A GflYERAUZED MOOEL WR QUANTITATIVE WALUAT1ON OF REUAB#UTY IlYPlCES OF WE NATIOMAL GRID
SYSTEM.
G
A, AJECSIKOKO',
0.A.
FAKOLUJO and T. I. RAll"
Department ofUecMcal
and EIectronkZngtnering Lado ke Akintola Universityof
Technology, O g b o m s ~Z~epamnent
ofaecaonk
and E W a l En&eerIngA S l m C T
R d h W # r y ~ d t p t m ~ t o b e ~ & k a m f C o g k w a y I t o j t t d p e t h e p e ~ o j o n ~ ~ ~ m . R e ~ h d i E c r w h M a m C H P p O S h d b y L h &
~ E E E a r e u s e d ~ ~ & t h a ~ o f 5 e ~ d k t r l . b v # o n s y s m 0 n t h e mtbmI g#.
T e n p r ~ o f o u ~ ~ ~ I ~ - ~ ~ ~ n ~ ~ ~ b l o n
~ o n t h a ~ ~ I ~ r v e r r ~ o r a t ~ C n L h ~ r e ~ ~ ~ r v o A A
~ ~ m o G C e l w r r s ~ f i r a ~ ~ o f r s ~ ~ s o f
t r # m ~ I ~ ~
~ d ~ o J t l r s m O d e I s t a W w l c h ~ o f t h e ~ t e l b b l & y C n d k e E u n d e s d m a t @ t h e ~ o f s p t m ~ t o t k ~ r e m t e
o f l h e ~ ~ ~ ~ r n t k ~ ~ * T h e # ~ n ~ ~
~ b m y I n d J E w m u s g d o ~ l i l p u t ~ j b r t C k g m ~ ~ m O d a I .
R e b t k W O I k P d e x b w m p u t e d h y ~ ~ l r r f n O ~ ~ 7 . T w h ~
~ ~ ~ m b # d k g m p h o J t l r c ~ C s r 6 1 o g o l h J t ~ o f f e e & m tha
p e r r m E L l q e ~ r ~ M M t t 9 1 D k ~ ~ ~ H o r r c w r t Q n d B e n k r d ~
~ mOrr 7 L W s
!am%
and z s v 7 9 A i W & ,tnw
Q r r C W &* kbvk I- IW, K&m and K w syrtkmf tmw palewrtape ~ ~ e r a o e r r h t h WDkqfll.S% 3876% und 42- t m mMhpaorf&&Mn& kwik wrth t h e o W o f w ~ ~ [ r f l ~ t w p d i r # l r d - q q W s w l a r a & w b @Fern W i m o g e m w model is lbmruldtd @f o qlmnmtiva ev~hwtbn
~
emlay mndksofthe mbmlgrld.
~ ~ & d n w d e d k p ~ p m d A o n w j r w e o r d a r d c p e n & ~
o n t h e k I ~ ~ ~ f h t d ~ ~ d f k m r m b c r r r f
~ t b n ~ r s .
-: Re- CPCW, m&Wtp h a s , mrnmmge nW&y krdsx WOI), sptern averopt h t e m m n e y ImW
Wn),
a m m r aylemge intemption d u W Jndw ( W W ] .I N T R O P U r n
The funcklm of an demk m r-s is bo the mrnload requhmmt with a reasonable assurance of continuity and qudw. The amof the s@em to prrrvlck an supply o f e ~ c a l e n e r g y t s u s u a l i y ~ ~ bythe temrofdhbtlity. (Roin!rtset d 1999,Aodemnand Bose 2003, Blnm 2 W ) .
