Distribution Network Reconfiguration To Minimize Resistive Line Losses 2

DISTRIBUTION NETWORK RECONFIGURATION TO MINIMIZE RESISTIVE LINE LOSSES G.3. Peponis

M.P. Papadopoulos Member IEEE

N. D.Ilatziargyriou Senior Member IEEE

Electric Power Division Department of Electrical and Computer Engineering National Technical University, Athens, Greece

A b s t r a c t The o b j e c t i v e of t h e a n a l y s i s prcsprited is t o o u l l i n e and v a l i d a t e a mcthodology € o r t h c o p t i m i z a t i o n of MV d i s t r i b u t i o n network o p e r a t i o n , s o t h a t v a r i a b l e loads a r e f e d under minimum encrgy losses. Loss minimizclliori is achieved by t h e i n s t a l l a t i o n of shimt c a p a c i t o r s and r e c o n f i g u r a t i o n of t h e netwot k. I h e impact of load v a r i a t i o n and load modelling on t h e optimizing d e c i s i o n s is examined. Two d i c f e r c n t recoriciguratj on mclhods a r e a p p l i e d and compared.

formula is used f o r -the e s t i m a t i o n of t h e l o s s r e d u c t i o n o b t a i n e d I J a~ p r t i c i i l a r swit.ching o p t i o n , t h a t is c l o s i n g a s w i t c h and opening a n o t h e r i n t h e loop formed ("Switch Exchange Metliod"- SEM). In the second [ 2 , 3 ] , a l l t i e s w i t c h e s a r e i n i t i a l l y c l o s e d , and an optimal load flow i.s o b t a j n e d . System i.s r c t u r n c d t o a r a d i a l c o n f i g u r a t i o n by s u c c e s s i v e openings of t h e switches having t h e lowest c u r r c n t flow, uritj.1 network r a d i a l i t y is obtained ("Seq u e n t i a l S w i b h Opening Method"- SSOM) Many p a p e r s , u s i n g t h e above i d e n s have been prescnted i n r e c e n t y e a r s .

1. IN'I'ROWCTION

In t h i s paper a combiiied method f o r t h c approach t o t h e optima 1 o p e r a t i n g c ondj:t i on I)f t1isi:r i.hi] I:i on ne t works i.s p r e s e n t c d . I t s two main s t e p s a r e : - Optimum o r xicar optj.muin network configurn-lion is obt a i n e d u s i n g one of .the two b a s i c methods mentioned above, t a k i n g i n t o account loading and v o l t a g e cons h - a i n t s . A v o l t a g e q u a l i t y index ['(] is a l s o Galculated. - Optimum c a p a c i t o r s i z e and l o c a t i o n a r e dct.ermined. 'l'lris is obtai.ned with t h e mcthod developed i n 151, based on dynamic programming t e c h n i q u e s . T h i s procedure is r e p e a t e d u n t i l t h e two steps produce the same c o n f i g u r a t i o n a i d c a p a c i t o r arrangements.

I _ _ -

.

.

Most e l e c t r i c d i s t r i b u l i o n networks a r e o p e r a t e d r a d i a l l y . Nevertheless, t h e r e a r e u s u a l l y s e v e r a l i n t e r c o n n e c t i n g t i e s w i t c h e s a v a i l a b l e , e s p e c i a l l y i n t h e undergroutid medium v o l t a g e networks. C o n f i g u r a t i o n a1 l c r a t i o n s may be performed by changes of t h e s t a t e of network s w i t c h e s , i n such a way t h a t r a d i a l i t y is always r e e s t a b l i s h e d a f t e r t h e end of l h e manipulations. The optimal o p e r a t i n g c o n d i t i o n of d i s t r i b u t i o n networks is u s u a l l y considcred t o be obtained when l i n e l o s s e s a r e mii~imized,without any v i o l a t i o n s of branches loading and v o l t a g e limits. Olher s e r v i c c q u a l i t y c r j t e r i a caii be Curt h e r used, l i k e s e r v i c e c o n t i n u i t y o r v o l t a g e s t a b i l i t y .

The computer program dcvcloped is a p p l i e d on a . t y p i c a l 2OKV network c o n s i s t i n g of f i v e f e e d e r s . The impact of load v a r i a t i o n arid load modelling on loss minjmization and

Loss minimization problem was formely f a c e d as a p a r t of d i s t r i b u t i o n networks p l a n n i n g s l u d i e s Recent advances i n d i s t r i b u t i o n automation technology have s u b s t a n t i a l l y i m proved c o n t r o l arid network management c a p a b i l i t i e s . Cons e q u e n t l y , t h e g e n c r a l problem of l o s s minimization has g r e a t e r e f f e c t on d i s t r i b u t i o n o p e r a t i o n d e c i s i o n s .

