A GflYERAUZED MOOEL WR QUANTITATIVE WALUAT1ON OF REUAB#UTYI lYPlCES 
OF WE NATIOMAL GRID SYSTEM. 
"G  A, AJECSIKOKO ', 0. A. FAKOLUJO and T. I. RAll Department of UecMcal and EIectronkZngtnering 
Lado ke Akintola University of Technology, Ogboms~ 
Z~epamnenotf  aecaonk and E W a lE n&eerIng 
A 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 ethea & m  
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 7s L W  !am%a nd 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 orreh th  
WDkqfll.S%3 876% und 42- t m m Mh paorf&&Mn& kwik 
wrth t h e o W o f w ~ ~ [ rtwfpldi~r#l rd-qqWswlara&wb@ 
Fern W i m  o g e m w m odel 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 ,  mrn mmge nW&y krdsx WOI), 
sptern averopt h t e m m n e y Im W Wn),a m m r a ylemge intemption 
d u W J ndw (WW].  
I N T R O P U r n  
The funcklm of an demk m r  -s  is bo the mrn load requhmmt with a 
reasonable assurance of continuity and qudw. The am of 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 ibyy~th~e t emrofdhbtlity. (Roin!rtset d 1999,Aodemnand Bose 
2003, Blnm 2W) .  
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 p hase worldng and afttn a study of the &c&W condkkns 4 one phase is st~ffidmto  
ghre a compkte analysis et at 2000). 7hk ehd& utility industry k moving tma& a demguhtd, 
c o r n ~ eenv lronrrwnt 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 sh ow'a the pmb~biDity of -maam d a t e d  to fMum emnts. An annrrallhda 
h 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 [ 2i0m~sf)@ ?d.a ~ ~ t I ; d c x h t k ~ ~ r n s W (nMS~S) t m r  
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  
vahthdlogte{~~~)funetbnbd~or&kt3ondthe~~inb.~s~lmeatlgsteths 
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 w  
optlmkatlbn 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 mpmatbn mlwWs. The mb with the proposed 
methad-, 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 da- WPI k c o m b b y JwMm q 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 @ Md  w ef# ttw (~dooQt,w o d M M m odd q m t k m sa m 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# + ~+pgg4 +  P$+P$ +P#+P, ...........1 5 )  
WtnenK=refaUwWDf 
x * n u * o f w t k  
PLPZIPSIP~PPS ehmkthewefficknkt. 
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 #m~od~sl-~&p mtbn dewlow k 
RC'=Q ~ ' + & ~ S  +aya+ayag. *-....-. .*..(.$ 1 
Whem RC = elatbe CAI# 
y = ~lmbrotfeed8m 
Qt&&Q*and.Qar?etkEoeffloients, 
The vdu& d t h a m t#klmits are obtahed h nth e 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,P he@iimdlredm odel 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 mn ww- 
0 = numbroffeadm 
n = runnlllgvwhbk 
k m 0 t d ~ otfb N WM~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) mdhrnzakkvrl 
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(Fflj 
(b) w W W & k J  
~ffwdtlw(lbadanI,  ~ , 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-, nmt M,n& um &. Thb is beam b mnrfnd, the W 
o 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 , thu s they have avmge relliibillty Mw hile I-, lkd4 
Keduna a d K am dMMlm system hwe avemge d a W e U 9101s of 119S%, 39.76%, ml7% 
and41d8%msm#velymsl8ngthsmtol?#8pow~hls. 
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RelathC AlM for &@a DbtdbutbnS y s b n ~  
d 
tabk Relatle CAtDt for Porthamurt DWrktlon Syrkn# 
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b.4768 
.b ~ a m a  D.4146 
b k l  103867 
bundun wada b.2772 - 
Table 6.a 
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UNIVERSITY OF IBADAN LIBRARY
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Roirertr, N H m , ~ t s nBrdplr mY(l9B): WhdmWcal~WhteUaMe~@ wrInf.Mc 
Gmw Hi!, New Y w k  P. -83. 
Sacket RK. 8ansaI R C a r r d ~ G O , f W W~ ~ ~ W ~*  ~ d ~ ~  
stabtl#y and m01nuatbn power fiaw on power *emf. IEEE T r a mrn  systems, val. 7, 
No* 1, Feb. 2m,p p 258-263 
Sakis Melitrpaulos A.P, Caml Cheng 5 and F a g  X P006k 'Pedo- evahratiwr of wrb 
anslysk m e t W . E EE TtgnxoEtSons on powsr systems, vd 9, Na*3 , pg U41-1449. 
Singtr U.a nd M hJ  (2006): YCWnpciiae  fern teItaUlity evslwmn using sWic space pmnfnf. lEEE 
Transactions on Power Sptms, vol. U,N al, pp 4x479. 
Wang P, BIlliaton RandG ad L (=I: "MmbE#y d W h t h w a ~ ~ d ~ t i o n s y s rtetefabmlfity  
i n d i  8 ~ s e q ~ l sIEEEt Tw~dms~ on gowuw By~s tem,  ~vol. 11 , No. 6, 
PP en. 
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