O i P V l b u t i m ~ e m b ~ n A f h t h e c o n ~ 1 ~ t o b ~ t o m ~ m e r s ~ m e a n s o f b w e r v o t t ; l g e ~ T h e ~ o f d ~ t l o n n ~ ~ k H K 1 I ~ t n o r m a l o p e r a t t m I s r e m ~ E t o w t o babme t h e phase worldng and afttn a study of the &c&W condkkns 4 one phase is st~ffidmt to
ghre a compkte analysis et at 2000). 7hk ehd& utility industry k moving tma& a demguhtd, c o r n ~ e envlronrrwnt where utilities must hue ammhii hfomwtion about system perftrmrana to
ensure that mahename casts ore spent w W y and that cudoms -ns are met (*t et
4
2W)+
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RmkwofRd.kdwQlG
A t k n P ~ h p ~ e ~ l 7 ~ b t k n t a e h n ~ r b r ~ p ~ ~ h ~
a f - * l u n b ) s t r m ~ ~ ~ t s ~ b y W a n g a s l t ~ . A n ~ b a s s d I n d a K h m m show'a the pmb~biDity of
-maam
d a t e d to fMum emnts. An annrrallhdah M ~ m ~ n t s h p r ~ b a b m b k s d ~ W b y ~ t h s ~ ~ ~ o v a r a y e P r * m ~ s h o w t h o t t h s t b r l h v w E p n e w b t ~ ~ ] h 9 s 1 ~ 1 ~ s l g k t ~ o n t h c
p r o b a b % ~ d ~ d t h e k a d ~ a R d ~ I n d l # r
K w s b d W m ~ ~ r ~ I f w e r r a ~ t i r e ~ d M c p o w e r s y s t e m f o t l m & e r m ~ ~ ~ ~ d ~ ~ t k d l a b # l t y d s n ~ p o w e r m d m - e k - M s n d a - h m n o f j h e p N m ,
w ~ a n d m a t W o f o b a a t n l n g O b s d r r H o n t r s ~ ~ ~ o n a p ~ d e t r e k p s d b s o k ~ ~ a n d r e w m m e n d e d ~ h H l h i C h t h b ~ m e a n b e d a r e a b ~
~ h ~ . n d V b l y [ 2 0 ~ ) i m s f @ ? d . a ~ ~ t I ; d c x h t k ~ ~ r n s W n ~ t m r (MSS)
m h M ~ . I t k a ~ ~ ~ ~ ~ 7 h a ~ I t o d d ~ ~ ~ a l e u k s o f m u # E v a h t h d l o g t e { ~ ~ ~ ) f u n e t b n b d ~ o r & k t 3 o n d t h e ~ ~ i n b . ~ s ~ l m e a t l g s t e t h s
o u t c a m ~ o f r m o d ~ o C a ~ O a v a l d r ~ ~ ~ ~ ~ o m p w # ~ b ~ ~ .
f h e s e I d ~ e a n b e ~ M d u r l r i g t k e d a s i g n q P J ~ ~ # d a t h e n b e W f woptlmkatlbn of MS$ mllablliky.
A h e a r cbntdadbn hem mdbi d &sWwMn m81dMIty indleere and b application in Marrte
~ s r l a s i m u l a t i o n a l s d s e r # l t M t y ~ b ~ b y ~ ~ o t a l ~ E T h t o h r m o d e l w n b e applied to dsk and snrsitMty anatylrla T d t t b m l eppmcks f# bMh a-b muire mew
~ t t t 0 p f i s d W ~ l n d l e x ~ m e n t ~ m o d a l f a W t a ~ ~ t h e ~ l n d k e g a f m o s t ~ m ~ t n m ~ w ~ ~ ~ . d t h e n a t l o n r l ~
~ ~ c t d ( ~ ) ~ a ~ m 9 v a i u a & t h e h p a c t d d f s t t l b u k d ~ ~ a t f w r a r t b r e a a W l f i W l c e s & h ~ n c t i w o r k ~ h d ~ . a i n t . T h l s b n p a c t k
sssarsedeol#lctwlnethatdMMgenemcanbecoMleetedtoanisoOatedWortoafesdw
w ~ W ) n e p ~ f h e ~ ~ ~ ~ u e c d I s W m a s I n r ~ v e ~ a C t h e p o w e r summath Foad fW
rrr-
and m p m a t b nmlwWs.
The mb with the proposedmethad-, ta nrodel the #salatd and intemmmd qmatbs
of
dktrsbmd genWitbn,d e m o n r t ~ t h s t d W ~ d ~ b a ~ k n ~ o n t h s ~ ~ o f ~ r P b u t i o n
n e t r v w k s , f h e & ~ h 9 . ~ ~ v a l S d a t e d i n a l a g b d i s t t i e u t C o n t e r t ~ e m . ~r e r u l t s s w t h e ~ m o b ~ t h e ~ e t a F $ i s t r 3 b u # d ~ r a t l o n m t h t r e H a b i n t y l n d k e s ofdwbuthRstworkc.
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' ~ d M ~ ~ m a r e d a s a w a s t u d k i n t h l s - r c t r d F w t h e ~ dlstdbuttan syskmb, the
d a -
WPI k c o m b by JwMmq
M A W 7.7 which autwmtblly~ t h e g r s r p h s d ~ l a t l \ r a ~ D k ~ n a m d k ~ ~ ~ .
with t k @ M
d
w e f#ttw ( ~ d o o Q , two d M M modd q m t k m s am f;ormulakd far the sewn dkblbtton system forthe quntMbe9vahatW ofdaMHy Wces ofthe natbmt grid.Ihdsn, I;@ Wuns, Port-lWmwt and tl&n dWibu0ton systems hawe the
-
t ? m h m c a l ~ l w h f e h i r ~ b y :
RC
=P# + ~ g
+pg4+ P$+P$ +P#+P, ...
1 5 )WtnenK=refaUwWDf x * n u * o f w t k
P L P Z I P S I P ~ P S Pehmkthewefficknkt.
T h e v a I u r r s a f t h ~ d d ~ ~ 0 b t a W f R l m ~ ~ ~ t h 9 " o i m u ~ ~ i w ~ o f t h e dtstrbutlonmr#r.