.

v o l t a g e q u a l i t y index improvement, is examined. 2 . GENI!RAL ALGORI"

The proposed method c o n s i s t s of t h e following steps: P r a c t i c a l l y , l o s s minimization is o b t a i n e d i n two ways: i n s t a l l a t i o n o f c a p a c i t o r s , when t h i s is economically justified, network r e c o n f i g u r a t i o n , t h a t i s t h e s e l e c t i o n of t h e p r o p e r t o p o l o g i c a l s t r u c C u r e of t h e network f o r miniinum losses.

-

1.. Iletermine the o p e r a t i n g c o n d i t i o n and cnergy I.ossc?s of

t h e c x i s t i r i g system. 2 . Reconfigure t h e system and determine the iiew o p c r a t i n g condition. 3 . Remove t h e i n s t a l l e d c a p a c i t o r s and connect t h e onas r e s u l t i n g i n the mmimuni net b e n e f i t OIL the ireconfigured system. 4 . Repeat s t e p s 2 and 3 u n t i l r e c o n f i g u r a t i o n and capac i.tor i n s t a l l a t i o n s t c p s produce t h e same confi.guration and capaci t.or arrangements. 5. l'erform a f i n a l load flow a i i a l y s i s and c v a l u a t c cnergy losses.

Determination of t h e optimum s i z e and p l a c e of c a p a c i t o r s i s a very o l d problem f o r d i s t r i b u t i o n enginpers atid s e v e r a l papers have been published on t h i s s u b j e c t . Reconf i g u r a t i o n problem has been r e l a l i v e l y r e c m t l y t a c k l e d , because of t h e advanced computing and c o n t r o l c a p a b i l i l i e s r c q u i r e d f o r i t s s t u d y . lhis i s dne t o the f a c t l h a t i n r e a l d i s t r i b u t i o n networks t h e numhrr o€ s w i t c h i n g o p t i o n s t o be t e s t e d and c o n t r o l l e d f o r l o s s minimization is very l a r g e .

In t h e f i v e s t e p s o u t l i n e d above, follows.

G e n e r a l l y , t h e t o t a l load a t each node consist:? of f i v e types ( e . g . r-csident.ia1, i i i d u s t r i a l e t c ) . Typical load v a r i a t i o n with time is dctermj.nec1 by a given p r o f i l e f o r each c h a r a c t e r i s t i c day ( c . g . w i n t e r worlti.ng tiily, snmmer weekend day e t c ) . Given t h e t o t a l power i n s t a l led and tlrc load composition a t each riotic, a c t i v e and r e a c t i v e load curves can be obtained.

l I e i i r i s t i c r a t h e r than a n a l y t i c a l methods appear t o be more c f f c c t i v c f o r f c e d c r r c c o n f i g u r a t i o n s t u d i e s . 'Two b a s i c methods have been developed. 111 t h e f i r s t [ l ] , a simple

Paper APT 425-06-21 accepted for presentation at the IEEE/NTUA Athens Power Tech Conference: "Planning, Operation and Contiol of Today's Electric Power Systems", Athens, Greece, Scpt. 54,1993.

load is modeled as

Loads caii be r c p r e s e n t e d by d i f f e r e n t models as c o n s t a n t c u r r e n t ( v o l t a g e independent c u r r e n t i n j e c t i o n s ) - CJ, c o n s t a n t power (i.nversely p r o p o r l i o n a l t o v o l t a g e vitlue) CS, c o n s t a n t impedance ( d i r e c t l y p r o p o r t i o n a l t o v o l t a g e valuc) CZ arid mixed - MX t h a t is any conil,inalion of t h c p r e v i o u s models.

-

-

GO 1

:

?'he t w o b a s i c reconf i g u r a t i o n methods have been irnproved and g e n e r a l i z e d i n o r d e r t o account f o r v a r i a b l e loads.

d ) A s w i t c h i n g o p t i o n l e a d i n g t o energy l o s s r e d u c t i o n can be c a r r i e d o u t i f no branch flow c o n s t r a i n t s a r e v i o l a t e d . R e f e r r i n g t o F i g . 1 , t h e checks r e q u i r e d a r e d e f i n e d . S u p e r s c r i p t s r e f e r t o the network c o n f i g u r a t i o n s b e f o r e and a f t e r t h e s w i t c h i n g a c t i o n .

