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  • 8/9/2019 380KV Network

    1/5

    F i r s t I n t e r n a t i o n a l P o w e r

    a n d

    E n e r g y C o f e r e n c e

    PECon 2 0 0 6

    November 2 8 - 2 9 , 2 0 0 6 , P u t r a j a y a , M a l a y s i a

    P a r a m e t e r s

    a n d

    Power

    F l o w

    A n a l y s i s

    o f t h e 3 8 0 -kV

    I n t e r c o n n e c t e d Power

    S y s t e m

    i n T u r k e y

    Mehmet

    KURBAN,

    Ummuhan BASARAN

    F I L I K

    A b s t r a c t

    -

    T h i s p a p e r

    p r e s e n t s

    a l l

    t h e g e n e r a l o v e r v i e w o f

    t h e i n t e r c o n n e c t e d p o w e r s y s t e m

    i n

    T u r k e y

    w h i c h

    c o n s i s t s

    of

    3 0

    g e n e r a t i o n

    a n d

    3 5

    l o a d b u s e s ,

    t o t a l i n g 6 5

    b u s e s

    c o n n e c t e d

    e a c h o t h e r w i t h 3 8 0 - k V p o w e r t r a n s m i s s i o n l i n e s . A l s o

    t h e

    p o w e r f l o w a n a l y s i s i m p l e m e n t e d u s i n g

    M A T L A B O i s

    made t o

    f i n d

    o p t i m a l

    o p e r a t i n g p o i n t s

    o f t h e s y s t e m

    a n d t o make p o w e r

    s y s te m s g en er at i on p l an n in g.

    A l l

    d a t a u s e d

    i n t h i s

    a n a l y s i s

    i s

    t a k e n f r o m

    TEIAS

    ( T r a n s m i s s i o n S y s t e m O p e r a t o r

    o f

    T u r k e y )

    a n d

    EUAS ( E l e c t r i c i t y G e n e r a t i o n C o . I n c . )

    I n d e x

    t e r m s

    -

    L i n e

    p a r a m e t e r s , power

    f l o w 3 8 0 k V ,

    t r a n s m i s s i o n l i n e

    I . INTRODUCTION

    The

    p o w e r t r a n s m i s s i o n

    s y s t e m

    i n T u r k e y i n v o l v e s

    7 7 1

    b u s e s ,

    9 5 5

    l i n e s

    a n d 3 6 6

    t r a n s f o r m e r s .

    I n

    t h e

    3 8 0 - k V

    i n t e r c o n n e c t e d p o w e r

    s y s t e m o f

    T u r k e y

    w h i c h

    c o n s i s t s

    o f

    3 0

    g e n e r a t i o n

    a n d 3 5 l o a d

    b u s e s , t o t a l i n g

    6 5

    b u s e s ,

    5 p l a n t s

    a r e

    o t o p r o d u c t o r , 6 p l a n t s

    a r e

    m o b i l e ,

    1 2

    p l a n t s a r e t h e r m a l

    a n d 7

    p l a n t s

    a r e

    h y d r o t h e r m a l . R a i l ,

    c a r d i n a l a n d

    p h e a s a n t -

    t y p e

    c o n d u c t o r s w h i c h

    a r e t w o

    o r t h r e e

    b u n d l e d

    a r e

    u s e d i n

    t h i s

    s y s t e m . L e n g t h s

    o f t r an s m i ss i o n

    l i n e s c h a n g e

    b e t w e e n 7

    km t o 4 6 8

    k m .

    T h e r e

    a r e a l s o s e r i e s c a p a c i t o r s

    i n

    t h e l o n g

    t r a n s m i s s i o n l i n e s . Some o f t h e t r a n s m i s s i o n

    l i n e s

    a r e

    d o u b l e l i n e s

    [ 1 ] .

