Dynamic Load Flow Solution In Radial Distribution Network

Dynamic Load Flow Solution In Radial Distribution Network

Vol. 1 Issue 7, September – 2012

Prak ash Ku mar Dr. Ramswaroop

I T M U n i ve r s i t y G wa l i o r , N I M S U n i ve r s i t y

D e p a r t me n t o f E l e c t r i c a l E n gi n e e r i n g . H O D , M a t he ma t i c s

A b s t r a c t T hi s p a p e r a i ms a t d e ve l o p i n g a n e w me t ho d o f l o a d f l o w i n vo l v i n g d i s t r i b u t e d ge ne r a t o r fo r t he i mp r o v e me n t o f vo l t a ge p r o f i l e . T h e i n vo l v e me n t o f d i s t r i b ut e d g e ne r a t o r r e s u l t s i n i mp r o v e d vo l t a g e r e g u l a t i o n d ue t o i n c r e a s e i n t he ma g ni t ud e o f t he vo l t a ge . W he r e a s t he l o a d f l o w s o l u t i o n gi v e s t he s o l ut i o n i n l e s s e r t i me d ue t o l o we r i t e r a t i o n a nd t h us l o we r c o mp u t a t i o na l t i me d ur i n g fa u l t . T he no d e a t wh i c h d i s t r i b ut e d ge ne r a t o r i s c o n ne c t e d i s i nd e p e nd e nt o f n o d e a nd b r a nc h n u mb e r . I n t h e me t ho d p r o p o s e d he r e , s i mp l e e q ua t i o n s ha ve b e e n u s e d t o c a l c u l a t e t h e ma g n i t ud e o f t he vo l t a g e a nd i n c a s e o f h i g h l o a d c o n d i t i o n ; t he vo l t a ge p r o f i l e c a n e a s i l y b e i mp r o v e d b y i mp l e me nt i n g d i s t r i b ut e d ge n e r a t i o n c o n ne c t e d wi t h s e l f c o n ve r t i n g s t a t i o n a r r a n ge me n t . T hi s me t ho d d e a l s wi t h t he t o t a l vo l t a g e p r o fi l e t o s p e c i fi e d a r e a o f l o a d a n d i n vo l ve s no d e s o f t he t he c o n ne c t e d d i s t r i b u t i o n s ub s t a t i o n , l a t e r a l s a nd s ub l a t e r a l s . D ur i n g fa ul t y c o nd i t i o n, t he d i s t r i b ut e d g e ne r a t o r c o mp a r e s t he vo l t a g e r a t i o ( o b t a i ne d b y d i v i d i n g t h e vo l t a g e a f t e r t h e f a ul t wi t h t he vo l t a g e j us t a ft e r t he fa ul t ) a nd c o mp e n s a t e d t h e vo l t a g e d i f fe r e nc e , a s r e q u i r e d , t o ma i nt a i n t he s ys t e m he a l t h y.

K e y w o r d s L o a d f l o w, vo l t a g e s a g, vo l t a ge p r o f i l e , fe e d e r s , D i s t r i b ut e d G e ne r a t i o n.

1. . I n t r o d u c t i o n

   I mp r o v e me n t o f p o we r q ua l i t y ha s a l wa ys b e e n a ma t t e r o f c o nc e r n f o r e l e c t r i c a l e n gi n e e r s . T he u s e r s , b e i n g mo s t u nt r u s t f u l p a r t o f t h e p o we r s ys t e m, ne e d t o b e mi t i ga t e d a nd s t ud i e d c a r e f ul l y fo r o b t a i n i n g fa ul t fr e e p o we r s ys t e m. E l e c t r i c a l d i s t r i b u t i o n s ys t e m b e i n g mo s t i mp o r t a n t p a r t o f p o we r s ys t e m e c o no mi c s , a s t h e ma i n s o ur c e o f r e ve n u e , ne e d t o b e c o mp e n s a t e d c a r e f u l l y t o ke e p hi g h R / X r a t i o . A r a d i a l d i s t r i b ut e d i s ge ne r a l l y r a d i a l i n na t ur e a nd ha s hi g h R / X r a t i o , wh e r e a s t h e t r a n s mi s s i o n s ys t e m i s g e n e r a l l y r i n g s ys t e m / me s h i n na t u r e a nd ha s hi g h X / R r a t i o [ 1] .

   I n t h i s q u e s t , ma n y r e s e a r c he r s ha v e ma d e r e ma r ka b l e wo r k t o i mp r o ve q ua l i t y fa c t o r b y i mp r o v i n g p o we r fa c t o r , r e d u c i n g vo l t a g e s a g , r e d uc i n g h a r mo ni c c o mp o ne nt s , e t c . i t i s c h a l l e n gi n g t o w o r k wi t h d i s t r i b u t e d s ys t e m, a s i t i s mo s t u nc e r t a i n a nd c o n t a i ns hi g h e s t d i s t ur b a nc e . A n u mb e r o f ne w s o p hi s t i c a t e d me t ho d s p r o ve d e f f i c i e nt fo r t h e s o l ut i o n o f p r o b l e ms a s s o c i a t e d wi t h t r a n s mi s s i o n s ys t e m; b u t t h e t he o r y ge t s l i mi t e d i n c a s e o f d i s t r i b u t i o n s ys t e m. T h e e f f i c i e nt me t ho d s l i k e G a u s s – S e i d e l a nd N e wt o n R a p s o n me t ho d s ha s a l s o n o t p r o v e n e f fi c i e n t e no u g h i n c a s e o f s o l v i n g p r o b l e ms a s s o c i a t e d wi t h d i s t r i b ut i o n s ys t e m.