3.1 SWITCII IXCIIANGE MLTlIOD (SEM) This method, d e s c r i b e d i n [ l J , i s a p p l i e d f o r C J loads. I t is based on t h e e s t i m a t i o n O C l o s s r e d u c t i o n from (l), r e s u l t i n g from a p a r t i c u l a r s w i t c h i n g optioii, t h a t i s t h e c l o s i n g of one open s w i t c h and t h e opening of one of t h e s w i t c h e s i n t h e loop formed.

where : D s e t of buses which a r e disconnected from Feeder-I1 and connected t o Feeder-I with t h i s s w i t c h i n g o p t i o n , m,n buses connected t o branch m-n, where t h e s w i t c h t o be c l o s e d is i n s t a l l e d . Dus m is connected on Feeder-I and bus n on Feeder-11, complex load c u r r e n t a t bus i , 3, R l o o p s e r i e s r e s i s t a n c e of t h e loop formed by c l o s i n g t h e s w i t c h of _branch-m-n, 5, component of E=R,,, J B t Icorresponding s t o bus m . R,,,, is t h e " r e s i s t a n c e matrix" of Feeder-I b e f o r e the load t_ransfer, found u s i n g ttie s u b s t a t i o n bus a s r e f e r e n c e . is t h e _ v e c t o r of bus c u r r e n t s f o r Feeder-I, %,, J,,; similar t o E, b u t d e f i n e d f o r 1ius n on Feeder-11, Re[. J , *, I . I r e a l p a r t , complex conjugate and magnitude operators, respectively. A f t e r c o n s i d e r i n g a l l p o s s i b l e s w i t c h i n g o p t i o n s , t h e one which provides ttie l a r g e s l l o s s r e d u c t i o n i s c a r r i e d o u t . This set of a c t i o n s is c a l l e d " s t e p " . Successive s t e p s a r e followed u n t i l no f u r t h e r l o s s r e d u c t i o n is p o s s i b l e . T h i s method does not e n s u r e convergeiice t o t h e optimum c o n f i g u r a t i o n , while it is dcpendent o n t h e i n i t i d 1 s t a t e of t h e network s w i t c h e s . 3.2 IMPROVED SWITCII EXCIIANGE ME7110D (ISEM) Let us c o n s i d e r t h e network of F i g . 1 and examine t h e e f f e c t s of c l o s i n g t h e s w i t c h of branch m-n and opening branch k-1.

., F i g u r e 1: Switching o p t i o n : c l o s i n g s w i t c h of branch m-n, operiing s w i t c h of branch k-I. Equation (1) can be more e f f i c i e n t l y a p p l i e d , i f we t a k e i n t o accouril t h e f o l l o w i n g g e n e r a l remarks. a)

zp31 =€kl

where

T,, i s

-

i i ) On t h e p a t h ( s t a r t i i i ) On t h e p a t h ( 1

- n)

m) :

f!ft =

: fjfe=

fP+f'zf

fyf-fEf

I n p r a c t i c e , changes i n t h e s t a t e of t h e two s w i t c h e s ( c l o s i n g , opening) a r e n o t simultaneous, and t h e loop formed remains f o r s e v e r a l minutes. During t h i s o p e r a t i n g c o n d i t i o n c o n s t r a i n t v i o l a t i o n s on t h e f o l l o w i n g branches should be examined :

iv)

p c p

m

-

- fbef n ,L%l

-bef

Vm

on t h e p a t h ( s t a r t On t h e p a t h ( s t a r t

- q ~ ) : fiw = f'pf+f&q - n) :"'f = fyf-f&mP

In both r e c o n f i g u r a t j on methods branches are numbered a f t e r each s t e p i n l a y e r s away from t h e r o o t , a s p r e s e n t e d i n 171. 3.3 SEQUENTIAL SWITCH OPENING METHOD (SSOM)

I n t h i s method, developed i n [2] and modified i n [3], a low l o s s c o n f i g u r a t i o n is determined by a p p l y i n g an optimal power flow a n a l y s i s t o t h e system w i t h a l l s w i t c h e s c l o s e d . The system is l e a d t o a r a d i a l c o n f i g u r a t i o n by opening t h e s w i t c h e s o f t h e branches with t h e lowest c u r r e n t , t h e optimal flow p a t t e r n being determined a f t e r each s w i t c h opening o p e r a t i o n , c a l l e d " s t e p " . Branch c u r r e n t flows should be checked f o r c o n s t r a i n t v i o l a t i o n s a f t e r each s t e p . Optimal flow a t each meshed network is determined a s t h e branch c u r r e n t flowing i n t h e r e s i s t i v e network ( w i t h branch r e a c t a n c e s n e g l e c t e d ) , t h e load nodal c u r r e n t i n j e c t i o n s considered c o n s t a n t . While t h i s i s t r u e f o r C J l o a d s , a s proved i n [3], it can n o t be g e n e r a l i z e d f o r a l l load models. This i s due t o t h e f a c t t h a t load dependence on v o l t a g e does n o t allow t h e d i r e c t t r a n s f e r of t h e load c u r r e n t i n j e c t i o n s c a l c u l a t e d f o r t h e complex network t o its r e s i s t j v e p a r t . Mathematically, t h e d e r i v a t i o n s r e q u i r e d by t h e Lagrange o p t i m i z a t i o n method do n o t g i v e simple r e s u l t s similar, t o t h o s e f o r C J loads i l l u s t r a t e d i n [3]. Load v a r i a t i o n complicates f u r t h e r t h e c h o i c e of t h e s w i t c h t o be opened a t each s t e p . Various t e s t s have shown t h a t t h e switch t o be opened corresponds t o t h e branch with

min

:Irkct)

