i s a s s u m p t i o r was e l i m i n a t e d
Paper A 76 018-2, recommended and approved by the Power Generation
Committee of the IEEE Power Engineering Society for presentation at the IEEE
PES Winter Meeting and Tesla Symposium, New York, NY January 25-30, 1976
This papr was upgraded to transactions status, F77 008-6, for presentation by title
for written discussion at the IEEE PES Winter Meeting, New York, NY January 30
printing September 30,1976
February 4, 1977 Manuscript submitted August 1 1 , 1975; made available for
i n t h e p r e s e n t w o r k by u s i n g a c o n d i t i o n a l p r o b a b i l i t y approach
Tha p r o g r a m d e s c r i b s d ir:r e f e r e n c e 1 was n o t i n -
t e n d e d t o a n a l y s e e a s i l y e s y s t e m h a v i n g more t h a n one
l o a d p o i n t The a u x i l i a r y e l e c t r t c a l systerr, o f a power s t a t i o n has many l o a d p o i n t s a l ; o f d h i c h may
a f f s c t t h e u n i t o u z p d t by d i f f e r e n t amounts The re-
l i a b i l i t y i n d i c e s o f e a c h l o a d p o i n t o f t h e a u x i l i a r y
s y s t e m d o e s n o t a l l o w t h e i m p a c t o f e a c h l o a d p o i n t o r
c o m b i n a t i o n o f l o a d p o i n t s o n t h e u n i t a v a i l a b i l i t y t o
be e v a l u a t e d v e r y e a s i l y The o v e r a l l r e l i a b i l i t y o f
t h e s y s t e m i s t h e r e f o r e v e r y d i f f i c u l t t o a s s e s s The
p r o b l e m o f a n a l y s i n g m u l t i - l o a d p o i n t s was overcome by
i n t r o d u c i n g a c o n c e p t o f s y s t e m m i n i m a l c u t s e t s a n d
a s s o c i a t i n g w i t h e a c h o f t h e s e c u t s e i t h e r a p a r t i a l
c a p a c i t y s t a t e o r a t o t a l o u t a g e s t a t e o f t h e u n i t These o v e r a l l s y s t e m m i n i m a l c u t s e t s a r e o b t a i n e d
f r o m t h e m i n i m a l c u t s e t s o f t h e i n d i v i d u a l l o a d
p c i n t s F o r e a c h o f t h e f e a s i b l e d e r a t e d s t a t e s o f
t h e u n i t due t o t h e u n r e l i a b i l i t y o f t h e a u x i l i a r y system, t h e e x p e c t e d e n c o u n t e r r a t e a n d a v e r a g e d u r a -
t i o n are e v a l u a t e d u s i n g t h e e q u a t i o n s d e s c r i b e d by
B i l l i n t o n and Groverl.2 From t h e s e v a l u e s an energy
a n d c a p a c i t y r e p l a c e m e n t d e s c r i b e d c o s t a s b y
B i l l i n t o n and R i n g l e e 3 c a n be e v a l u a t e d a n d a s s i g n e d
t o any design changes i n t h e a u x i l i a r y system
LOA0 POINT FAILURE MODES The a n a l y s i s i s commenced b y c a l c u l a t i n g t h e re-
l i a b i l i t y in d i c e s o f e a c h b u s b a r in th e e l e c t r i c a l
a u x i l i a r y s y s t e m The component f a i l u r e modes t h a t
a r e c o n s i d e r e d a r e i d e n t i c a l t o t h o s e d e s c r i b e d b y Grover and B i l l i n t o n l To deduce t h e b u s b a r f a i l u r e modes i t was assumed t h a t t h e p r o b a b i l i t y o f h a v i n g
s i m u l t a n e o u s l y more t h a n th r e e fa u l t y components i s
n e g l i g i b l e a n d t h e r e f o r e o n l y e v e n t s up t o t h i r d o r d e r
w e r e c o n s i d e r e d A l s o tw o fa i l u r e e v e n t s a t a busbar were c o n s i d e r e d in d e p e n d e n t i f t h e s e t o f components
d e f i n i n g one f a i l u r e e v e n t d i d n o t i n c l u d e t h e s e t o f components d e f i n i n g t h e o t h e r f a i l u r e e v e n t T h i s
assumption i s v a l i d because t h e f a i l u r e p r o b a b i l i t y o f any e l e c t r i c a l component i s n u m e r i c a l l y v e r y s m a l l
I was a l s o assumed t h a t , a f t e r a b u s b a r f a i l u r e , n o
o t h e r h e a l t h y component i n t h e p a t n s f r o m any source
t o th e b u s b a r c a n s u b s e q u e n t l y fa i l d u r i n g th e ti m e
t h e p a t h s a r e d e - e n e r g i s e d T h i s i s a c c e p t a b l e b e c - ause t h e components wig e n e r a l l y h a v e a much s m a l l e r
f a i l u r e r a t e when t h e y a r e o u t o f s e r v i c e All t h e a b o v e a s s u m p t i o n s p e r m i t t h e b u s b a r
f a i l u r e modes t o oe i d e n t i f i e d w i t h t h e m i n i m a l c u t
s e t s a s s o c i a t e d w i t h t h e m i n i m a l p a t h s f r o m a l l t h e sources o f s u p p l y to th e b u s b a r u n d e r c o n s i d e r a t i o n
An e f f i c i e n t a l g o r i t h m was developed t o deduce these
m i n i m a l p a t h s and c u t s e t s f r o m a s i m p l e d e s c r i p t i o n
o f t h e t o p o l o g y o f t h e n e t w o r k T h i s m e t h o d o f d e d u c -
t i o n fa c i l i t a t e d th e e v a l u a t i o n o f th e m i n i m a l c u t
s e t s f o r e v e r y s y s t e m b u s b a r u s i n g t h e same s e t o f
i n p u t d a t a
T h e s y s t e m c o n f i g u r a t i o n a s seen f r o m e a c n lo a d
p o i n t o r busbar was c o n s i d e r e d t o e x i s t a t any i n s t a n t
o f t i m e i n one o f t h e t h r e e f o l l o w i n g s t a t e s :
Trang 21 - s y s t e m w i t h o u t a n y f a i l u r e , i e n o r m a l o p e r a t i o n
2 - s y s t e m w i t h a f a u l t b u t b e f o r e s w i t c h i n g
3 - s y s t e m w i t h a f a u l t b u t a f t e r s d t c h t n g
The s t a t e space diagram s b m i n F i g , 1 i l l u s -
t r a t e s t h i s t h r e e s t a t e m o d e l
a c t i v e
p a s s i v e
r e p a i r
W
F i g 1 - S t a t e s p a c e d i a g r a m o f 3 - s t a t e model
E a c h t i m e s t a t e s 2 o r 3 a r e e n c o u n t e r e d b y a
component w i t h e i t h e r one, two o r t h r e e o v e r l a p p i n g
outages o r f a i l u r e s , t h e e v e n t i s c h e c k e d t o e s t a b l i s h
whether itl e a d s t o a b u s b a r f a i l u r e I i t does t h e
components d e f i n i n g t h i s e v e n t a r e c o n s i d e r e d a b u s b a r
c u t s e t a n d t h e n c h e c k e d t o e s t a b l i s h w h e t h e r t h e y
f o r m a m i n i m a l c u t s e t
The m i n i m a l c u t s e t s w e r e g r o u p e d i n t o f o u r
t y p e s ; e a c h t y p e b e i n g a s s o c i a t e d w i t h d i s t i n c t l y
d i f f e r e n t ways o f r e s t o r i n g t h e s u p p l y t o t h e b u s b a r
u n d e r c o n s i d e r a t i o n These t y p e s a r e :
a ) a c u t s e t f o r w h i c h a b u s b a r f a i l u r e o c c u r s when