   T he d i s t r i b u t e d ge n e r a t o r b a s i c a l l y i nc l ud e s r e c i p r o c a t i n g e n g i ne s , s o l a r c e l l s , f ue l c e l l s , c o mb u s t i o n ga s t ur b i ne , mi c r o t ur b i ne s a nd wi n d t ur b i n e s ; i . e . a l t e r n a t e e ne r g y s o ur c e s a s c o mp a r e d t o c o n v e nt i o na l fo s s i l f ue l b a s e d e ne r g y s o ur c e s . I t c a us e s l o w e mi s s i o n, l o w p o l l ut i o n, h i g h e f f i c i e nc y a nd u ni n t e r r up t e d s up p l y t o l o a d s wh e r e i nt e r r up t i o n i n p o we r i s no t a c ho i c e e . g . ho s p i t a l , mi n e s , r e l e v a nt i nd u s t r i e s , e t c . ; ho we v e r i mp l e me n t a t i o n o f d i s t r i b u t e d ge ne r a t o r i n e l e c t r i c a l d i s t r i b ut i o n s ys t e m i nc r e a s e s i t s c o mp l e xi t y. D i s t r i b u t e d ge ne r a t o r s c a n wo r k no t o nl y i n up s t r e a m f o r i mp r o ve me n t o f vo l t a g e d ur i n g t he d i p b u t a l s o i n d o wn s t r e a m t o r e g u l a t e t h e vo l t a g e o r r e ma i n s t a nd s t i l l w he n no a n y a c t i o n i s r e q u i r e d i . e . a s r e s e r ve d a l t e r na t e s o l u t i o n f o r p o we r fa i l u r e .

2. . R e v i e w o f l i t e r a t u r e

   M a n y r e s e a r c h e r s ha ve ma d e s i g n i fi c a n t e f fo r t i n t h e fi e l d o f D G i n s t a l l a t i o n a nd a l l o c a t i o n. I n [ 2 ]

   o p e r a t i o n a nd c o nt r o l m o d e l o f D G ha s b e e n e x p l a i n e d t o i mp r o v e vo l t a g e e f f i c i e nc y. I n [ 3 ] , t h e e f fe c t

   o f D G o n e l e c t r i c a l p o w e r l o s s , i mp a c t o n vo l t a ge p r o f i l e a nd c o n s e c ut i ve c a s e s we r e d i s c us s e d . I n t h i s c a s e t h e a u t ho r a i me d a t o p t i mi z i n g D G l o c a t i o n, mi n i mi s i n g l o s s e s a n d i mp r o ve p o we r q u a l i t y. I n [ 4 ] , t h e e f f e c t o f D G o n p o we r s ys t e m h a s b e e n d i s c us s e d wi t h r e f e r e nc e t o l o s s e s , vo l t a ge r e g ul a t i o n, vo l t a g e fl uc t ua t i o n s , s h o r t c i r c ui t c o nd i t i o n , i s l a nd i n g o p e r a t i o n a nd ha r mo n i c s . I n [ 5 ] , s i m ul a t i o n t e c h n i q ue h a s b e e n u s e d t o o b t a i n vo l t a ge r e g u l a t i o n t o o p t i mi z e p o we r s up p o r t b y D G i n t he d i s t r i b u t i o n s ys t e m. I n [ 6 ] , t a p c h a n gi n g t r a ns fo r me r me t ho d ha s b e e n p r o p o s e d fo r vo l t a ge r e g ul a t i o n i n u nd e r vo l t a ge a nd o v e r vo l t a ge c o nd i t i o n s .

3. . N o t a t i o n s u s e d

   A b b .	F u l l f o r m
   DG	D i s t r i b ut e d G e ne r a t o r
   | V |	S ys t e m v o l t a ge & a n g l e
   | I |	S ys t e m c ur r e n t & a n gl e
   S	A p p a r e n t P o we r
   S ub s c r i p t p q	O ve r t he b u s p t o q
   a	P ha s e a
   L F	Lo a d F a c t o r
   P	R e a l P o we r
   Q	R e ac t i ve P o we r
   Y	A d mi t t a n c e
   S up e r s c r i p t *	C o nj u g a t e
   N F	N o d e s o f f e e d e r
   N L	N o d e s o f L a t e r a l
   N SL	N o d e s o f S ub – L a t e r a l
   B F	B r a n c h o f f e e d e r
   B L	B r a n c h o f L a t e r a l
   B SL	B r a n c h o f S ub – L a t e r a l
   x, y	N o d e x, y
   P ml	P o i n t e r me mo r y l o c a t i o n
   F TS	F , L & S L t o t a l s u m
   F , L & S L	F e e d e r , L a t e r a l & S ub – L a t e r a l
   LLF	L i ne Lo s s F a c t o r
   V C F	vo l t a g e c o mp e ns a t i o n fa c t o r

4. . L o s s e s i n d i s t r i b u t i o n s y s t e m

   I f t he p ha s o r e xp r e s s i o n fo r vo l t a g e a nd c ur r e nt a r e k no wn , t he n t he c a l c u l a t i o n o f r e a l a nd r e a c t i ve p o we r c a n b e d o n e e a s i l y. I f t h e vo l t a ge a c r o s s a nd c u r r e nt i n t o a c e r t a i n l o a d o r p a r t o f c i r c u i t i s

   | V | a nd | I | , r e s p e c t i v e l y , a p p e r e n t p o we r i s gi ve n b y [ 7 ]

   S = V I *= | V | e j . | I | e – j = | V | | I |e j ( – ) = | V | | I | ( – ) . . . . ( i )

   T he c o mp l e x p o we r i nj e c t e d fr o m b u s p t o q i s g i ve n b y S p q o r fr o m b u s q t o p i s g i ve n a s S qp

   i . e .