,

where

f k ( t ) t h e complex c u r r e n t

flowing on hranch k a t time t .

t h e load c u r r e n t flown

through t h e s w i t c h whose opening is being examined.

b) @# = RBmm*d ( 1 , m), f . where: R B R A N C H - diagonal m a t r i x of branch r e s j d a n c e s , A(i,m) - m column of t h e branch i n c i d e n c e m a t r i x adapted t o t h e r a d i a l o p e r a t i o n of d i s t r i b u t i o n networks [ 6 ] and YBRANC,,- brancl1 c u r r e n t v e c t o r . Avoiding c o n s t r u c t i o n of R,,,matrix is very advantageous for reconfiguratiori processes. c ) Lost energy can be e s t i m a t e d by adding AP(t) f o r a l l d i f f e r e n t network l o a d i n g s (time p o i n t s ) . This summation p r e v e n t s u s from t h e u s e of t h e I i e u r i s t i c rule_ t h a t I_oss r e d u c t i o n may occur l o r t h e s w i t c h e s where IB,I < IE,I, r e d u c i n g t h e number of s w j Lching o p t i o n s [ I ]

.

GO2

However, t h i s method p r e s e n t s t h e advantage of being independent from t h e i n i t i a l c o n f i g u r a t i o n arid s o i l is more l i k e l y t o o b t a i n t h e a b s o l u t e optimum r a t h e r t h a n a l o c a l minimum. Power flow s o l u t i o n of meshed networks. Using d i a c o p t j c s [ 7 ] , it can he proven, t h a t a branch having a normally open s w i t c h can be p r e s e n t e d i n c l o s e d p o s i t i o n a s nodal c u r r e n t i n j e c t i o n s on t h e nodes connected. Current from

'ii3 is calcuIat$d

fi;l

-

I f more than one normally open s w i t c h e s e x i s t , c l o s i n g of each one a f f e c t s c u r r e n t _ j n j z c t i o n s r c p r e s c n t i n g t h e o t h e r s through t h e v o l t a g e s V i , Vi. I n such c o n f i g u r a t i o n s i t e r a t i v e power flows a r e requiked t o determine branch flows a c c u r a t e l y , as accuracy h i g h l y a f f e c t s t h e r c s u l ts of t h i s method.

a r e 50 branch s w i t c h e s i n s t a l l e d . A t t h e i n i t i a l configu r a t i o n , shown i n Fig.2, 17 of them a r e open. Haiti l i n e s conductors a r e of ACSR-95 and ACSR-50 t y p e s and l a t e r a l s of ACSR-50 and ACSR-16 t y p e s ,

'This powcr flow method may resul-t i n v o l t a g e i u s t a h i l i t y f o r C S o r CZ loads f o r c e r t a i n poor i n i t i a l nctwork conf i g u r a t i o i i s . I n g e n e r a l , however i t is computational l y e f f i c i e n t and a c c u r a t e . 4 . CAPACITOR 1NSTAI.I.ATION PROCESS 7

Reactive powrr compeiisation i s t h e most w i d r l y a r c c p t c d mean of improving v o l t a g e p r o f i l e and energy l o s s e s i n d i s t r i b u t i o n rielworks. W j th this approach next to vol tage/ v a r c o n t r o l o t h e r o p e r a t i o n a l pilramei e r s a r e a l s o i m proved, I i k e t h e p r a k c u r r e n t flows on network br anchcs and the t o t a l peak MVA of t h e system. Thr t o t a l peak M W r e d u c t i o n however, i s qiiestionable and j t depends on t h e t y p e of load. For C J lodds power l o s s reducl i o n r e s u l t s i n an equal i n c r e a s e of power consumption arid ronst a n t incoming MW f e d t o t h e network. Reduction i s obscrved f o r CS loads and i n c r e a s e , i n m o s t c a s e s , f o r CZ l o a d s . Voltage improvement cannot Le d i r e c t l y f i n a i i c i a l l y astimaterl, whi l e t h e prof j t rcsril t i n g from t a t a l NVA and branch c u r r e n t flow r e d u c t i o n s depends as well on o t h e r operatioii parameters and long term planning d e c i s i o n s . On t h e c o n t r a r y , l o s s r e d u c t i o n can be d i r e c t l y f i n a n c i a l l y estimated. The o b j e c t i v e c o s t f u n c t i o n of t h i s problcm is: F = : [ s L ~ ( I ~-~ C(i,) ) 1 wherc : summation i n c l u d e s a1 1 nel-work brnncltes, SLk(Ick) t h e p r o f i t d u r t o annual energy l o s s reduct ion on branch k, r e s u l t i n g from t h e flow of c a p a c i t i v e c u r r e n t Ick on it. annual c o s t ( d e p r e c i a t i o n p l u s o p e r a t i o n a l C(ick) c o s t ) of t h e c a p a c i t o r i c ki n s t a l l a d a t bus k. Power l o s s r e d u c t i o n on branch k is proven l o be: A P ~= 3~~(2r&..-r&) where : R, I,,

t h e k-th liraiich r e s i s t a n c e and t h e r e a c t i v e load c u r r e n t flow on branch k.