a l l t h e components o f t h e c u t a r e o u t o f s e r v i c e ,
i e ; b e i n g m a i n t a i n e d o r r e p a i r e d S e r v i c e is r e t u r -
ned t o n o r m a l a f t e r r e s t o r i n g t o s e r v i c e a t l e a s t one
o f t h e components,
b l a c u t s e t f o r w h i c h a b u s b a r f a i l u r e o c c u r s when
a l l t h e components o f t h e c u t a r e o u t o f s e r v i c e b u t
s e r v i c e can be r e s t o r e d b y c l o s i n g a n o r m a l l y open
p a t h
c l a c u t s e t f o r w h i c h a b u s b a r fa i l u r e o c c u r s when
one component i s a c t i v e l y f a i l e d and t h e o t h e r s a r e
o u t o f s e r v i c e S e r v i c e i s r e s t o r e d by i s o l a t i n g t h e
a c t i v e l y f a i l e d component and c l o s i n g t h e b r e a k e r s
t h a t were opened due t o t h e a c t i v e f a u l t
d l a c u t s e t f o r w h i c h a b u s b a r fa i l u r e o c c u r s when
one component i s a c t i v e l y f a i l e d , t h e o t h e r s a r e o u t
o f s e r v i c e and one b r e a k e r o f t h e p r o t e c t i o n z o n e o f
t h e a c t i v e l y f a i l e d component i s s t u c k S e r v i c e i s
r e s t o r e d by i s o l a t i n g t h e a c t i v e l y f a i l e d component
and c l o s i n g t h e b r e a k e r s t h a t w e r e opened d u r i n g t h e
f a u l t
A f o u r f a i l u r e e v e n t s l were considered i n r e f -
erence 1 However t h e r e l i a b i l i t y i n d i c e s a s s o c i a t e d
w i t h t h e s e c o n d t y p e o f t h e s e c u t s e t s w e r e c a l c u l a t e d
a s s u m i n g t h a t t h e n o r m a l l y open p a t h w h i c h was c l o s e d
t o r e s t o r e t h e s u p p l y d i d n o t f a i l d u r i n g t h e r e p a i r
t i m e s o f t h e c o m p o n e n t s o f t h e c u t s e t T h i s assurnp-
t i o n was e l i m i n a t e d u s i n g t h e f o l l o w i n g t e c h n i q u e ,
C o n s i d e r :
e v e n t A J
event BJ
a f a i l u r e e v e n t t h a t can be e l i m i n a t e d
by c l o s i n g any o f t h e n o r m a l l y o p e n
p a t h s k, j, 1 m
a n e v e n t d e f i n e d as, " a t le a s t one o f
t h e n o r m a l l y open p a t h s k, j , 1 m, does n o t f a i l b e f o r e r e s t o r i n g t o
s e r v i c e one component o f f a i l u r e e v e n t A"
U s i n g t h e c o n d i t i o n a l p r o b a b i l i t y a p p r o a c h , t h e
f o l l o w i n g e q u a t i o n c a n be w r i t t e n :
P [ A I = P(AIB1 PCB1 + P(AIE1 P(E1 [ 1 1 P(A181 i s t h e p r o b a b i l i t y o f e v e n t A g i v e n t h a t
a t l e a s t one o f t h e n o r m a l l y open p a t h s i s always
a v a i l a b l e and P [ A I B I i s t h e p r o b a b i l i t y o f e v e n t A
g i v e n t h a t none o f t h e n o r m a l l y open p a t h s a r e a v a i l -
a b l e to r e s t o r e s e r v i c e F o r e a c h o f th e e v e n t s A I B and A[B t h e c o n t r i b u t i o n t o t h e a v e r a g e f a i l u r e r a t e ,
t h e a v e r a g e o u t a g e d u r a t i o n a n d a v e r a g e a n n u a l o u t a g e
t i m e due t o fo r c e d o u t a g e s (A, r , U l a n d f o r c e d o u t -
a g e s o v e r l a p p i n g a m a i n t e n a n c e o u t a g e [ X " , r", U " 1 a r e
e v a l u a t e d T h e s e ' i n d i c e s a r e :
f o r A I B + X 1 and XI", rl and r l " , U 1 and til"
f o r AlE -+ A2 and Az", r 2 and r2" U2 and U2"
n o t i n g t h a t X1 = A2 and 11'' = Az"
To c a l c u l a t e t h e same i n d i c e s f o r t h e e v e n t r e p -
r e s e n t e d by 8, t h e m i n i m a l c u t s e t s f o r t h e p a t h s k ,
j , 1 , m a r e e v a l u a t e d Any o f t h e s e t h a t a r e a l s o
l o a d p o i n t m i n i m a l c u t s t s a r e e l i m i n a t e d The m i n i -
m a l c u t s e t s o f e v e n t B a r e e v a l u a t e d up t o second
o r d e r if e v e n t A i s o f f i r s t o r d e r , up t o f i r s t o r d e r i
f e v e n t A i s o f s e c o n d o r d e r and a r e n o t e v a l u a t e d i f
e v e n t A i s o f t h i r d o r d e r From t h e s e m i n i m a l c u t
s e t s t h e r e l i a b i l i t y i n d i c e s o f t h e " e l e m e n t " e q u i v a -
l e n t t o t h e n o r m a l l y open p a t h s a r e e v a l u a t e d ; th e s e
b e i n g d e f i n e d as A, and X,", r e and r e 1 ' , Ue and U," The n o r m a l l y o p e n b r e a k e r s , w h i c h a r e f i r s t
o r d e r c u t s e t s o f t h e m i n i m a l p a t h s k , j , 1 m a r e
a l s o c o n s i d e r e d i n o r d e r t o i n c l u d e t h e s t u c k b r e a k e r
p r o b a b i l i t y P, o f t h i s e q u i v a l e n t e l e m e n t
N o t i n g t h a t t h e a v e r a g e a n n u a l o u t a g e t i m e o f
e v e n t A, when expressed i n y e a r s l y e a r , r e p r e s e n t s P [ A I
t h e f o l l o w i n g e q u a t i o n s a r e o b t a i n e d f r o m e q u a t i o n 1:
UA = u1 [1 - P S I ] + u 2 [ u e + P S I ( 2 )
up," = U l ' ' ( 1 - u e " ] + u 2 " u e " [ 3 1 The f o l l o w i n g e q u a t i o n s c a n a l s o be o b t a i n e d :
( 7 I
H a v i n g c a l c u l a t e d t h e r e l i a b i l i t y i n d i c e s o f a l l
t h e i n d e p e n d e n t f a i l u r e e v e n t s o f e a c h b u s b a r , t h e
o v e r a l l b u s b a r i n d i c e s a r e e v a l u a t e d by s i m p l y a d d i n g
t h e e x p e c t e d f a i l u r e r a t e s and t h e a n n u a l o u t a g e t i m e s
o f e a c h f a i l u r e e v e n t
REPRESENTING BRANCHES OFF THE BUSBARS
To c a l c u l a t e t h e r e l i a b i l i t y i n d i c e s o f each
b u s b a r , t h e b r a n c h e s o f f t h e b u s b a r s c a n n o t b e i g n o r e d
s i n c e t h e y c o u l d h a v e a s i g n i f i c a n t i m p a c t on t h e b u s -
b a r in d i c e s , p a r t i c u l a r l y on i t s f a i l u r e r a t e T h i s
i s due t o t h e e f f e c t o f a c t i v e f a i l u r e s and a c t i v e
f a i l u r e s o v e r l a p p i n g a s t u c k b r e a k e r c o n d i t i o n o f t h e components i n t h e s e b r a n c h e s b e i n g re f l e c t e d b a c k t o
t h e b r e a k e r s o n t h e in p u t s i d e o f t h e b u s b a r s I n a
t y p i c a l power s t a t i o n th e number o f branches o f f a busbar may exceed 60 o r so w i t h e a c h b r a n c h c o n t a i n i n g
a t l e a s t t h r e e components, e.g a b r e a k e r , a c a b l e
Trang 3a a
number o f a d d i t i o n a l components t h a t w o u l d n e e d t o b e
i n t r o d u c e d a d e q u a t e l y t o r e p r e s e n t t h e s e b r a n c h e s