   S pq = V pq ….. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( ii)

   O r , S qp = V qp

   W he r e , I * r e p r e s e n t s t he c o nj u ga t e o f t he c ur r e n t . V o l t a ge a t p h a s e a o f p th b u s i s g i ve n a s :

   | |= ( V , L F ) a nd a n g l e

   = ( V , L F ) . . . . . . . . . . . . . . . . . ( i i i )

   T he c ur r e nt fo r m p t o q b u s fo r p h a s e R i s g i ve n a s :

   | |= ( V , L F ) =

   ( ) . . . . . ( i v )

   | |

   W he r e i s t he b u s vo l t a g e a t b u s p o ve r p h a s e a a nd i s e l e me n t o f b r a nc h a d mi t t a n c e ma t r i x.

   R e a l a nd r e a c t i ve p o we r f l o w me a s ur e me nt fr o m b u s p t o b u s k o ve r p ha s e a i s g i ve n a s :

   = ( V , L F ) + j ( V , L F ) = ( )* . . . . . . . . . . . ( v)

   P o we r s up p l i e d a t b u s q fo r p h a s e a c a n b e me a s ur e d a s :

   = ( V , L F ) + j ( V , L F )

   ,

   ,

   ,

   = ( ( ) )* . . . . . . . . . . . . . . ( vi )

   F i g u r e 4. 1 : A 1 5 no d e t e s t s ys t e m wi t h r e g u l a r a nd s y m me t r i c n u mb e r i n g o f no d e s a nd b r a nc he s .

   C o n s i d e r i n g a 1 5 no d e t e s t s ys t e m wi t h r e g ul a r a nd s y m me t r i c n u mb e r i n g o f no d e s a nd b r a n c h e s a s i l l u s t r a t e d i n F i g . 4. 1 a n d a 1 5 no d e t e s t s ys t e m wi t h i r r e g u l a r a nd a s y m me t r i c n u mb e r i n g o f no d e s a n d b r a n c he s a s i l l u s t r a t e d i n F i g . 4. 2 :

   F i g u r e 4 . 2 : A 1 5 no d e t e s t s ys t e m wi t h i r r e g u l a r a nd a s y m me t r i c n u mb e r i n g o f no d e s a nd b r a n c he s

   T he f i g . 4. 1 r e p r e s e nt s a r a d i a l d i s t r i b u t i o n s ys t e m, t he b r a nc h e s a nd no d e s ha ve b e e n s ub – d i vi d e d i n t o fe e d e r , l a t e r a l a nd s ub – l a t e r a l . F o r r e p r e s e nt i n g t he f e e d e r s , l a t e r a l s a nd s ub – l a t e r a l s i n fo r m o f t wo d i me n s i o n a l a r r a ys i n w hi c h t he f i r s t n u mb e r r e p r e s e nt s t he f e e d e r ( 1 ) , l a t e r a l ( 2 ) a nd s ub – l a t e r a l ( 3 ) ; a nd t he s e c o nd n u mb e r r e p r e s e nt s t he o r d e r o f n o d e o r b r a n c h, a s a p p l i c a b l e .

   I n c a s e o f N o d e s :

   N F ( 1 , 1 ) = 1 , N F ( 1 , 2 ) = 2 , N F ( 1 , 3 ) = 3 , N F ( 1 , 4 ) = 4 , N F ( 1 , 5 ) = 5 , N F ( 1 , 6 ) = 6 , N F ( 1 , 7 ) = 7 , fo r f e e d e r s .

   N F ( 2 , 1 ) = 4 , N F ( 2 , 2 ) = 8 , N F (2 , 3 ) = 9 , N F ( 2 , 4 ) = 1 0 , N F ( 2 , 5 ) = 1 1 , N F ( 2 , 6 ) = 1 2 f o r l a t e r a l s . N F ( 3 , 1 ) = 1 0 , N F ( 3 , 2 ) = 1 3 , N F ( 3 , 3 ) = 1 4 , N F ( 3 , 4 ) = 1 5 fo r s ub – l a t e r a l s .

   I n c a s e o f B r a nc he s :

   B F ( 1 , 1 ) = 1 , B F ( 1 , 2 ) = 2 , B F ( 1 , 3 ) = 3 , B F ( 1 , 4 ) = 4 , B F ( 1 , 5 ) = 5 , B F ( 1 , 6 ) = 6 fo r fe e d e r s .

   B F ( 2 , 1 ) = 7 , B F ( 2 , 2 ) = 8 , B F ( 2 , 3 ) = 9 , B F ( 2 , 4 ) = 1 0 , B F ( 2 , 5 ) = 1 1 fo r l a t e r a l . B F ( 3 , 1 )= 12 , B F ( 3 , 2 ) = 1 3 , B F ( 3 , 3 ) = 1 4 f o r s ub – l a t e r a l .

   I n e i t he r c a s e , t he s e q u e nc e s a r e i nd e p e nd e nt o f no d e s o r b r a nc h e s . I n t hi s q u e s t :

   L e t = B F ( x , y) ; 1 = N F ( x , y) a nd 2 = N F ( x , y+ 1 ) S o , V ( 2 ) = V ( 1 ) – I Z

   W he r e ,

   V ( 2 ) = | V ( 2 ) | 2 V ( 1 ) = | V ( 1 ) | 1 I = | I | –

   Z = | Z | = R + j X

   V o l t a ge a t no d e 2 i s g i v e n a s

   | V ( 2 ) |= | V ( 1 ) |- [ { ( 2 + 2 ) 1/2 }. | Z |]/ | V ( 1 ) | . . . . . . ( vi i )

   W he r e , ( 2 + 2 ) 1 / 2 = | S |= | V ( 1 ) | | I |

   P & Q a r e t he r e a l & r e a c t i ve p o we r a t o u t p ut p o r t o f no d e 1 .