Summing up energy l o s s e s f o r a l l d i f f e r e n t network loading c o n d i t i o n s over one y e a r , g i v e s the annual encrgy l o s s reduction.

2 E13

t- c l o s e d s w i t c h

.\. open s w i t c h

F i g u r e 2: A p p l i c a t i o n network. For C J load model t h e i n i t i a l annual maximum load of each feeder is: Feeder A I3 C D E Load (MVA) : 2.42 5.1 2.96 3.11 5.2 D i s t r i b u t i o n s u b s t a t i o n u n i t s o r groups a r e connected a t each node. Loading has been determined t a k i n g i n t o account t h e load composition ( r e s i d e n t i a l , i n d u s t r i a l e t c ) of each f e e d e r arid t h e corresponding load p r o f i l e . Estimation of network v o l t a g e q i a l i t y is o b t a i n e d u s i n g Cw index. l'his is r v a l u a t e d as t h e summai ion of node v o l t a g e v a r i a n c e s I J ~ ' . Each v a r i a n c e is c a l c u l a t e d based on t h e nominal v o l t a g e and t h e summation is weighted by t h e c o n t r i b u t i o n of t h e n o d e ' s load t o t h e t o t a l . The r e s u l t s of t h e h e u r i s t i c methods a r e compared t o t h e a b s o l u t e optimum f o r each load modal. The l a t t e r is obt a i n e d f r o m t h e examination of a l l p o s s i b l e c o n f i g u r a t i o n s and t h e e v a l u a t i o n of energy l o s s e s f o r t h o s e t e c h n i c a l l y a c c e p t e d . The time r e q u i r e d f o r t h i s d e t a i l e d s e a r c h i s , of c o u r s e , p r o l i i b i t i v c f o r a c t u a l system a p p l i c a t i o n s .

5.1 APPLICATION OF IECONFIGURATION METIION 5.1.1 Constant current loads The optimal c o n f i g u r a t i o n found by t h e d e t a i l e d s e a r c h of a11 p o s s i b l e c o i i f i g u r a t i o n s , is i l l u s t r a t e d i n Fig.3.

Dynamic programming t e c h n i q u e s , a r e proven t o be w r y e f f i c i e n t i n t h e s o l u t i o n of t h i s o p t j n i i z a t i o n problem [5,0] and have been used i n o u r approach.

INFEED

An h e u r i s t i c method f o r t h e a p p l i c a t i o n of f i x c d cnpa-

c i t o r s on networks with load models d i f f e r e n t than C J c o n s i s t s of t h e f o l l o w i n g s t e p s : a ) Determine t h e o p e r a t i n g c o n d i t i o n of 1 he network t a k i n g i n t o account load v o l t a g e dependence ( c a p a c i t o r s a r e modelled as CZ l o a d s ) . h) Remove t h e c a p a c i t o r s i n s t a l l e d . c ) For t h e c u r r e n t flows determined i n s t e p 1, f i n d t h e c a p a c i t o r set t h a t minimizes o p e r a t i o n c o s t , cl) Repeat s t e p s a-c u n t i l t h e c a p a c i t o r s e t i n s t a l l e d is not altered.

A3

F i g u r e 3: Optimum c o n f i g u r a t i o n f o r C J loads.

5. STUDY CASE ____-

The overhead system i l l u s t r a t e d i n F i g . 2 was s e l e c t e d f o r t h e a p p l i c a t i o n of t h e methods p r e s e n t e d . I t c o n s i s t s of f i v e 20KV f e e d e r s , w i t h 63 nodes and 00 braiiches. 'There

GO3

The s t e p s followed a p p l y i n g t h e two h e u r i s t i c methods are i l l u s t r a t e d i n Fig.4. ISEM g i v e s s u c c e s i v e r a d i a l configu r a t i o n s with decreilsiug l o s s e s a f t e r each s l e p . Cw index

is a l s o c o n t i n u o u s l y improvrd. SSOM hegins f r o m lhe mrshetl nelwork ( a l l switclies c l o s e d ) arid by s e q u e n t j a l s w i t c h openings radia1il.y is achieved. 'The change of minimum l o s s e s a f t e r l h e optjinal flow a t each s t e p i s i l l u s t r a t e d i n Fig.4.

4000 3600

-

il

3200 -

1f

2800 2400 2000

Lt

-

'

'

'

'

'

'

'2 - d - u .