c o u l d e x c e e d s e v e r a l h u n d r e d The c o m p u t e r t i m e a n d
s t o r a g e r e q u i r e m e n t s o f a computer program i s a f u n c -
t i o n o f t h e number o f components Therefore t o
i n c l u d e a l l t h e s e a d d i t i o n a l components would s e r i o -
u s l y d e g r a d e c o m p u t a t i o n a l e f f i c i e n c y
T h i s d i f f i c u l t y was o v e r c o m e b y r e p r e s e n t i n g t h e
branches o f f e a c h b u s b a r b y a n " e q u i v a l e n t b r a n c h "
The a c t i v e f a i l u r e r a t e o f e a c h component i n t h i s
e q u i v a l e n t b r a n c h i s o b t a i n e d b y s u m n i n g t h e a c t i v e
f a i l u r e r a t e s o f t h e components e x i s t i n g i n t h e r e a l
branches The s w i t c h i n g t i m e a n d s t u c k b r e a k e r p r o b a -
b i l i t y a r e t h e same as any one o f t h e r e a l components
U s i n g t h i s t e c h n i q u e t h e r e l i a b i l i t y i n d i c e s o f e a c h
b u s b a r a r e c a l c u l a t e d p r e c i s e l y a n d t h e i n c r e a s e i n
c o m p u t e r ti m e a n d s t o r a g e re q u i r e m e n t s i s a minimum
REPRESENTING ALTERNATIVE SOURCES OF SUPPLY
The e l e c t r i c a l a u x i l i a r y s y s t e m o f e a c h u n i t i s
n o r m a l l y f e d f r o m i t s own g e n e r a t o r a n d / o r fr o m th e
g r i d s y s t e m H o w e v e r a l t e r n a t i v e s o u r c e s o f s u p p l y
such a s d e i s e l g e n e r a t o r s a n d g a s t u r b i n e s may be
a v a i l a b l e e i t h e r f o r b l a c k s t a r t s o r f o r use when t h e
n o r m a l f e e d i n g p o i n t s a r e n o t a v a i l a b l e I n t h e p r e s -
e n t s y s t e m m o d e l th e s e a l t e r n a t i v e s o u r c e s o f s u p p l y
w e r e r e p r e s e n t e d a s n o r m s 1 s y s t e m b r a n c h e s c o n n e c t e d
t o t h e s y s t e m t h r o u g h a n o r m a l l y o p e n b r e a k e r ; t h e
s w i t c h i n g t i m e o f t h i s n o r m a l l y o p e n b r e a k e r i n c l u d i n g
t h e s t a r t - u p t i m e o f t h e a l t e r n a t i v e s o u r c e o f s u p p l y
F o r e a c h b u s b a r a n y s u c h s o u r c e i s i n c l u d e d a s
o n e o f t h e n o r m a l l y open p a t h s F o r e a c h f a i l u r e
e v e n t t h a t d o e s n o t i n c l u d e a component a c t i v e l y f a i l -
ed, t h e p r o g r a m c h e c k s w h e t h e r iti s p o s s i b l e t o e l i -
m i n a t e i t b y c l o s i n g a n o r m a l l y open p a t h When t h e
f a i l u r e e v e n t u n d e r c o n s i d e r a t i o n i n v o l v e s t h e loss o f
t h e n o r m a l s o u r c e s o f s u p p l y t h e n o r m a l l y open p a t h s
t h a t a r e c o n s i d e r e d in c l u d e th a t o f th e a l t e r n a t i v e
s o u r c e B e c a u s e t h e s e a l t e r n a t i v e s o u r c e s o f t e v h a v e
v e r y h i g h u n r e l i a b i l i t i e s i t i s g e n e r a l l y n o t a c c e p t -
a b l e t o assume t h a t th e y c a n n o t fa i l when r e q u i r e d ,
i e d u r i n g t h e o u t a g e t i n e o f t h e m i n i m a l c u t s e t
T h e r e f o r e t h e c o n d i t i o n a l p r o b a b i l i t y t e c h n i q u e s d e s -
c r i b e d p r e v i o u s l y w e r e i n c o r p o r a t e d f o r t h e s e s o u r c e s
o f s u p p l y and i n f a c t was t h e m a i n r e a s o n f o r t h e i r
development
LOSS OF POWER DUE TO UNRELIABILITY OF SYSTEM
I i s n o t p o s s i b l e t o compare o b j e c t i v e l y d i f -
f e r e n t d e s i g n s o f e l e c t r i c a l a u x i l i a r y s y s t e m s f r o m
o n l y a knowledge o f t h e r e l i a b i l i t y i n d i c e s o f e a c h
b u s b a r T h i s i s b e c a u s e t h e r e q u i r e m e n t i s a know-
l e d g e o f t h e i m p a c t o f t h e a u x i l i a r y e l e c t r i c a l s y s t e m
on t h e a v a i l a b i l i t y o f th e g e n e r a t i n g u n i t a n d n o t
s i m p l y t h e i n d i c e s o f e a c h b u s b a r O b j e c t i v e c o m p a r i -
son becomes d i f f i c u l t because t h e s y s t e m b b s b a r s h a v e
d i f f e r e n t i m p o r t a n c e a s - a r as t h e o u t p u t o f t h e u n i t
i s concerned and many f a i l u r e e v e n t s a r e common t o
m o r e t h a n one busbar However t h i s d i f f i c u l t y can be
a l l e v i a t e d i f a l l t h e in d e p e n d e n t f a i l u r e e v e n t s o f
t h e s y s t e m b u s b a r s a r e c o n s i d e r e d a s a s e t o f e v e n t s
t h a t i n c l u d e t h e u n i t l n d e p e n d e n t f a i l u r e e v e n t s
l h e r e f o r e th i s s e t o f e v e n t s a r e t h e u n i t c u t s e t s
f r o m w h i c h t h e u n i t m i n i m a l c u t s e t s m u s t b e o b t a i n e d
The c o m p l e x i t y o f t h i s p r o c e d u r e i s due t o t h e f o l l o w -
i n g r e a s o n s :
( a 1 c u t s e t s o f d i f f e r e n t t y p e s h a v e t o be compared
i n o r d e r t o d e c i d e w h e t h e r o r n o t one i s i n c l u d e d i n
t h e o t h e r
c a u s e d e r a t e d s t a t e s o f t h e u n i t a r e i n c l u d e d i n
o t h e r s , a l l h a v e t o be t a k e n i n t o a c c o u n t b e c a u s e t h e
s i m u l t a n e o u s l o s s o f t w o o f t h e s e b u s b a r s may cause a
d e r a t e d s t a t e t h a t i s d i f f e r e n t f r o m t h a t a s s o c i a t e d
w i t h t h e l o s s o f e a c h b u s b a r s e p a r a t e l y
To c a l c u l a t e th e in d i c e s o f e a c h fe a s i b l e d e -
r a t e d s t a t e o f t h e u n i t due t o t h e u n r e l i a b i l i t y o f
t h e e l e c t r i c a l a u x i l i a r y system, t h e l o s s o f each bus-
b a r i s c o n s i d e r e d t o c a u s e one o f t h e f o l l o w i n g
s t a t e s : ( a ) t o t a l loss o f t h e u n i t [ b l n o i n f l u e n c e o n t h e o u t p u t o f t h e u n i t ( c ) a loss o f x % o f t h e o u t p u t o f t h e u n i t where x may h a v e a n y v a l u e a n d b e d i f f e r e n t f o r e a c h b u s b a r
a n d c o m b i n a t i o n o f b u s b a r s
I was assumed t h a t i f an e v e n t c a u s e s t h e loss
o f t h r e e b u s b a r s , e a c h o f w h i c h c r e a t e s i n d i v i d u a l l y a
d e r a t e d s t a t e , t h i s e v e n t wicause t o t a l loss o f t h e
u n i t G e n e r a l l y h o w e v e r th e s i m u l t a n e o u s l o s s o f t w o