   A n d , I = [ ( 2 + 2 ) 1/2 ]/ | V ( 2 ) |; wi t h r e f e r e nc e t o p r i ma r y s i d e i . e . e nt e r i n g p o r t o f no d e ( x, y) no d e .

   A n d , I = [ ( 2 + 2 ) 1/2 ]/ | V ( 1 ) | ) |; wi t h r e fe r e nc e t o s e c o nd a r y s i d e i . e . o ut p u t p o r t o f no d e ( x, y) no d e .

   T he c ur r e nt | I |= [ | V ( 1 ) | – | V ( 2 ) |] / | Z | . . . . . . . ( v i i i ) R e a l & r e a c t i ve p o we r l o s s c a n b e g i ve n a s

   P L=| 2|R

   Q L=| 2|X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( i x)

   T he p o we r c a n b e g i ve n fo r b r a nc he s a s F o r fe e d e r b r a nc he s :

   P S[B F ( 1 , 6 ) ] = T L[N F ( 1 , 7 ) ] + P L [N F ( 1 , 6 ) ]

   P S[B F ( 1 , 5 ) ] = T L[N F ( 1 , 6 ) ] + P L [N F ( 1 , 5 ) ] + P S [B F ( 1 , 6 ) ]

   P S[B F ( 1 , 4 ) ] = T L[N F ( 1 , 5 ) ] + P L [N F ( 1 , 4 ) ] + P S [B F ( 1 , 5 ) ]

   P S[B F ( 1 , 3 ) ] = T L[N F ( 1 , 4 ) ] + P L [N F ( 1 , 3 ) ] + P S [B F ( 1 , 4 ) ]

   P S[B F ( 1 , 2 ) ] = T L[N F ( 1 , 3 ) ] + P L [N F ( 1 , 2 ) ] + P S [B F ( 1 , 3 ) ]

   P S[B F ( 1 , 1 ) ] = T L[N F ( 1 , 2 ) ] + P L [N F ( 1 , 1 ) ] + P S [B F ( 1 , 2 ) ]

   F o r l a t e r a l b r a nc h e s :

   P S[B F ( 2 , 5 ) ] = T L[N F ( 2 , 6 ) ] + P L [N F ( 2 , 5 ) ]

   P S[B F ( 2 , 4 ) ] = T L[N F ( 2 , 5 ) ] + P L [N F ( 2 , 4 ) ] + P S [B F ( 2 , 5 ) ]

   P S[B F ( 2 , 3 ) ] = T L[N F ( 2 , 4 ) ] + P L [N F ( 2 , 3 ) ] + P S [B F ( 2 , 4 ) ]

   P S[B F ( 2 , 2 ) ] = T L[N F ( 2 , 3 ) ] + P L [N F ( 2 , 2 ) ] + P S [B F ( 2 , 3 )]

   P S[B F ( 2 , 1 ) ] = T L[N F ( 2 , 2 ) ] + P L [N F ( 2 , 1 ) ] + P S [B F ( 2 , 2 ) ]

   F o r s ub – l a t e r a l b r a nc h e s :

   P S[B F ( 3 , 3 ) ] = T L[N F ( 3 , 4 ) ] + P L [N F ( 3 , 3 ) ]

   P S[B F ( 3 , 2 ) ] = T L[N F ( 3 , 3 ) ] + P L [N F ( 3 , 2 ) ] + P S [B F ( 3 , 3 ) ]

   P S[B F ( 3 , 1 ) ] = T L[N F ( 3 , 2 ) ] + P L [N F ( 3 , ) ] + P S [B F ( 3 , 2 ) ]

   T hu s fr o m t h e a b o ve c a s e s o f fe e d e r , l a t e r a l a nd s ub – l a t e r a l b r a nc h e s , we c o nc l ud e : F o r d e a d e nd b r a nc he s

   P S[B F ( x, y) ] = T L[N F ( x, y+ 1 ) ] + P L[N F ( x, y) ] . . . . . . . ( x)

   A n d fo r o t he r mi d b r a n c he s

   P S[B F ( x, y) ] = T L[N F ( x, y+ 1 ) ] + P L[N F ( x, y) ] + P S [N F ( x, y+ 1 ) ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( xi )

   T he e q ua t i o n ( x) & ( x i ) a r e va l i d fo r a l l b r a nc he s o f f e e d e r , l a t e r a l a nd s ub – l a t e r a l ne t wo r k. S i mi l a r l y, r e a c t i ve p o we r l o s s e s a r e g i ve n a s :

   F o r d e a d e nd b r a nc he s

   Q S[B F ( x, y) ] = T Q L[N F ( x , y + 1 ) ] + Q L [N F ( x, y) ] .. . . ( x ii )

   A n d fo r o t he r mi d b r a n c he s

   Q S[B F ( x, y) ] = T Q L[N F ( x, y+ 1 ) ] + Q L[N F ( x, y )] + Q S [N F ( x, y+ 1 ) ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( xi ii )

   F o r s ub – l a t e r a l a nd l a t e r a l ne t wo r k c o n ne c t e d t o N F ( 2 , 3 ) , t he t o t a l p o we r fl o wi n g t hr o u g h b r a n c h B F ( 2 , 1 ) i s g i ve n a s