- 50

2900

F i g u r e 5: Reconfiguration r e s u l t s f o r o t h e r load models. Configu ra1.i on

Cw

Initial Optimum SSOM

224.02 179.73 179.73

3,700.11 3,531.76 3,531.76

Initial Optimum SSOM

155.72 137.45 132.72

2,777.70 2,605.75 2,607.52

Losses (MWh)

from

from

F i g u r e 4 : Reconfiguration r e s u l t s f o r C J l o a d s . From Pig.4 i l is c l c a r t h a t v o l t a g e improvement i s a l s o o b t a i n e d by network r e c o n f i g u r a t i o n aimjng a t l o s s reduction.

C

The numerical r e s u l t s a r e summarized i n Table 1.

C Z

1

~~

ConIj g u r ation

InInliaI

Optimum ISEM

1 I 179.35

3,109.43

0.00

150.11

3,0/1Ll.37

4.55

152.1.4

3,049.01

4.40

150.11

3,044.37

4.55

I 1 cw

Losses (MWh)

-~

I

Reduction from initial %

s

Devia 1ioii from optimum % 11.

76

Table 2.

5.1.3 I n i t i a l a l e e f f e c t s 0.15 In o r d e r t o examine t h e dependence of t h e h e u r i s t i c methods on t h e iriilial s t a t u s of t h e nelwork s w i t c h e s , both methods a r e a p p l i e d on a p a r t i c u l a r l y poor i n i t i a l c o n f i g u r a t i o n , r e s u l t i n g i n i n i t i a l l o s s e s of 6,073.5GMWh and Cw = 701.

Table 1

The e x e c u t i o n t i m e of t h e two a l g o r i l h m s depends h i g h l y on the management of t h e d a t a f i l e s r e q u i r e d t o account f o r t h e loads v a r i a t i o n . Itowever, it should be noted t h a t ISEM appears much f a s t e r (105 s e c s on a PC 306, 33 MIlz f o r 16 d i f f e r e n l network l o a d i n g s , whj l e SSOM r e q u i r e s 477 s e c s ) .

5.1.2 Other load models The d i f f e r e n t load models a r e considered and r e s u l t s a r e compared w i t h those f o r C,J loads. 111 p a r t i c u l a r , mixed loads a r e considered c o n s i s t i n g o f : 30% C J loacls, 25% CS and 115% CZ f o r t h e w i n t e r p e r i o d and 30%, 45I, 25% r e s p e c t i v e l y f o r t h e summer p e r i o d . 'The optimum' c o n f i g u r a t i o n f o r CS arid MX loads is t h e one i l l u s t r a t e d i n F i g . 3 (same with t h a t f o r C J l o a d s ) . For CZ loads minimum encrgy loss is achieved by c l o s i n g branches C2-D7 and D4-Dl4 and opening branches D2-D7 and C9-Dl4 i n P i g . 3.

t o t h e optjmum f o r each load model is i l l u s t r a l e d i n F i g . 5 . l'lie e f f e c t of t h o s e models on t h e network l o s s e s p r e s e n t s p a r t i c u l a r i n t e r e s t .

A p p l i c a t i o n of ISEM provides t h e optimum network configu r a l i o r i of Fig.3. The i n i t i a l s t a t e considered r e q u i r e s 20%more t i m e t h a n t h e i n i t i a l s t a t e of Fig.2. SSOM g i v e s l h e same r e s u l t s f o r C J loads b u t 125% more t i m e i s r e q u i r e d due t o t h e meshed power flow method used. For o t h e r load models SSOM g i v e s no r e s u l t s , as v o l t a g e i n s t a b i l i t y is noted. I t can he concluded t h a t i n i t i a l c o n f i g u r a t i o n a f f e c t s ISEM r e s u l t s and SSOM coiiiputing t i m e . A l t e r n a t i v e power flow methods could he used w i t h SSOM f o r CP, CZ and MX loads when needed f o r s p e c i a l i n j t i a l c o n f i g u r a t i o n s .

5.2 APPLJCATION OF RECONFIGURATION AND CAPACITOR INSTALLATION MEIIIODS In t h i s s e c t i o n t h e i n s t a l l a t i o n of f i x e d c a p a c i t o r banks a t t h e network a f t e r r e c o n f i g u r a t i o n i s examined. The i t e r a t i v e a l g o r i t h m p r e s e n t e d i n paragraph 2 is a p p l i e d .

SSOM was a p p l i e d and convergence

The numerical r e s u l t s a r e summarized i n Table 2 .

As mentioned, c a p a c i t o r i n s t a l l a t i o n l a k e s i n t o conside r a t i o n energy l o s s r e d u c t i o n , a s well a s c a p a c i t o r c o s t t o maximize t h e n e t economical p r o f i t , arid can be implemented f o r a l l load models.

I t can be n o t i c e d t h a t load model h i g h l y a f f e c t s calcul a l e d l o s s e s . MX load model, which can be considered t h e

GOO and 9UO CKVA c a p a c i t o r s is examined.