s u c h b u s b a r s i s assumed t o c r e a t e a d e r a t e d s t a t e t h a t may o r may n o t be e q u a l t o t h e d e r a t e d s t a t e s t h a t a r e
c r e a t e d by t h e i n d i v i d u a l l o s s o f t h e s e b u s b a r s The a l g o r i t h m d e v e l o p e d f o r a n a l y s i n g t h i s p r o b -
l e m i s d e s c r i b e d i n t h e A p p e n d i x a s s u m i n g t h a t t h e
i n d e p e n d e n t f a i l u r e e v e n t s o f e a c h b u s b a r a r e a l r e a d y known I n t h e a s s o c i a t e d c o m p u t e r p r o g r a m t h e s e f a i l - ure modes a r e s t s r e d i n a c o m p a c t f o r m w h i c h p r e v e n t s
e x c e s s i v e i n c r e a s e c o m p u t e r i n s t o r a g e The d a t a
r e q u i r e d t o c a l c u l a t e t h e r e d u c t i o n o f power due t o
t h e u n r e l i a b i l i t y o f t h e e l e c t r i c a l a u x i l i a r y s y s t e m
a r e a s f o l l o w s : ( a ) c o n s e q u e n c e s o f l o s i n g e a c h b u s b a r ( b l consequences o f l o s i n g a l l c o m b i n a t i o n s o f t w o
b u s b a r s b o t h o f w h i c h s e p a r a t e l y l e a d t o a d e r a t e d
s t a t e Use o f t h e a l g o r i t h m d e s c r i b e d i n t h e A p p e n d i x
g i v e s t h e a v e r a g e r a t e o f o c c u r r e n c e o r e n c o u n t e r , t h e
a v e r a g e d u r a t i o n a n d t h e a v e r a g e a n n u a l r e s i d e n c e t i n e
o f e a c h f e a s i b l e l e r a t e d s t a t e From t h e s e i n d i c e s i t
i s p o s s i b l e t o a s s i g n a r e l i a b i l i t y c o s t t o e v e r y d e s -
i g n a n d a n i n c r e m e n t a l c o s t o f e a c h d e s i g n change
T h i s p e r m i t s t h e " q u a l i t y " o f d i f f e r e n t d e s i g n a l t e r n -
a t i v e s t o be a s s e s s e d o b j e c t i v e l y
AIJALYSIS OF TYPICAL AUXILIARY SYSTEM The t e c h n i q u e s a n d c o n c e p t s d e s c r i b e d i n t h e
p r e v i o u s s e c t i o n s were a p p l i e d t o t h e t y p i c a l a u x i l i -
a r y s y s t e m shown i n F i g 2
T h i s s y s t e m c o n s i s t s o f a s e t o f u n i t b u s b a r s shown on t h e l e f t hand s i d e o f t h e F i g u r e a n d a s e t o f
s t a t i o n b u s b a r s shown on t h e r i g h t h a n d s i d e A t each
v o l t a g e l e v e l t h e b u s b a r s a r e i n t e r c o n n e c t e d w i t h n o r -
m a l l y open b r e a k e r s From each busbar a number o f
m o t o r s a r e c o n n e c t e d A s t a n d b y g e n e r a t o r [ 5 6 j i s connected t o t h e h i g h v o l t a g e u n i t b u s b a r ( 4 1 t h r o u g h
a n o r m a l l y o p e n b r e a k e r ( 5 7 1 The component r e l i a b i l i t y d a t a u s e d i n t h i s a n a -
l y s i s i s shown i n T a b l e l and the consequences o f b u s -
b a r o u t a g e s i n T a b l e 2
Trang 4F i g 2 - T y p i c a l a u x i l i a r y s y s t e m
d o u b l e a r r o w s i n d i c a t e b i d i r e c t i o n a l
b r a n c h e s , a l l o t h e r s a s s u m e d u n i d i r e c t i o n -
a l E n c i r c l e d numbers i n d i c a t e number of
m o t o r s @ r e p r e s e n t n o r m a l l y o p e n b r e a k -
e r s , a l l o t h e r s a s s u m e d n o r m a l l y c l o s e d
Component 56 i s a s t a n d b y g e n e r a t o r , n o r -
mal s u p p l y s u r c e s are 58 and 59
U s i n g t h e r e l i a b i l i t y d a t a shown i n Table 1, a l l
t h e f a i l u r e e v e n t s f o r e a c h b u s b a r were deduced and
t h e r e l i a b i l i t y i n d i c e s o f e a c h e v e n t and t h e o v e r a l l
i n d i c e s o f e a c h b u s b a r were c a l c u l a t e d I t was a s s u - med t h a t a component i s n o t t a k e n o u t f o r m a i n t e n a n c e
i f i t c a u s e s a b u s b a r f a i l u r e or i f a n o u t a g e a l r e a d y
e x i s t s i n t h e system T h e r e f o r e m a i n t e n a n c e d e t a i l s
a r e n o t g i v e n f o r some components i n Table 1 a s t h e s e
a r e n o t r e q u i r e d
I n g e n e r a l t h e modes o f f a i l u r e were assumed t o
be f o r c e d o u t a g e s , o v e r l a p p i n g f o r c e d o u t a g e s or
f o r c e d o u t a g e s o v e r l a p p i n g a m a i n t e n a n c e o u t a g e A l l
t h e t e c h n i q u e s d i s c u s s e d i n t h e p r e c e d i n g S e c t i o n s
bere i n c l u d e d i n t h e a n a l y s i s , t h a t i s , s e r v i c e c o u l d
b e r e s t o r e d ( i f p o s s i b l e ) by c l o s i n g n o r m a l l y o p e n
p a t h s w h i c h th e m s e l v e s c o u l d s u b s e q u e n t l y fa i l , ser- vice c o u l d be r e s t o r e d u s i n g t h e s t a n d b y p l a n t when
n o r m a l s o u r c e s o f s u p p l y f a i l e d a n d s e r v i c e c o u l d b e
r e s t o r e d f o l l o w i n g a n a c t i v e f a i l u r e by i s o l a t i n g t h e
f a i l e d c o m p o n e n t a n d r e c l o s i n g t h e a p p r o p r i a t e b r e a k -
e r s
From t h i s a n a l y s i s , t h e t o t a l number o f f a i l u r e
e v e n t s fo u n d fo r a l l b u s b a r s was 183 of w h i c h some
w o u l d c a u s e fa i l u r e o f more t h a n o n e b u s b a r A sum-
mary o f t h e number o f p a t h s a n d number of f a i l u r e
e v e n t s a s s o c i a t e d w i t h e a c h b u s b a r i s shown i n T a b l e 3
TO i l l u s t r a t e t h e t y p e o f r e s u l t s o b t a i n e d from
t h i s p a r t of t h e a n a l y s i s , c o n s i d e r t h e 32 f a i l u r e
e v e n t s a s s o c i a t e d w i t h b u s b a r 1 3 I t i s e v i d e n t t h a t
t h e r e a r e t w o n o r m a l l y c l o s e d p a t h s f r o m s o u r c e 58 and
S e v e n n o r m a l l y o p e n p a t h s fr o m so u r c e s 56, 58 and 59
t h r o u g h th e n o r m a l l y o p e n b r e a k e r s 9 , 55 and 57 A l s o Table 1 - R e l i a b i l i t y d a t a
component
t o t a l
1, 5
2 , 6 , 11, 15, 18, 22, 26, 30, 35
3 , 7 , 10, 1 4 , 1 7 , 3 9 , 4 1
4 , 8, 13, 20, 24, 28, 32, 37
9 , 3 3 , 3 8 , 55
1 2 , 1 6 , 1 9 , 2 1 , 2 3 , 2 5 , 2 7 , 3 1 , 3 4 , 3 6 , 4 3 , 4 5 , 4 7 , 4 9 , 5 1 , 5 3
29
40, 42
4 4 , 4 6
56
57
48, 50, 52, 54
0.020
0 0 2 0
0 0 1 2 0.005
0.020 0.010 0.010
0 0 5 0 0.025
1 2 0
0 0 2 0
0 0 3 5
Table 2 - C o n s e q u e n c e s o f b u s b a r o u t a g e s
number o f
f a i l e d b u s b a r s I busbar number I r e d u c t i o n o f
4, 13 24, 28
8 , 37
20
32
8 and 37
20 and 37
8 and 2 0
a n y c o m b i n a t i o n
100
30
20
0
50
45
40
1 W
-4-= a c t i v e
0 0 1 5
10 0.005
20
0.008
8 0 0 0 0 1 5
20
20