   P S[B F ( 2 , 1 ) ] = P L[ B F ( 2 , 1 ) + T L[ N F ( 2 , 3 ) ] + P S[B F ( 2 , 3 ) ] + P S[B F ( 3 , 1 ) ] . . . . . . . . . . . . . . . . . . . . . . . ( xi i i )

   A n d Q S [B F ( 2 , 1 ) ] = P QL [B F ( 2 , 1 ) + T QL [N F ( 2 , 3 ) ] + Q S [B F ( 2 , 3 ) ] + Q S[B F ( 3 , 1 ) ] . . . . . . . . . . . . . . . . . . . . . . ( x i v )

   T hu s we f i nd t ha t t h e c o mmo n no d e s o f s u b – l a t e r a l & l a t e r a l , f e e d e r & l a t e r a l s ho ul d b e p o i nt e d f i r s t . I f N F ( x, y) i s t h e no d e fr o m wh i c h o t h e r l a t e r a l a nd s u b – l a t e r a l ha ve e me r ge d , t he n t h e f e e d e r b r a n c h B F i s s t o r e d a s B F ( x, y – 1 ) .

   I n t he me t ho d o l o g y s u g ge s t e d i n t h i s p a p e r c h e c ks t he no d e fr o m wh i c h l a t e r a l a nd s ub – l a t e r a l ha v e e me r ge a nd s t o r e t he b r a n c h n u mb e r i r r e s p e c t i v e o f t he a c t u a l n u mb e r i n g o f t he no d e a s d e p i c t e d i n f i g 4. 2 ; i . e . i f t h e fe e d e r no d e i s N F ( x , y) , l a t e r a l no d e i s N F ( x+ 1 , y) a nd s ub – l a t e r a l no d e a s N F ( x+ 2 ) , t h e n N F ( x, y) o f fe e d e r & N F ( x+ 1 , 1 ) a nd N F ( x+ 1 , y) & N F ( x + 2 , 1 ) a r e s a me ; a nd t he b r a nc h B F ( x, y – 1 ) i s s t o r e d i n t he p o i n t e r me mo r y l o c a t i o n p ml ( F TS – 1 ) ( s a y) . H e r e ( F TS – 1 ) r e fe r s t o t he p o i n t e r me mo r y a d d r e s s s t o r a ge s i z e . I n t h i s wa y, t he c o m mo n no d e s o f F e e d e r s & l a t e r a l s , l a t e r a l s & s ub – l a t e r a l s c a n b e i d e nt i fi e d e a s i l y. T h e l a t e r a l no d e i n c a s e o f F e e d e r & l a t e r a l c o m m o n no d e o r l a t e r a l & s u b – l a t e r a l c o m mo n no d e ; t he l a t e r a l a nd s ub – l a t e r a l no d e r e s p e c t i ve l y c a n b e s ho wn t o b e s t o r e d i n p o i n t e r p ml ( F TS – 1 ) fo r s i mp l i c i t y.

   T hu s t he fo l l o wi n g r e s ul t s a r e o b t a i ne d :

   P S(B F ( x, y) = T L[N F ( x , y+ 1 ) ] + P L[B F ( x, y) ] + P S[B F ( x, y + 1 ) + P S [B F (F TS , 1 ) . . . . . . . . . . . . . . . . . . . . . . . ( x v)

   A n d Q S (B F ( x , y) = T Q L [N F ( x, y+ 1 ) ] + Q L[B F ( x, y) ] + Q S [B F ( x, y + 1 ) + Q S[B F ( p ml , 1 ) . . . . . . . . . . . . . . . . . . ( x v i )

   T hu s fr o m t he a b o ve r e s ul t s , i t i s o b t a i ne d t h a t t he s u g ge s t e d me t ho d d o e s no t d e p e nd o n t h e n o d e o r b r a n c h n u mb e r i n g o f F , L & S L. T hi s ma k e s t hi s me t ho d mo r e r e l i a b l e a nd fa s t a s t he c a l c ul a t i o n o f P S a nd Q S i s i nd e p e nd e nt o f t he no d e & b r a n c h c o m p l e x no me n c l a t ur e .

   N o w a ft e r c a l c u l a t i n g p o we r a t r e s p e c t i v e no d e s , t he c o n ve r g e nc e i s c he c ke d fo r t h e vo l t a g e s a t t h e r e s p e c t i ve no d e s . I n c a s e o f no n – c o n ve r gi n g s ys t e m, t he D G i s p l a c e d a t t he c o m mo n no d e s a nd c o n v e r ge nc e i s o b t a i ne d . N o w we d e t e r mi n e vo l t a g e c o m p e ns a t i o n fa c t o r ( V C F ) b y fo l l o wi n g fo r mu l a .