In {.lie f o l l o w i n g a p p l i c a t i o n s i n s t a l l a t i o n of 300, 450,

most a c c u r a t e , g i v e s almost t h e same r c s u l t s with C J model. Ilowever, load model does n o t s e r i o u s l y a f f e c t convergencc t o optimum corifj g u r a t i o n .

5.2.1 Corislanl c u g e n t loads ? h e ISEM is chosen f o r network r e c o n f i g u r a t i o n as t h e e f f e c t s of r a p a c i t o r i n s t ~ i l l a l i o ncan be more c l e a r l y illustrated.

604

A f t e r rcconf i g n r a t i o n , c a p d c i t o r s arc o p t i m a l l y i n s t d l l e d a t nocles ( s i z e s i n CKVA): A2 900, 03 900, D4 1150, C2 900, D2 900, E2 GOO and E 3 900 (5550 CKVA i n t o t d l ) . Configuration is s l i g h t l y a l t e r e d a f t e r t h i s i n s t a l l a t i o n . 'The r e s u l t s are given i n F i g . 6 . 'The f i n a l artnrial energy l o s s e s a r e 2,250.93 MWh, which g i v e s il t o t a l 29.432 r e d u c t i o n of t h e i n i t i n 1 l o s s e s .

cw

Lost onorgy / year (MWh)

180

Capadtor Installallon

.-

-Losses

- 60

-

coiitr 01 by shunt c a p a c i t o r s . Cotlstant c u r r e n t load modrl appears t o g i v e t h e most accurate calculation r e s u l t s .

REFERENCES

111: S . C i v a n l a r ,

J.J.Grainger, II.Yin, S.S.II.Lee, " n i s t r i b i i t i o n f e e d e r r e c o n f i g u r a t i on f o r l o s s r e d u c t i o n " , JEEE Trans. on Power Delivery, V01.3, J u l y 1980. [2] : A.Merlin,H.Dack, "Srarch € o r a Minimal-l,oss Operating Spanning Tree C o n f i g u r a t i o n f o r an Urban Power D i s t r i b u t i o n System", Proc. I'SCC, Cambridge 1975, Paper 1.2/6. [3] : D.Sliirmohammadi , ll.W.llong, "Reconfiguration of Elect r i c 1 ) i s t r i b u t i o n Networks f o r R e s i s t i v e 1,ine Losses Reduction", IEEE Trans. on Power Delivery, V a l - 4 , A p r i l 1909. [[I] : J .D. Bunch, R . D. M i 1 l e r , J . E. Wheeler, " D i s t r i b u t i o n System I n t e g r a t e d Voltage and Reactive Power C o n t r o l " , IEEE Trans. on ?AS, Vol. PAS-101, No 2 ,

-Cw

Figure 6 : Reconfiguration and c a p a c i t o r i i t s t a l l a t i o n f o r C J loads.

[6] :

5 . 2 . 2 Other l o a d models

For CS loads t h e i n i t i a l energy l o s s i s 3,700.1 1 M W h . A f t e r r e c o n f i g u r a t i o n , tlie f o l l o w i n g c a p a c i t o r s a r e i i i s t a l l e t l : A2 900, 113 900, 1J4 600, C2 900, 112 900, D4 300, E2 600 arid E3 900 CKVA (6000 CKVA i n t o t a l ) . The r e s u l t i n g energy l o s s is reduced by 3 0 . 4 3 2 .

[7 J :

For CZ l o a d s , t h e c a p a c i t o r s i n s t a l l e d are: A2 900, B3 900, U 4 450, C2 900, D2 900, E2 600 and E3 900 CKVA (5550 CKVA i n t o t a l ) , r e s u l t i n g i n t o t a l energy l o s s r e d u c t i o n 16.072.

[9] :

For MX l o a d s , t h e c d p a c i t o r s i n s t a l l e d are: A2 900, D3 900, D4 600, C2 900, 112 900, E2 GOO and E 3 900 CKVA (5700 CKVA i n t o t a l ) , r e s u l t i n g i n t o t a l eiiergy l o s s r e d u c t i o n 27.89%.

We observe t h a t energy l o s s e s a r e s e r i o u s l y a f f e c t e d by t h e load model used, although t h e r e a r e n o t important d i f f e r e n c e s i n t h e proposed c a p a c i t o r s . I t is a l s o i n t e r e s t i n g t h a t t h e r e s u l t s obtairied f o r C J and MX loads are approximately t h e same. This c o n c l u s i o n i s i n agreement w i t h experimental r e s u l t s p u b l i s h e d i n [ 9 ] .