    I n t h i s

    p a p e r ,

    t h e

    T u r k e y ' s 3 8 0 - k V i n t e r c o n n e c t e d

    s y s t e m

    a r e

    e x p l a i n e d

    i n d e t a i l s a n d t h e N e w t o n

    R a p h s o n

    p o w e r

    f l o w

    a n a l y s i s

    i s

    p e r f o r m e d

    t o t h e

    s y s t e m

    w h i c h

    c o n s i s t s

    o f 6 5 b u s e s . .

    I I .

    NEWTON

    RAPHSON POWER

    FLOW ANALYSIS

    P o w e r f l o w s t u d i e s

    a r e i m p o r t a n t

    i n

    p l a n n i n g

    a n d

    d e s i g n i n g

    t h e f u t u r e

    e x p a n s i o n

    o f

    p o w e r s y s t e m s

    a s w e l l a s

    i n

    d e t e r m i n i n g

    b e s t

    o p e r a t i o n

    o f e x i s t i n g s y s t e m s . T h e

    p r i n c i p a l i n f o r m a t i o n

    o b t a i n e d

    f r o m

    p o w e r f l o w

    s t u d y i s

    t h e

    m a g n i t u d e a n d t h e p h a s e

    a n g l e

    o f

    t h e v o l t a g e a t

    e a c h b us

    a n d t h e

    r e a l

    a n d t h e r e a c t i v e

    p o w e r

    f l o w i n g

    i n

    e a c h l i n e

    [ 2 ] .

    T h e p o w e r f l o w

    p r o b l e m

    c a n

    b e

    f o r m u l a t e d a s

    a

    s e t o f

    n o n l i n e a r

    a l g e b r a i c e q u a l i t y / i n e q u a l i t y

    c o n s t r a i n t s .

    E i t h e r t h e b u s s e l f a n d

    m u t u a l

    a d m i t t a n c e s w h i c h

    c o m p o s e

    t h e

    b u s

    a d m i t ta n c e m a t ri x

    Y b u ,

    o r t h e

    d r i v i n g p o i n t

    a n d t r a n s f e r

    i m p e d a n c e s

    w h i c h

    c o m p o s e

    Z b u s

    may

    b e u s ed

    i n

    s o l v i n g p o w e r

    f l o w

    p r o b l e m .

    P o w e r

    f l o w

    c a l c u l a t i o n

    p r o v i d e s

    p o w e r

    f l o w s

    a n d

    v o l t a g e s

    f o r

    a

    s p e c i f i e d

    p o w e r

    s y s t e m s u b j e c t

    t o

    r e g u l a t i n g

    c a p a b i l i t y

    o f

    g e n e r a t o r s ,

    c a p a c i t o r s

    a n d

    t a p

    c h a n g e r s ,

    t r a n s f o r m e r s a s w e l l

    a s

    s p e c i f i e d

    n e t

    i n t e r c h a n g e

    b e t w e e n

    i n d i v i d u a l

    o p e r a t i n g

    s y s t e m

    [ 3 ] .

    M . K u r b a n i s

    w i t h

    t h e

    D e p a r t m e n t

    of E l e c t r i c a l a n d E l e c t r o n i c s

    E n g i n e e r i n g ,

    A n a d o l u

    U n i v e r s i t y ,

    E s k i s e h i r , 2 6 4 7 0

    T u r k e y ( e - m a i l :

    m k u r b a r n ( d

    a n l a d o l u . e d u . t r ) .

    U . B a s a r a n

    F i l i k

    i s

    w i t h

    t h e

    D e p a r t m e n t

    o f E l e c t r i c a l a n d E l e c t r o n i c s

    E n g i n e e r i n g ,

    A n a d o l u

    U n i v e r s i t y ,

    E s k i s e h i r , 2 6 4 7 0

    T u r k e y ( e - m a i l :

    u b a s a r a n @ a n a d o l u . e d u . t r ) .