   Improved voltaage profile with DG

   V C F =

   Voltage profile with out DG

   W he r e , vo l t a ge p r o f i l e d e p e nd s o n t he ma g n i t u d e o f vo l t a g e a t wh i c h t h e D G i s p l a c e d a nd t he l o a d c o n n e c t e d t o t ha t b r a n c h o r no d e . W h i l e c o n s i d e r i n g t he f a c t o r V C F , o ne mo r e f a c t o r s h o ul d b e c o n s i d e r e d v e r y ke e nl y, i . e . l o a d l o s s f a c t o r d u e t o D G i ns t a l l a t i o n . T he i n s t a l l a t i o n o f D G n o t o nl y r e d u c e s l i n e l o s s e s b ut c a n a l s o r e s u l t i n i nc r e a s e d l i n e l o s s a s d e p i c t e d i n f i g . 4. 3 b e l o w. T hi s i s o b s e r v e d i n t h e d i s t r i b u t e d s ys t e ms wh e r e s u f f i c i e n t l y h i g h c a p a c i t y D G i s in s t a l l e d i n t he n e t wo r k. T he a t mo s t s i z e o f D G s ho ul d b e s uc h t ha t t he ge n e r a t e d p o we r s ho ul d e a s i l y b e c o n s u m ed wi t hi n t he c o n e d c o m mo n p o i n t s o f F , L & S L . A n y a t t e mp t t o i n s t a l l hi g h c a p a c i t y D G wi t h t he p ur p o s e o f e xp o r t i n g p o we r b e yo nd t he s ub s t a t i o n ( r e v e r s e f l o w o f p o we r t ho u g h d i s t r i b ut i o n s ub s t a t i o n) , w i l l l e a d t o v e r y hi g h l o s s e s . S o , t h e s i z e o f d i s t r i b ut i o n s ys t e m i n t e r m o f l o a d ( M W ) wi l l p l a y i m p o r t a n t r o l e i s s e l e c t i n g t he s i z e o f D G . S o we a l wa ys t r y t o k e e p l o w l i ne l o s s f a c t o r ( L L F ) g i ve n a s

   L L F = Reduction of line lossess by using DG Reduction of line losses without using DG

   T he fa c t o r L L F s ho ul d a l wa ys b e l e s s t h a n 1 o t h e r wi s e t he l o s s wi t h D G wi l l b e c o me mo r e a s c o mp a r e d t o l o s s e s wi t ho ut D G . I n c a s e L L F 1 , e i t he r t he s i z e o f D G i s r e d uc e d o r t he l o c a t i o n o f D G i s c ha n ge d t o g i ve t he va l ue o f L L F l o we r t ha n 1 . T h e f a c t o r s a f f e c t i n g t he l o s s e s b y u s i n g D G i nc l u d e s l i ne l e n gt h, l i ne r e s i s t a n c e , l o a d d i s t r i b ut i o n e t c . I n c a s e o f t h e l o s s e s wi t h o ut D G , t h e l o a d i s a s s u me d t o b e d i s t r i b ut e d u ni fo r ml y t hr o u g ho ut t he no d e s o f t he F e e d e r s .

   F i g u r e 4 . 3 : E f f e c t o f s i z e a nd l o c a t i o n o f D G o n s ys t e m l o s s

5. . P r o p o s e d A l g o r i t h m

   S t e p 1 : O b t a i n t he n u mb e r o f F , L & S L .

   S t e p 2 : l e t n u mb e r o f N F ( x, y) = P , n u mb e r o f N F ( x+ 1 , y) = Q , n u mb e r o f N F ( x+ 2 , y) = R S t e p 3 : F TS = P + Q + R .

   S t e p 4 : I f t he n u mb e r i n g o f t he no d e s a r e s e q ue n t i a l , r e a d t he f i r s t n o d e fo r F , L, S L i . e . N F ( x, 1 ) , N F ( x+ 1 , 1 ) & N F ( x + 2 , 1 ) . P r o c e e d t o s t e p 7 .

   S t e p 5 : I f t h e n u mb e r i n g o f t h e no d e s is no t s e q ue n t i a l , c a l l t he p o i n t e r a nd s t o r e t he v a l ue o f n u mb e r e d no d e u nd e r d i f fe r e n t F , L & S L a s N F ( x, y) , N F ( x+ 1 , y) & N F ( x+ 2 , y) i r r e s p e c t i ve o f a c t ua l no d e n u mb e r i n g.

   S t e p 6 : C a l l t h e va l ue o f f i r s t no d e fo r F , L , S L i .e . N F ( x, 1 ) , N F ( x+ 1 , 1 ) & N F ( x + 2 , 1 ) . P r o c e e d t o s t e p 7. S t e p 7 : O b t a i n c o m mo n no d e s fo r l a t e r a l & f e e d e r a nd s ub – l a t e r a l & l a t e r a l , a s e me r gi n g p o i n t fo r l a t e r a l a nd s ub – l a t e r a l n o d e s .

   S t e p 8 : fo r c o m mo n no d e s o f l a t e r a l & s ub – l a t e r a l i . e . N F ( x+ 1 , y) & N F ( x + 2 , 1 ) fo r x = F T S t o F TS – R + 1 a nd y= 1 , 2 , . . . . . . , F TS . C a l l t he p o i n t e r & s t o r e b r a nc h o f l a t e r a l B F ( x, y – 1 ) fo r c o r r e s p o nd i n g no d e N F ( x, y) i n p ml ( z ) fo r z = 1 , 2 , . . . . . , R .

   S t e p 9 : o b t a i n c o m mo n no d e s o f l a t e r a l & f e e d e r i . e . N F ( x, y) & N F ( x, 1 ) fo r x= F TS – R t o F T S – R – Q + 1 fr o m N F ( 1 , y) fo r y= 1 , 2 , . . . . , F T S . S t o r e p ml ( x ) fo r x= R + 1 , . . . . , R + Q a nd B F ( x , y – 1 ) c o r r e s p o nd i n g t o N F ( x, y) i n p ml ( x) fo r x = R + 1 , . . . , R + Q

   S t e p 1 0 : C a l c u l a t e P S [B F ( x , y) ] a nd Q S [B F ( x, y ) ] fo r x= F TS t o F TS – R + 1 a nd y= N ( x) – 1 , . . . . , 2 , 1 u s i n g e q u a t i o n

   S t e p 1 1 : C a l c u l a t e P S[B F ( x, y) ] a nd Q S[B F ( x, y) ] f o r x = F TS – R t o F TS – R – Q + 1 u s i n g e q ua t i o n.