0 0 0 7 20
0 0 4 0
0 0 2 I 7 8
0 0 3
I
s w i t c h i n g
t i m e
hr
1 0 1.0 1.0
1 0
1 0
1 0 1.0
1 0 1.0 1.0
1 0
p r o b a b i l i t y rate
o / y r
0 0 0 1
0.001
0 2 5
0 0 1 3
0 2 5
0 0 0 1 0 2 5
0.001
0 5
1 6
0 1 1 3 0 2 5
E
t iml
h r
-
4 0
20
20
20
315
20
-
i f a c t i v e f a i l u r e modes a r e i g n o r e d t h e r e a r e 14 m i n -
i m a l c u t s e t s o n l y o n e o f w h i c h , f a i l u r e o f b u s b a r 13,
c a n n o t be e l i m i n a t e d u s i n g a n o r m a l l y o p e n p a t h
T h e s e c u t s a r e shown i n Table 4
C o n s i d e r now t h e f a i l u r e o f b r e a k e r 1 and t h e
s u b s e q u e n t r e s t o r a t i o n o f s u p p l y t o b u s b a r 1 3 [ a simi-
l a r a n a l y s i s e x i s t s f o r f a i l u r e s o f t r a n s f o r m e r 2 and
b r e a k e r 31 From T a b l e 1 t h e f a i l u r e r a t e o f t h i s
e v e n t i s 0 0 2 f / y r a n d t h e o u t a g e t i m e i f a n o r m a l l y open p a t h was n o t a v a i l a b l e [ e v e n t AIEI would be 20hr
T h e r e f o r e :
X 2 = O.OZf/yr, r2 = 20hr U2 = 0 4 h r / y r
Trang 5T a b l e 3 - S m r y o f f a i l u r e e v e n t s
busbar
o v e r l a p p i n g f o r c e d o u t a g e s I a c t i v e 1 a c t i v e f a i l u r e s 1 total '
n o r m a l l y c l o s e d o p e n I Amally t o t a l I c l o s e d by n / o path f a i l u r e s 6 s t u c k b r e a k e r ,
13
9
a
17
18
16
2
24
6
4 7
a
a
1
20
a
13
14
7
2
4
11
12
17
32
35
9
Table 4 - M i n i m a l c u t s a s s o c i a t e d w i t h b u s b a r 13
f i r s t o r d e r c u t s s e c o n d o r d e r c u t s
I however a t l e a s t one n o r m a l l y o p e n p a t h i s
a v a i l a b l e ( e v e n t Ala] t h e n th e fa i l u r e ra t e re m a i n s
unchanged b u t t h e o u t a g e t i m e becomes t h e s w i t c h i n g
t
i
mef o r r e s t o r i n g t h e s u p p l y T h e r e f o r e :
A 1 = 0 0 2 f / y r , rl = l h r , U1 = O.OZhr/yr
The m i n i m a l c u t s e t s o f t h e n o r m a l l y o p e n p a t h s
t o busbar 13 t h a t a r e n o t a l r e a d y i n c l u d e d i n t h e
f a i l u r e modes o f b u s b a r 13 a r e o v e r l a p p i n g o u t a g e s of
5 and 56, 5 and 57, 6 and 5 6 , 6 and 57, 7 and 56, 7
and 5 7 , 8 and 56, 8 and 57 C o m b i n i n g t h e r e l i a b i l i t y
i n d i c e s f o r t h e s e e i g h t o v e r l a p p i n g e v e n t s g i v e s t h e
r e l i a b i l i t y i n d i c e s f o r t h e e q u i v a l e n t e l e m e n t d i s c u s -
s e d p r e v i o u s l y T h e r e f o r e :
Ae = 0.2899x10-1f/yr, re = 0.7024x10c2yr,
Ue = 0 2 0 3 6 ~ 1 0 - ~ y r / y r
A; = 0 3 3 1 2 ~ 1 0 - ~ 0 / y r , r; = 0 1 0 2 7 ~ 1 0 y r -1
ue 0 3 4 0 1 x 1 0 - ~ y r / y r
Ps = 0.0
Then;
UA 0 0 2 f l - 0 2 0 3 6 ~ 1 0 - ~ 1 + 0.4 X 0.2036 X
= 0.20077 x lO-'hr/yr
r A = G = 1 W 3 8 h r
A p p l y i n g t h e same c o n c e p t s a n d t e c h n i q u e s t o t h e
o t h e r m i n i r h a l c u t s a s s o c i a t e d w i t h b u s b a r 13 and i n c -
l u d i n g t h e a c t i v e f a i l u r e modes w i t h a n d w i t h o u t s t u c k
b r e a k e r s g i v e s t h e f a i l u r e modes and e f f e c t s a n a l y s i s shown i n Table 5
S e t s o f i n d i c e s s i m i l a r t o t h o s e shown i n T a b l e
5 can be corrputed f o r a l l busbars The o v e r a l l i n d i - ces for e a c h b u s b a r c a n n o t b e u s e d d i r e c t l y t o d e t e r -
m i n e t h e o u t p u t r e d u c t i o n o f t h e u n i t b e c a u s e , as d i s -
c u s s e d p r e v i o u s l y , f a i l u r e e v e n t s may be comnon t o
m o r e t h a n o n e b u s b a r T h e r e f o r e t h o s e t h a t a r e u n i t
m i n i m a l c u t s must be d e t e c t e d f r o m t h e b u s b a r m i n i m a l
c u t s O f t h e 1 8 3 b u s b a r m i n i m a l c u t s o n l y 65 a r e u n i t
m i n i m a l c u t s , 1 e c u t s t h a t c a u s e t h e o u t p u t p o w e r
t o be reduced These u n i t m i n i m a l c u t s a r e shown i n Table 6
H a v i n g d e d u c e d t h e u n i t m i n i m 1 c u t s shown i n
T a b l e 6, t h e p e r c e n t a g e o u t p u t r e d u c t i o n t h a t i s caused by these events must be e v a l u a t e d I t h e
e v e n t c a u s e s f a i l u r e o f o n l y o n e b u s b a r t h e n t h a t
e v e n t c r e a t e s an o u t p u t re d u c t i o n e q u i v a l e n t to th e
e f f e c t o f t h a t b u s b a r Ithe event however causes
f a i l u r s o f more t h a n o n e b u s b a r t h e n t h e o u t p u t r e d u c -
t i o n is d e p e n d e n t o n t h e c o m b i n e d e f f e c t o f t h o s e b u s -
b a r s U s i n g t h i s t e c h n i q u e , t h e b u s b a r c o n s e q u e n c e s shown i n T a b l e 2 a n d a c c u m u l a t i n g t h e a p p r o p r i a t e i n -
d i c e s g i v e s t h e r e l i a b i l i t y i n d i c e s shown i n Table 7
f o r e a c h f e a s i b l e s t a t e The d e t a i l s o f t h e s i x f a i l -
u r e e v e n t s t h a t c o n t r i b u t e t o t h e 30% d e r a t e d s t a t e
a r e shown i n T a b l e 8
From Table 7 i t i s e v i d e n t t h a t some d e r a t e d
s t a t e s d e f i n e d i n T a b l e 2 , i e 2 0 5 , 40%, and 5 0 % ,
do n o t a p p e a r a s fe a s i b l e d e r a t e d s t a t e s The reason
f o r t h i s i s t h a t t h e f a i l u r e e v e n t s c a u s i n g t h e loss
o f th e a p p r o p r i a t e b u s b a r ( s 1 a l s o c a u s e th e loss o f
o t h e r b u s b a r k l C o n s e q u e n t l y t h e d e r a t e d s t a t e i s
g r e a t e r t h a n t h e a b o v e v a l u e s a n d t h e r e l e v a n t e v e n t s
a r e a b s o r b e d i n e i t h e r t h e 30% 45% o r 1 W % d e r a t e d
s t a t e s
The i n d t c e s shown i n Table 7 e n a b l e d i f f R r e n t
s y s t e m d e s i g n s t o be compared e a s i l y a n d e n a b l e o t h e r
r i s k i n d i c e s t o be e v a l u a t e d One s u c h in d i c e i s t h e
e x p e c t e d e n e r g y lo s t e a c h y e a r d u e t o f a i l u r e o f t h e
Trang 6T a b l e 5 - R e l i a b i l i t y i n d i c e s a s s o c i a t e d w i t h b u s b a r 13
f a i l u r e event h
f / yr
I
o u t
o u t
o u t
o u t
3 o u t
0 + 14 o u t
1 0 + 1 5 o u t
1 0 + 1 6 o u t
11 + 1 4 o u t
1 + 1 5 o u t
1 + 1 6 o u t
2 + 1 4 o u t
2 + 1 5 o u t
2 + 1 6 o u t
0 a c t i v e
2 a c t i v e
4 a c t i v e
6 a c t i v e
1 a c t i v e
5 a c t i v e
9 a c t i v e
3 a c t i v e
1 a c t i v e + 10 s t u c k
1 a c t i v e + 1 2 s t u c k
5 a c t i v e + 1 4 s t u c k
5 a c t i v e + 1 6 s t u c k