    Bus

    A d m i t t a n c e

    M a t r i x :

    An

    a d m i t t a n c e

    m a t r i x

    r e l a t e s

    t h e

    i n j e c t e d

    c u r r e n t s a t t h e n o d e s o f

    an

    i n t e r c o n n e c t e d

    n e t w o r k t o t h e v o l t a g e s a t t h e n o d e s ,

    a n d

    g i v e s t h e

    e l e c t r i c a l

    b e h a v i o r

    o f

    t h e

    v a r i o u s n e t w o r k

    c o m p o n e n t s .

    T h e

    a d m i tt a n c e m a tr i x

    i s

    o b t a i n e d

    b y m a k i n g n o d a l a n a l y s i s

    on

    t h e n e t w o r k

    T h e

    Y b u ,

    i s

    s y m m e t r i c .

    Y i i ,

    d i a g o n a l t e r m s

    ar e

    t h e

    s e l f -

    a d m i t t a n c e w h i c h

    i s

    t h e

    sum

    o f a dm i tt a nc es o f a l l

    t h e

    components

    c o n n e c t e d t o t h e i t h n o d e .

    Y i j ,

    n o n - d i a g o n a l

    e l e m e n t s

    ar e n e g a t i v e

    o f a d m i t ta n c e

    o f a l l components

    c o n n e c t e d b e t w e e n t h e i t h a n d t h e

    j t h

    n o d e .

    I f

    a p a r a l l e l

    c o n n e c t i o n b e t w e e n

    t h e i t h a n d j t h

    n o d e

    e x i s t , o n e must

    c a l c u l a t e t h i s a d m i t t a n c e i n a d v a n c e .

    Y b u s

    m a t r i c e s

    c an

    b e

    r e p r e s e n t e d as

    f o l l o w s

    ( N x N ) :

    Y 1

    Y 1 2

    i Y N

    Y 2 1

    Y 2 2 Y 2 N

    _ Y N I

    Y N 2

    * * Y N N _

    N X N

    Y i j Y i j

    O i j

    Y i 1

    cos

    O i j

    j | Y i j

    s in

    O i j

    =

    G i j

    j B i

    1

    F o r

    l a r g e power

    s y s t e m s , t h e Newton

    R a p h s o n m e t h o d

    i s f o u n d

    t o

    b e more

    e f f i c i e n t a n d p r a c t i c a l . T h e n u m b e r o f

    i t e r a t i o n s r e q u i r e d t o o b t a i n

    a

    s o l u t i o n i s

    i n d e p e n d e n t

    o f

    t h e

    s y s t e m s i z e ,

    b u t more f u n c t i o n a l

    e v a l u a t i o n s ar e r e q u i r e d

    a t

    e a c h

    i t e r a t i o n .

    T h e

    c o m p l e x power

    a t b u s i

    i s ;

    N

    N

    P i

    - j Q i

    V i

    I i

    V i

    Y

    i n V

    =

    Y n i V

    6 i n

    / 6 - / i )

    2

    n = l n = l

    S e p a r a t i n g

    i n t o

    r e a l a n d

    i m a g i n a r y components y i e l d s

    two

    e q u a t i o n s

    f o r b u s

    i ,

    N

    n = l

    N

    Q i

    E

    V i V r Y i ,

    s i n f 0 i r

    +

    l ,

    i

    n = l

    A P i

    a n d

    A Q i

    APi

    Pi,g

    P , c a l

    =

    P g i

    )

    ,cal

    A Q i

    Q i , g Q i , c a l

    Q g i

    Q i

    Q i , c a l

    ( 4 )

    ( 5 )

    ( 6 )

    The

    J a c o b i a n

    m a t r i x

    g i v e s

    t h e l in ea ri z ed r e l a t i o n s h i p

    b e t w e e n

    s m a l l

    c h a n g e s

    i n

    v ol ta g e a ng le

    a n d

    v o l t a g e

    m a g n i t u d e

    w i t h

    t h e s m a l l

    c h a n g e s

    i n r e a l a n d r e a c t i v e

    po w er.