   S t e p 1 2 : C a l c u l a t e t o t a l P S a nd Q S fo r t he F , L & S L. T o t a l p o we r l o s s t h u s o b t a i n e d i s S L =P S+ Q S .

   S t e p 1 3 : C a l c u l a t e t he F , L & S L vo l t a ge a nd c h e c k i f t he t e r mi n a l vo l t a ge c o n v e r ge s wi t h t he o b t a i n e d vo l t a g e wi t h i n p e r mi s s i b l e l i m i t i . e . V l o s s =V S – V 0 = ±5 % o f V S , wh e r e V 0 =S L / F e e d e r no d e c ur r e n t . I f t h e vo l t a g e i s wi t hi n p e r mi s s i b l e l i mi t go t o s t e p 1 6 o r go t o s t e p 1 4 .

   S t e p 1 4 : S t a r t D G p l a c e d ne a r c o m mo n no d e o f f e e d e r & l a t e r a l i . e . N F ( x, y) & N F ( x + 1 , 1 ) o r l a t e r a l & s ub – l a t e r a l i . e . N F ( x + 1 , y ) & N F ( x+ 2 , 1 ) . C h e c k f o r c o n v e r ge nc e . I f t he v o l t a g e c o n ve r ge s wi t h r e q u i s i t e vo l t a g e , c a l c u l a t e vo l t a ge c o mp e n s a t i o n fa c t o r ( V C F ) a nd l i n e l o s s fa c t o r ( L L F ) . I f L L F < 1 , go t o s t e p 1 6 o r go t o s t e p 1 5 .

   S t e p 1 5 : c h a n ge D G l o c a t i o n a nd p l a c e i t t o a n o t h e r l o c a t i o n ne a r c o m mo n no d e o f fe e d e r & l a t e r a l i . e . N F ( x , y) & N F ( x + 1 , 1 ) o r l a t e r a l & s ub – l a t e r a l i . e . N F ( x + 1 , y) & N F ( x+ 2 , 1 ) a nd go t o s t e p 1 4 .

   S t e p 1 6 : v e r i f y r e s ul t s fo r B F ( x, y) fo r y= N ( x) – 1 , . . . , 2 , 1 a nd x= F TS – R t o F T S – R – Q + 1 wi t h p ml ( z ) fo r z = 1 , 2 , . . , R .

   S t e p 1 7 : C a l c u l a t e P S[B F ( 1 , y) ] & Q S [B F ( 1 , y) ] fo r y= N ( x) – 1 , . . . . , 2 , 1 u s i n g e q ua t i o n

   S t e p 1 8 : c h e c k t he r e s u l t s fo r f e e d e r b r a nc h B F ( 1 , y) fo r y= N ( x) – 1 , . . . , 2 , 1 wi t h p ml ( z ) fo r z = R + 1 , . . . , R + Q .

   S t e p 1 9 : I f t he r e s ul t c o n ve r g e s , go t o s t e p 2 0 o r go t o s t e p 1 6 . S t e p 2 0 : S t o p .

6. . R e s u l t a n d C o n c l u s i o n

I n d i s t r i b u t i o n s ys t e m, i t i s c o m mo n t o c o n s i d e r a r a d i a l s ys t e m. I n t he t a b l e 6 . 1 , t h e l o a d a t d i f fe r e nt no d e s h a s b e e n c o n s i d e r e d . T he s e l o a d s ha ve b e e n c o n s i d e r e d i r r e s p e c t i ve o f t h e a c t u a l no d e n u mb e r i n g r a t he r t he p o s i t i o n o f t h e F , L & S L . I n t a b l e 6 . 2 , t he l o s s h a s b e e n c o n s i d e r e d u n i fo r ml y t hr o u g ho u t t h e d i s t r i b ut i o n s ys t e m a nd t h e r e l a t i ve mi n i mu m vo l t a ge i n t he s ys t e m i n p . u. s ys t e m. T he d i s t ur b a n c e ha s b e e n c o n s i d e r e d t o b e ma xi mu m i . e . 5 % . I n t a b l e 6 . 3 , t he l o s s ha s b e e n c o n s i d e r e d r a nd o m

t h r o u g ho ut t he d i s t r i b u t i o n s ys t e m a nd t he r e l a t i ve vo l t a ge i n t h e s ys t e m i n p . u . s ys t e m. T he d i s t ur b a nc e ha s b e e n c o n s i d e r e d t o b e wi t hi n ±5 % .

T a b l e 6 . 1 . Lo a d o n t h r e e p h a s e s ys t e m

T a b l e 6 . 2 . R e s u l t s fo r u ni f o r m p o we r l o s s wi t ho ut D G

T a b l e 6 . 3 . R e s u l t s fo r R a nd o m p o we r l o s s wi t ho ut D G

N o w u s i n g D G a t t he c o m mo n no d e o f l a t e r a l a nd fe e d e r i . e . NF (1,4), the net rective need of the system reduces due to injected power of the DG. Thus the net voltage regulation improves and the minimum voltage at different nodes of the

distribution system is as obtained in in figure 6.4 and 6.5. The selection of node can vary for the variation of load at different nodes with the proposed algorithm which will depend on the F, L & SL rather the actual node.

T a b l e 6 . 4 . R e s u l t s fo r u ni f o r m p o we r l o s s wi t h D G .

T a b l e 6 . 5 . R e s u l t s fo r R a nd o m p o we r l o s s wi t h D G .