-6 . CONCLUSIONS I n t i t i s paper a combiiied r e a c t i v e power c o n t r o l and network r e c o n f i g u r a t i o n m e t h o d is p r e s e n t e d and a p p l i e d on a t y p i c a l 20KV overhead network. The e f f e c t i v e l i e s s o f t h e most widely used network r e c o n f i g u r a t i o n methods f o r l o s s minimization is i n v e s t i g a t e d t a k i n g i n t o account t h e load modelling a l t e r n a t i v e s . The most important c o n c l u s i o n s a r e t h e following:

-

I n t h e c a s e s c o n s i d e r e d , t h e same f i n a l c o n f i g u r a t i o n i s p r a c t i c a l l y o b t a i n e d by any of t h e two methods, "Switch Exchange" - SZM, o r "Sequential Switch Opening" SSOM. However, t h e f i r s t method r e q u i r e s substant i a l l y l e s s computer time while t h e second method is independent from t h e i n i t i a l coiifigur a t i o n and thus more l i k e l y l e a d s t o t h e a c t u a l optimum. Voltage q u a l i t y i s i n g e n e r a l improved w i t h l o s s reduction. Load model s u b s t a n t i a l l y a f f e c t s l i n e l o s s e s , b u t has no s i g n i f i c a n t i n f l u e n c e on t h e s w i t c h i n g a c t i o n s o p t i m i z i n g network c o n f i g u r a t i o n and on r e a c t i v e power

-

-

605

[U] :

" S e l e c t i o n 01 the Optimum S i z e and Locatioii of Capacitor nanks on Pledium Voltage Networks", CIRED 1903. M.Papadopoulos, N.D.HaCziargyriou, M.E.Papadakis " G r a h i c s Aided l n t o r a c t i v e Analvsis o f Radial D i s t k i b u t i o n Networks", IEEE Trans. on Power D e l i v e r y , Vol. 1'WRD-2, Nr.4, October 1987. A .Dramcl l e r , R. N. A1 l a n , Y . M. Hamam, " S p a r s i t y " , Pitman Pub1 i s h i n g JJtd, Loridon, 1976. H.Duran, "Optimum Number, Location, and S i z e of Shunt C a p a c i t o r s i n lladial Disl r i but ion F r e d e r s . A Dynamic Programming Approach", IEEE Trans. on Power Appar atus and Systems, Vol .J'AS-07, Septernlm- 1968. E.F.Gorzelnik, "Switching i n C a p a c i t o r s does n o t Ileducr Real Power 0 1 1 Feeders" , E l e c t r i c a l World, March 1980.

G . , J . Peponis was born i n Preveza, Greece i n 1967. He r e -

ceived t h e 1)iploma i n E l e c t r i c a l Engineering Irom t h e Nat i o n a l Technical U n i v e r s i t y of Athens, Greece i n 1991. A t p r e s c u t tie is pur4uing p o s t g r a d u a t e s t u d i e s l e a d i n g t o tlie doctor a t e degree. His r e s e a r c h d e a l s w i t h p l a n n i n g and des i g n of d i s t r i b u t i o n systcins and renewable energy s o u r c e s .

E1.P. Pdpadopoulos born i n Ioannina, Greece i n 1932. lie receivrrl t h e Diploma i n E l e c t r i c a l arid Mechanical Engine e r i n g i n 1956 and t h e 1'h.D. degree i n 1974 from t h e Nnt i o i i a l 'Technical U n i v e r s i t y o f Alliens, Groece. I n 1956 he j o i n e d t h e P u b l i c Power Corporation of Greece. lie has beeir engoged i n t h e p l a a n i n g , d e s i g n , o p e r a t i o n and c o n t r o l o r r u r a l and urban d i s t r i b u t i o n networks, as well as in t h e u t i l i z a t i o n o f e l e c t r i c energy. From 1965 t o 1970 and from 1972 t o 1905 he was a l s o employed as a part-time A s s i s t a n t i n t h e E l e c t r i c a l Engineering Department of NTUA. lie is c u r r e n t l y Associate P r o f e s s o r i n t h e same Ilepartment. llis main r e s e a r c h iiit c r e s t s concern d i s l ri hukioii s y s tcms diid renewable energy s o u r c e s . N.D. 1latziargp-i~ was born i n Alhens, Grrcce i n 1954. lie r e c e i v e d t h e Diploma i n E l e c t r i c a l and Mechanical Engine e r i n g from the Nati onal Technical U n i v e r s i t y of Atlieiis (NTUA), Greece i n 1976 and M.Sc. and Ph.D. degrees Zrom t h e U n i v e r s i t y of Manchester I n s t i t u t e oE Science and Technology (UMIST), Manclirstrr , England i n 1979 and 1902, r e s p e c t i v e l y . He is c u r r e n t l y Associate P r o f e s s o r at the Power D i v i s i o n of t h e E l e c t r i c a l Engineering Department of NIUA. His r e s e a r c h iiil e r e s t s i n c l u d e Modelling and D i g i t a l Techniques f o r Power System Analysis and C o n t r o l . D r . l i a t z i a r g y r i o u is a s o n i o r meriber of IEEE and member of CIGRE and t h e Technical Chamber of Greece.