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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 of

UecMcal

and EIectronkZngtnering Lado ke Akintola University

of

Technology, O g b o m s ~

Z~epamnent

of

aecaonk

and E W a l En&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 .

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~ ~ ~ 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

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and z s v 7 9 A i W & ,

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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 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 [ 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 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 m p m a t b n

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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(3)

' ~ 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 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 @ 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 m

Qt&&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 =

runnlllgvwhbk

k 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) mdhrnzakkvrl

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(4)

(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

- ,

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 ,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.

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(5)

Relath CAlM for &@a Dbtdbutbn S 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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(8)

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(9)

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(10)

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(11)

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 258-263

Sakis 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 Transactions

on

Power Sptms, vol.

U,

Nal, pp 4x479.

Wang

P,

BIlliaton Rand

Gad L (=I:

"MmbE#y d W h t h w a ~ ~ d ~ t i o n s y s t e m retfablfity i n d i 8 ~ s e q ~ l sIEEETwdms t ~ ~on goww u B y s t e m , vol. ~ ~ 11, No. 6,

PP en.

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