I n t he a b o v e c a s e s , b y t he p r o p e r p l a c e me n t o f D G c a n gi v e b e t t e r vo l t a g e r e g ul a t i o n a nd t h e p l a c e me nt o f D G c a n e a s i l y b e o b t a i n e d b y s i n g t h e d yn a mi c a l go r i t h m p r o p o s e d a b o ve . S i nc e t he a l go r i t h m i s i nd e p e nd e n t o f a c t u a l n o d e n u mb e r i n g a nd d e p e nd s o n t he p o s i t i o n o f t h e no d e , t he t i me t a ke n b y t h e C P U i s mu c h l e s s e r a s c o mp a r e d t o e a r l i e r p r o p o s e d a l go r i t h ms a s s ho w n b e l o w.

T a b l e 6 . 6 . C o mp a r i s o n b e t we e n t he p r o p o s e d me t ho d a nd t he p r e v i o us l y p r o p o s e d me t ho d .

R e f e e n c e :

1. ] I r fa n W a s e e m, I m p a c t s o f D i s t r i b u t e d G e n e r a t i o n o n t h e R e s i d e n t i a l D i s t r i b u t i o n N e t w o r k O p e r a t i o n , F a l l s C h ur c h V i r g i ni a , p p . 1 1 – 1 4 , D e c e mb e r 2 0 0 8 .

2. ] G . Le d wi c h, D i s t r i b u t e d g e n e r a t i o n a s V o l t a g e s u p p o r t f o r s i n g l e w i r e E a r t h r e t u r n s y s t e m s , I E E E T r a ns a c t i o n s o n P o we r D e l i ve r y , vo l . 1 9 , no . 3 , p p . 1002 – 1 0 1 1 , J ul y 2 0 0 4 .

3. ] C . L . T . B o r ge s a nd D . M . F a l c a o , I m p a c t o f d i s t r i b u t e d g e n e r a t i o n a l l o c a t i o n a n d s i z i n g o n r e l i a b i l i t y , l o s s e s a n d v o l t a g e p r o f i l e , P o we r T e c h C o n fe r e nc e P r o c e e d i n g s I E E E B o l o g n a , vo l . 2 , p p . 5 , J u ne 2 0 0 3 .

4. ] P . P . B a r k e r a nd R . W . M e l l o , D e t e r m i n i n g t h e i m p a c t o f d i s t r i b u t e d g e n e r a t i o n o n p o w e r s y s t e m s . I . R a d i a l d i s t r i b u t i o n s y s t e m s , P o we r E n g i ne e r i n g S o c i e t y S u m me r M e e t i n g , I E E E , vo l . 3 , p p . 1 6 4 5 – 1656 , 2000 .

5. ] M . A. K a s he m a nd M. N e g n e vi t s k y, C o n t r o l S t r a t e g y o f D i s t r i b u t e d G e n e r a t i o n f o r V o l t a g e S u p p o r t i n D i s t r i b u t i o n S y s t e m s , I nt e r na t i o na l C o n fe r e nc e o n P o we r E l e c t r o n i c s ,

   D r i ve s a nd E ne r g y S ys t e ms , p p . 1 – 6 , 1 2 – 1 5 D e c . 2 0 0 6 .

6. ] C h e ns o n g D a i a nd Y. B a g h z o uz , I m p a c t o f d i s t r i b u t e d g e n e r a t i o n o n v o l t a g e r e g u l a t i o n b y L T C t r a n s f o r m e r , 11 th I n t e r na t i o n a l C o n f e r e nc e o n H a r mo n i c s a nd Q ua l i t y o f P o we r , p p . 7 7 0 – 7 7 3 , 1 2 – 15 S e p t . 2 0 0 4 .

7. ] P . V . V . R a ma R a o a n d S . S i v a na ga R a j u , V o l t a g e r e g u l a t o r p l a c e m e n t i n r a d i a l d i s t r i b u t i o n s y s t e m u s i n g p l a n t g r o w t h s i m u l a t i o n a l g o r i t h m I n t e r na t i o n a l J o ur na l o f E n g i ne e r i n g, S c i e n c e a nd T e c h no l o g y , V o l . 2 , N o . 6 , p p . 2 0 7 – 217 , 2010 .

8. ] D . D a s , H . S . N a gi , N o v e l M e t h o d f o r s o l v i n g r a d i a l d i s t r i b u t i o n n e t w o r k s , P r o c e e d i n g s I E E P a r t C , V o l . 1 4 1 , no . 4 , p p . 2 9 1 2 9 8 , 1 9 9 1 .

9. ] S . G ho s h a nd D . D a s , M e t h o d f o r L o a d F l o w S o l u t i o n o f R a d i a l D i s t r i b u t i o n N e t w o r k s , P r o c e e d i n g s I E E P a r t C , V o l . 1 4 6 , no . 6 , p p . 6 4 1 6 4 8 , 1 9 9 9 .

10. 0 ] R . R a nj a n a nd , D . D a s , S i m p l e a n d E f f i c i e n t C o m p u t e r A l g o r i t h m t o S o l v e R a d i a l D i s t r i b u t i o n N e t w o r k s , I n t e r n a t i o na l J o u r na l o f E l e c t r i c P o we r C o mp o n e nt s a nd S ys t e ms , V o l . 3 1 , no . 1 , p p . 95

    1 0 7 , 2 0 0 3 .

11. 1 ] Y . Z h u a nd K . T o ms o vi c , A d a p t i ve P o we r F l o w M e t ho d fo r D i s t r i b ut i o n

S ys t e ms W i t h D i s p e r s e d G e n e r a t i o n , I E E E T r a n s a c t i o ns o n p o we r d e l i ve r y, p p . 8 2 2 – 8 2 7 , V O L. 1 7 , N O . 3 , J U L Y 2 0 0 2 .