2 a c t i v e + 2 1 s t u c k
3 a c t i v e + 2 1 s t u c k
6 a c t i v e + 25 s t u c k
7 a c t i v e + 25 s t u c k
0 a c t i v e + 3 9 s t u c k
0.20001~ x 10-1 0.12001 x 10-1 0.20053 x 10-1 0.50007 x 10-2 0.50000 x
0.65759 x 0.22469 x
0.54799 x 0.22469 x 10-4 0.73300 x 0.18724 x 0.54799 x
0.18724 x 0.45666 x
0.700 x
0.800 x
0.700 x 10-2 0.700 x lo-' 0.700 x lo-' 0.480 x 10-1 0.980 x 10-1 0.150 x 0.150 x 0.150 x
0.150 x
0.700 x 10-5 0.150 x 0.700 x 0.240 x 10-3 0.150 x 10-4
4 a c t i v e + 4 3 s t u c k I 0.280 x 10-3
t o t a l 0 2 5 2 8 3
r
h r 1.0038 1.1597 1.0038 1.1513 10.00 1.0874 1.2739 1.0874 1.8739 6.9346 1.2739 1.0874 1.2739 1.0874
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0 1.0 1.0
1 0
1 0
1 0
1 0
1 0
1 0 L.1959
0.20077 x 10-1 0.23255 x 10-1 0.12046 x 10-1 0.57575 x
0.50000 x 10-1 0.71507 x 10-6
0.23853 x
0.91423 x l o T 4 0.50830 x
0.38830 x 0.28624 x 10-4 0.12561 x
0.59589 x
0.38830 x 10-4 0.28624
x 10-4
0.13703 x 10-4
0.150 x 0.980 x 10-1 0.480 x 10-1 0.700 x 0.700 x 0.700 x lo-'
0.800 x
0.700 x 10-2 0.800 x
0.11416 x 0.49657
x 10-6
0.34262 x 0.23853 x 0.12561 x 0.59589 x 10-6 0.34262 x
0.150 x
0.150 x 0.150 x 0.700 x 0.150 x 0.700 x 10-5 0.240 x 10-3 0.150 x 10-4
0.280 x 10-3 I
0.30237 I 0.28783 x 10-3
T a b l e 6 - F a i l u r e e v e n t s c a u s i n g power r e d u c t i o n of u n i t
0.95727 0.97645 0.95727 0.97645 0.99571 0.97567 0.95727 0.97567 0.95727
0.97904
0.13117 x 0.37915 x 0.12024 x 0.37915 x
0.91032 x 0.33428 x 0.12024 x
0.33428 x
0.10931 x
0.28181 x 10-5
4
1 3
20
24
28
37
p a s s i v e o u t a g e s
a c t i v e f a i l u r e s
p a s s i v e o u t a g e s
r e s t o r e d by r e p a i r r e s t o r e d b y n / o p a t h s a c t i v e failures p l u s s t u c k b r e a k e r
1, 2 , 3 , 5 , 6 , 7 , 17
1 8 , 1 9 , 2 1 , 2 2 , 23, 25
26, 27, 34, 35, 36,
l o - + 1 4 , 1 0 + 1 5 ,
10 + 1 6 , 11 + 1 4 ,
11 + 1 5 , 11 + 1 6 ,
1 2 + 1 4 , 1 2 + 1 5 ,
1 2 + 16
10 41
14 43
16 45
17 47
39
12
11 + 1 0 , 1 5 + 1 6
15 + 1 4 , 18 + 17
19 + 1 7 , 30 + 29
31 + 29, 35 + 34
36 + 34, 40 + 39
42 + 4 1 , 44 + 43
46 + 45, 48 + 47
52 + 51 54 + 53
J
T a b l e 7 - E n c o u n t e r r a t e a n d d u r a t i o n of u n i t s t a t e s T a b l e B - E v e n t s c a u s i n g 30% d e r a t e d s t a t e s
berated
e v e n t s time,hr/yr
h r
r a t e / y r
9
of
r e s i d e n c e
d u r a t i o n e n c o u n t e r
s t a t e
number annual
a v e r a g e expected
30
45 2.1627 1.7640
1.2260 100
12 0.34027 4.1927
0.81159 x 10-1
45
6 0.53812 2.161 0.24901
a u x i l i a r y system As an exampIe consider t h e system
shown i n F i g 2 b e i n g t h e a u x i l i a r y s u p p l y o f a 500 MW
u n i t T h e e x p e c t e d e n e r g y l o s t i s t h e n shown i n T a b l e
9
F r o m Table 9 i t i s e v i d e n t t h a t t h e s i n g l e V a l u e
f a i l u r e
e v e n t
e x p e c t e d
f e i l b r s r,-;ta f / y r
37 o1:t O ~ C X ? O - ~
34 o u t , n/o r l i 3 0 0 1 6 ~ 1 0 - ~
35 c u t , n / o 0 2 0 1 1 3 x 1 0 - ~
p a t h closet
p s t h L l o s e d
36 o u t , n / u 0 9 9 9 4 6 ~ 1 0 - 2
Trang 7T a b l e 9 - E x p e c t e d e n e r g y l o s t w i t h a 500 NW u n i t
crated c a p a c i t y a n n u a l r e s i d e n c e
t i m e , h r / y r l o s t /
80.718
7 6 5 6 1
1238.629
o f 1238 MWhr l o s t p e r y e a r r e p r e s e n t s one method o f
d e f i n i n g t h e " q u a l i t y " o f t h e a u x i l i a r y s y s t e m a n d i s
s t l i t a b l e f o r c o m p a r i n g s y s t e m s t h a t may b e v a s t l y d i q -
f e r e n t i n r o n c e p t and deslgn
CDNCLUSIONS
To a s s o c i a t e a c o s t t o t h e r e l i a b i l i t y o f a p r o -
p o e t d e s i g n 1 ope o f t h e m a i r o b j e c t i v e s o f l o p 2
t e r r r r e l i a b i l i t y o r a v a i l a b i l i t y s t u d i e s T h i s p a p e r
? a s p r c p o s e d t e c 9 n i q u e s t h a t a s s i s 1 t h e s e o b j e c t i v e s
t o 38 f u l f i l l e d witri r e g a r d t o t h e s p e c i f i c a r e a o f
e l e c t r i c a l a ~ x i l i a r y s y s t e r s a f p o w e r s t a t i o n s The
z o n c e o t c f s y s t e m m i n i m a l c u t s e t s d e r i v e d f r o m n o d a i
m i n i r r a l c u t s e t s w h i c h l e a d s t o t h e e v a l u a t i o n o f t h e
r e l i a b i l i t y i n d i c e s of^ t h e mit d e r a t e d s t a t e s i s v e r y
2 o d e r i u l and can Se a p c l i e d t o many d i f f e r e v t 9rckler-s
'r,e ;omouter D r o g r s r r t h a t ?as Deen a e v e l o c e 3 T O
i n c a r c a r a t e t n e s e t e c h n i q u e s i s v e r y e f f i c i e n t and
r e q Q i r e s o n l y 2 3 5 kwords C o r a system havirig 1OL e l e -
meqts s l d 37 t c lGCC f e i l g r e e v a n t s F u r t % r m o r e th e
c o m p u t i n g t i m e t a s n a l y s e t c e s y s t e r c o n s i d e r e d i n
t n i s c a p e r was 2 3 sec on a C O C 7 5 0 C A d e s c r i p t i o n c f
t h i s pr0gra.n 2nd i t s a p F i l c a t i o n t o f u r t n e r p r a c t i c a i
s t u d i e s s u c h a s p o w e r s t s t i o n s w i t h m o r e t n a n one b n i t
wi@ e t h e s u c j e c t o f f u t u r e p u b l i c a t i o n s
ACKNCh'LEOGENENTS The a u t h o r s w o u l d l i k e t o tb,ank Professor C 6
Cooper o f t h e O e p e r t m e n t o f E l e c t r i c a l E n g i n e e r i n g a n d
E l e c t r o n i c s , U M I S T f o r p r o v i d i n g t h e f a c i l i t i e s n e c e s -
s a r y t o c o n d u c t t h e s e s t u d i e s , t h e C e n t r a l E l e c t r i c i t y
G e n e r a t i n g B o a r d f o r t h e L r f i n a n c i a l a s s i s t a n c e a n d
p a r t i c u l a r l y Yr J.A Chambers, M r A K o z l o w s k i a n d
Mr A Macnrei; o f t h e CEGa G e n e r a t i o n C o n s t r u c t i o n
a n d D e v e l o p m e n t D i v i s i o n fo r th e i r k e e n in t e r e s t a n d
i n v a l u a b l e a s s i s t a n c e M r De O l i v e i r a i s a l s o i n d e b -
t e d t o INVOTAN, L i s b o n f o r o r o v i d i n g h i m w i t h f i n a n c -
i a l s u o p o r t
APPENDIX Assumptions
The loss of any busbar causes one o f t h e f o l l o w -
i n g consequences:
i a j 100% r e d u c t i o n o f o u t p u t p o w e r
( k ) x % ( 0 < x < 1001 r e d u c t i o n o f o u t p u t p o w e r
(cl n o r e d u c t i o n o f o u t p u t p o w e r
The loss o f more than two busbars causes 100%
r e d u c t i o n o f o u t p u t p o w e r
TCIe loss o f a n y c o m b i n a t i o n o f t w o b u s b a r s i f r o m
t h o s e d e f i n e d b y b j causes a known l o s s o f o u t p u t