~ W e I B c p t a P l ~ n f w W d k t r l ~ ~ b a ~ W ~ d ~ n a f M d e r &
FwKdnoBnd Bmh d & t r l b c i t # m # ~ ~ ~ modsl-&pmtbn dewlow k
RC'= Q ~ ' + & ~ S +aya+ayag .*-....- ..*... ($1
Whem RC = elatbe CAI#
y
=
~ l m b r o t f e e d 8 mQt&&Q*and.Qar?etkEoeffloients,
The vdu&
d
t h a mt#klmits are obtahed h n the shulaaton mutts oF the dkMbutson s W ? ~~ m o d e l c q l s a t h b w t h e r e t l # o ~ t l o n s y s k m i s o p ~ m l a l d a r d e r r C ,
Maw, from equations (5) and
[a,
Phe@iimdlred model e;quadm Ds oMafnd a:whera RC r reltkrq WDI
~ = o o e f f l d m o f ~ d ~ ~ ~ m a r c ~ W I t r w n . t h a d d * s b n u ~ work. %we meflldm .mn be d e b m i d using la#mp rntidhd, Newton #tathod
I ; h e w m nww-
0 = numbroffeadm
n =
runnlllgvwhbkk m 0 t d ~ o f t b
NWM~I
~ s n d ~ s
E W ~ ~ m m m s f ~ ~ ~ a n ~ u ~ e d m ~ s t u d b I R t h a : d pgperhll i n b ~ ~ ~ w k k h m b e ~ w .
(iJ
Mndl
scale h l.
@I) mdhrnzakkvrlUNIVERSITY OF IBADAN LIBRARY
(Fflj
(b)
w W W & k J
~ f f w d t l w ( l b a d a n , I ~ , m d ~ n s , ~ a n d I M n ~ t h a t e b y S ? d t h e ~ m a ~ l equatbn fall fnto
am
d t h e- ,
nmtM ,
n&um&.
Thb is beamb
mnrfnd, the Wo f t n d ~ ~ ! ~ h t h e s e ~ o o m p a r e d w f f h ~ ~ ~ b t h e w o r W . I ~ w d l b f n
~ e s m a l l d e ~ F o r t h e ~ ~ t o ~ d c P c r l b e d ~ ~ ~ ~ k ~ b a s s ~ I n t e m w o f
p o w e r ~ I ~ n t w M Q w # k ? t r u c P o r ~ r ~ ~ R v e ~ s r e m o r e t n d W W x e d t h a n O ( a n o a r w t B e n l n . f h e m o r e M ~ r ~ & h ~ r ~ ~ d t h o ~ t h e o *
q f t h e ~ l a l ~ u p r w ~ ~ h ~ b ~ m f u # y ~ . T h e r e l a t I r e ~ s f w t h e d b f t l b r $ t o n ~ a e ~ d ~ I n t a b b
l.Oto7.0,wh&thesDrmrliltton m u b a r e a b d b & y e d i n ~ l.OtuT.0
~ ~ ~ r d a t h f % ~ f w I b s d a n , P a M m r t s n d B a n i n d ~ s y o t s r r r r are 7288%, 52.79% ?Sw79% W b ,thus they have avmge relliibillty M while I-, lkd4
Keduna a d Kam dMMlm system hwe
avemge
d a W e U9101s of 119S%, 39.76%, ml7%and41d8%msm#velymsl8ngthsmtol?#8pow~hls.
UNIVERSITY OF IBADAN LIBRARY
Relath CAlM for &@a Dbtdbutbn S y s b n ~
d
tabk Relatle CAtDt for Porthamurt DWrktlon Syrkn#
UNIVERSITY OF IBADAN LIBRARY
b.4768
.
b ~ a m a
D.4146b k l 103867
bundun wada b.2772
-
Table 6.a
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UNIVERSITY OF IBADAN LIBRARY
UNIVERSITY OF IBADAN LIBRARY
UNIVERSITY OF IBADAN LIBRARY
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Roirertr, N H m , ~ t s n d BrplrmY(l9B): W h d m W c a l ~ W h t e U a M ~ [email protected] G m w Hi!, New Y w k P. -83.
Sacket RK. 8ansaI R C a r r d ~ G O , fW W ~ ~ W * ~ ~ ~ ~ d ~ ~
stabtl#y and m01nuatbn power fiaw on power *emf. IEEE T r a m
rn
systems, val. 7, No* 1, Feb. 2m, pp 258-263Sakis Melitrpaulos A.P, Caml Cheng 5 and F a g X P006k 'Pedo- evahratiwr of wrb anslysk m e t W . EEE TtgnxoEtSons
on
powsr systems, vd 9, Na* 3, pg U41-1449.Singtr
U.
and M h J (2006): YCWnpciiae fern teItaUlity evslwmn using sWic space pmnfnf. lEEE Transactionson
Power Sptms, vol.U,
Nal, pp 4x479.Wang