power
I d e n t i f y i n g a M i n i m a l C u t S e t
E a c h c u t s e t i s d e f i n e d b y a s e t o f s i x v a l u e s
as f o l l o w s :
where
x d e f i n e s t h e t y o e o f c u t
N d e f i n e s t h e b u s b a r t o w h i c h t h e c u t i s
a t t a c h e d a,b,c a r e t h e c o m p o n e n t s o f t h e c u t a n d b a n d / o r c
may be z e r o
R i s t h e r e d u c t i o n o f p o w e r o u t p u t o f t h e u n i t due t o t h e c u t
The v a l u e o f x may b e : -1: a c u t f o r w h i c h e v e r y component i s o u t b u t
s e r v i c e i s r e s t o r e d b y a r e p a i r a c t i o n -2: a c u t f o r w h i c h e v e r y component i s o u t b u t
s e r v i c e may be r e s t o r e d b y c l o s i n g a n o r -
m a l l y o p e n b r e a k e r
- 3 : a c u t f o r w h i c h component a i s a c t i v e l y
f a i l e d and a l l o t h e r components a r e o u t
S e r v i c e i s r e s t o r e d b y i s o l a t i n g component a
k : a c u t as d e f i n e d b y - 3 b u t one i n w h i c h
b r e a k e r k i s s t u c k
A l g o r i t h v
C o n s i d e r t h e t w o m i n i m a l c u t s :
i' = x i N i a i b i c i R i
L e t I and J be a s e t of t h r e e numbers d e f i n e d a s :
ni = number o f n o n - z e r o e l e v e n t s o f I
n j = number o f n o n - z e r o e l e m e n t s o f J
nm = m i n i m u l l o f n and I
j
D e f i n e t h e s e t A = InJ a n d l e t ne be the number
o f n o n - z e r o e l e m e n t s o f A, t n e n na 6 nm
L e t R [ N i l a n d R r N j l b e t h e o u t p u t p o w e r l o s t when b u s b a r s N i a n d N j a r e l o s t r e s p e c t i v e l y
L e t L = 1 when 0 < R ( N i I < 100 0 < R [ N j l < 100 and i n t h i s case l e t R [ N i , N j ) r e p r e s e n t t h e o u t p u t
power i o s t when b o t h b u s b a r s Ni a n d N j a r e l o s t
O t h e r w i s e l e t il = 0
The a l g o r i t h m t h e n p r o c e e d s a s f o l l o w s : [ i l If R ( % l = 0 n e g l e c t i and if R j = 0 s e t
R j = R ( N j 1
i f R ( N j 1 = 0 n e g l e c t j and i f R i = 0 s e t [Ri=RINil [ i i l if Ni = N t h e c u t s a r e i n d e p e n d e n t The v a l u e s
o f R i and J R a r e a s i n lil
J [ i i i l i f na < nm t h e c u t s a r e i n d e p e n d e n t a s i n ( i i l
If N i f N j a n d na = nm t h e a l g o r i t h m proceeds
a s f o l l o w s :
[ i v l x i = x j = x
Trang 8(a1 x = -1 o r -2 and n i = n j
R e j e c t t h e a s s o c i a t e d w i t h t h e b u s b a r
causing minimum power loss, i e i f R ( N i 1 < R C N j l
r e j e c t c u t i
I I = 0 s e t RJ = -100 i f i i s r e j e c t e d a n d s e t
R i = -100 i f j i s r e j e c t e d
I I = 1 and j has been r e j e c t e d t h e n , fi Rf or
R j < 0 s e t Ri = -100 b u t i f Ri and R j 3 0 - s e t
R i = - R ( N i , N j )
S i m i l a r l y i f i h a s b e e n r e j e c t e d t h e v a l u e o f RJ
i s s u i t a b l y s e t
( b ) x = -1 o r - 2 and ni
+ " j
R e j e c t t h e c u t a s s o c i a t e d w i t h t h e b u s b a r
c a u s i n g th e m i n i m u m loss o f e n e r g y p e r y e a r ( p r o d u c t
o f o u t p u t p o w e r l o s t a n d a v e r a g e a n n u a l o u t a g e mti e)
I f I = 0 o r 11 = 1 use a p p r o p r i a t e c o n d i t i o n a l
s t a t e m e n t i n ( a ) above
( c l x # -1 o r - 2
I a i = a j and ni=nj : as i n case (a)
I a i = a j and n i # n j : as i n case cbl
I a i I a j t h e n t h e c u t s a r e c o n s i d e r e d i n d e p e n -
dent
The v a l u e s o f R i and R j a r e s e t as i n ( i ) above
( V I x i # x j
(a1 i f n i # n j th e n th e c u t s a r e c o n s i d e r e d in d e p -
e n d e n t a n d t h e v a l u e s o f R i and R j a r e s e t a s I n (il
above
( b ) i f n i = n j , a d e c i s i o n i s t a k e n a c c o r d i n g t o t h e
f o l l o w i n g t a b l e
-1 - 2 - 3 k i d x i
If 11 = 0, t h e c u t in d i c a t e d in th e ta b l e is
e l i m i n a t e d a n d t h e r e d u c t i o n o f p o w e r o f t h e r e m a i n i n g
c u t i s s e t t o 100% b u t fi r e d u c t i o n o f p o w e r o f t h e
r e m a i n i n g c u t i s x%, p r o c e e d as f o r t = 1
If 11 = 1 [ i n t h e f o l l o w i n g assume t h a t c u t i i s
i n d i c a t e d ; a s i m i l a r r e a s o n i n g e x i s t s i f i t i s c u t j ) ,
t h e n
Ri i s s e t t o -100 if p r e v i o u s l y e i t h e r R i or R j
i s n e g a t i v e
R i i s s e t t o - R ( N i , N j ) if p r e v i o u s l y R i and R j
R i s s e t t o -100 if i t s p r a v i o u s v a l u e i s
R i s s e t t o R[N 1 ifi t s p r e v i o u s v a l u e i s n o t The average annual outage miteo f c u t j i s
d e c r e a s e d b y th e a v e r a g e a n n u a l o u t a g e miteo f c u t i ( X ) - i n t h i s c a s e t h e c u t s a r e c o n s i d e r e d
i n d e p e n d e n t a n d t h e v a l u e s o f R i and R j a r e s e t a s i n
( 1 1 above
a r e n o t n e g a t i v e ' n e g a t i v e
j n e g a t i v e j
( v i ] Scan a l l th e c u t s n o t r e j e c t e d in th e above
l o g i c and make R i = IRil Combine a l l t h e c u t s t h a t
l e a d t o t h e same r e d u c t i o n o f o u t p u t p o w e r o f t h e u n i t
REFERENCES
(11 M.S Grover and R B i l l i n t o n , " A c o m p u t e r i s e d approach t o s u b s t a t i o n r e l i a b i l i t y e v a l u a t i o n " , I E E E Trans Power Apparatus and Systems, V o l PAS-93.1974,
pp 1488-1497
( 2 ) R B i l l i n t o n and M.S Grover, "A s e q u e n t i a l method f o r r e l i a b i l i t y m e l y s i s o f d i s t r i b u t i o n and
t r a n s m i s s i o n s y s t e m s " , P r o c e e d i n g s 1 9 7 5 A n n u a l R e l i -
a b i l i t y and M a i n t a i n a b i l i t y Symposium, pp 460-469, January 1975
( 3 ) R B i l l i n t o n and R.J Ringlee, "Models and
t e c h n i q u e s f o r e v a l u a t i n g p o w e r p l a n t a u x i l i a r y e q u i p -
m n t r e l i a b i l i t y " , 1971 Power Generation Conference
S t L o u i s , IEEE paper 7 1 CP702-PW
Trang 9Discusion
the authors for presenting a very interesting and useful paper The
operation of a generating unit is vitally dependent on the availability of
its associated auxiliaries This paper has presented some algorithms for
quantitatively evaluating the effect of failures in auxiliary electrical sps-
tem on the reliability of a generating unit We would like t o note that
the performance of auxiliary electrical system (and of other systems)
depends on the reliability and maintainability (R&M) characteristics of
its constituents and the configuration in which they are connected The
authors have not illustrated these aspects Perhaps the authors may like
to comment on this
In regard t o the other material presented in the paper, we offer the
following comments and questions
estimates have been associated with the calculated reliability indices
1 The cost of unreliability is mentioned in the paper but no cost
The authors may like t o explain why this was not done How is the cost
of unreliability expressed? Is it expressed in terms of MWhr not supplied
or 1% increase in Forced Outage Rate (FOR) of a particular unit? We,
in Ontario Hydro, use the latter method and consider cost of additional
reserves required and energy replacement costs
2 The results given for the MWhr/yr not supplied by a generating
unit (due to the failures in its auxiliary electrical system) are based on
the assumption that the auxiliary electrical system is required to oper-
ate throughout the year This may not be true when the generating unit
due to failures in other auxiliary systems The actual values of MWhr/yr
is on a planned outage, on a reserve shutdown or on a forced outage
not supplied due to the failures in auxiliary electrical system will be,
therefore, less than those given in the paper
3 The authors have considered the case of a single unit station
For a multi-unit station, the MWhrs not supplied cannot be calculated
by multiplying the single unit values by the number generating units in
the station Some of the buses can be supplied from the station com-
mon bus or the buses of other units For this reason, the whole auxiliary
electrical system of the station will have to be considered for a reliability
analysis This may require a very large computer storage with the pro-
cedures described in the paper
4 It is t o be noted that in those cases where many single con-
deratings or outages of a generating unit caused by the failures of its
tingency events exist, a very little effort is required t o evaluate the
auxiliary system This is evident from tables in the
paper We have used a very simple manual approach in our work on
breakers on the reliability of a 4x500MW fossil station[ 11 It was con-
evaluating the effect of reliability performance of 4.16 kV in-station
cluded that considerable savings in capitalized costs can be obtained if
breaker failure rates were decreased by an order of magnitude
We fully endorse the viewpoint of the authors that there is much
t o be gained by cost-benefit analysis of auxiliary equipment in stations
The capitalized cost of 1% increase in FOR of a 500MW nuclear unit
at present is of the order of $10M This cost figure clearly shows the
magnitude of savings to be obtained by improvement in reliability of
various systems and subsystems associated with a unit It also provides
a designer with a dollar figure which can be used in evaluating the
worth of improvement of various equipment and systems
In conclusion, we again compliment the authors for a useful
contribution
REFERENCE [ 1 ] Grover, M S and M T G Gillespie, “A Cost Oriented Reliability
and Maintainability Assessment of Circuit Breakers in the Design
Manuscript received February 24, 1977
of Auxiliary Electrical Power Systems of a Generating Station”,
Proceedings of the IEEE/ASQC Third Reliability Engineering Con-
ference for the Electric Power Industry, September 1976
R N Allan, R Billinton, and M F De Olivdra: We would first like to thank Mr Grover for his kind remarks and for the very pertinent com- ments he has made
Mr Grover is quite correct in noting that the performance of the
auxiliary electrical system is dependent on the R & M characteristics of the components and their configuration Although we have considered only one set of characteristics and one configuration, the importance of
ies[ 1 1 to be performed by varying the R & M characteristics and thus these techniques is that they permit a wide range of sensitivity stud- the component indices used and by varying the configuration of the components The ability t o assess objectively the impact of both aspects
by evaluating one overall index is considered of great benefit when com- very different sets of busbar indices and derated states
paring different systems and characteristics, all of which may produce
We deliberately did not extend the overall index (MWhr not s u p
method for costing the unreliability, although the one used by Ontario
plied) into one of cost since, at present, there is no universally accepted Hydro seems t o be an important and practical measure We considered
it more appropriate in the discussion of the techniques however to
limit the analysis to evaluating the overall unreliability index which can
be subsequently translated into one of cost depending on the policy and philosophy of individual utilities
per calendar year may be less than the values quoted m the paper due
Mr Grover is again correct in noting that the MWhr not supplied
to the reasons he quotes However the results should be interpreted as
the MWhr not supplied per year of operation and therefore they should
be weighted by the proportion of a year that the unit is required to operate in order t o evaluate the MWhr not supplied/calendar year Although the techniques considered in the paper relate to a single unit, the authors have extended these to consider multi-unit stations These additional techniques permit stations having up to 5 units or 4
units plus a common station supply to be evaluated and include the as-
sessment of busbars fed from common station supplies or from busbars
of other units Although computational effort clearly will increase both the storage requirements and computational time remain within very practical limits The CEGB in the UK are currently using a program based on these techniques for evaluating multi-unit stations and it is anticipated that this will be the subject of a future paper
We were very pleased to note that Ontario Hydro have made similar, albeit -simpler, analyses and have found that considerable savings can be obtained This is a view which we endorse and justifies the development of realistic reliability evaluation techniques that per- mit utilities t o perform cost-benefit analyses
REFERENCES [ 1 ] Allan, R N., Billinton, R and De Oliveira, M F., “Evaluating the reliability of auxiliary electrical systems of generating stations” Canadian Electrical Association, Thermal Power Section, Spring Meeting, Toronto 1976
Manuscript received April 5 , 1977