    I n s h o r t

    f o r m c an

    b e w r i t t e n

    a s ;

    AP

    ][lJl

    j12 ILAvI

    7

    F o r

    v o l t a g e

    c o n t r o l l e d

    b u s e s

    t h e v o l t a g e m a g n i t u d e s

    ar e

    k n o w n .

    T h e r e f o r e

    i f m

    b u s e s

    o f

    t h e

    s y s t e m

    ar e

    v o l t a g e

    c o n t r o l l e d ,

    m

    e q ua t i on i n vo lv i n g

    AQ

    a n d AV a n d

    t h e

    c o r r e s p o n d i n g

    c o l u m n s

    f

    t h e J a k o b i a n m a t r i x

    c an

    b e

    e l i m i n a t e d .

    The

    d i a g o n a l

    a n d o f f

    d i a g o n a l

    e l e m e n t s o f

    J l l ,

    J 1 2 ,

    J 2 1 , a n d

    J 2 2

    [ 2 ] :

    1 - 4 2 4 4 - 0 2 7 3 - 5 / 0 6/ 2 0 . 0 0

    C2006

    IE E E

    2 3 5

  • 8/9/2019 380KV Network

    2/5

    2 36

    J 1 1 :

    a P 5

    a J i

    a , 5 j

    Jk

    Ji2:

    N

    >

    | V i | | y i ,

    1|Vj

    s i n ( . i

    - d 5 j

    -

    O i j

    V = l ,

    s i n

    - Y

    Y i ,

    | | V j

    s i n , 5 i

    -i

    j -

    i , ,

    k

    i

    ai

    N

    Ii , j

    | | V j

    s i n g i

    g j

    O t i j

    )

    2 y V i | | Y i , i

    s i n ( - t i , i

    )

    aQ

    -

    Vi

    i y k s i n ( 5 i -

    O k

    i

    a ~ k

    J 2 1 :

    a Q i

    a Y

    a Q

    a l 5 k

    N

    yij| V j 1 s i n ( g i -j

    - 6 i j )

    Y=l

    i

    | V i | |

    Y i , k

    | | V j

    C O S ( ( i

    i

    i , k

    ,

    k

    i

    J 2 2 :

    3 P i

    N

    =

    Y i , A v j l c o s i

    -

    j

    - o i s j

    +

    2 V

    l y j j

    n c o s ( - 0 6 )

    | v

    V i

    Y i , k

    | |

    C O S 0 5 i

    - j

    - O i , k

    k

    i

    III.

    T HE

    SYSTEM

    PARAMETERS

    E l e c t r i c i t y

    G e n e r a t i o n o f t h e s y s t e m

    I n 1 9 2 3 , t o t a l power

    o f t h e

    system

    i s

    3 3 MW b u t

    3 5 5 8 7

    MW

    i n 2 0 0 3 .

    T h e

    t o t a l power

    o f t h e

    system

    i s

    g i v e n

    b e t w e e n 1 9 7 3 a n d 2 0 0 3 years

    i n

    t h e t a b l e

    1 .

    TABLE

    1

    TO TAL

    POWER

    OF

    THE SYSTEM

    BETWEEN 1 9 7 3 AND 2 0 0 3

    YEARS

    Y e a r T he rm al H y d ro th er ma l

    J e o t e r T o t a l I n c r e a s e

    ( M W )

    +Wind M W)

    ( )

    1 9 7 3

    2 2 0 7 , 1

    9 8 5 , 4

    3 1 9 2 , 5

    1 7 , 7

    1 9 7 4 2 2 8 2 , 9

    1 4 4 9 , 2 3 7 3 2 , 1

    1 6 , 9

    1 9 7 5 2 4 0 7

    1 7 7 9 , 6 4 1 8 6 , 6

    1 2 , 2

    1 9 7 6 2 4 9 1 , 6

    1 8 7 2 , 6

    4 3 6 4 , 2 4 , 2

    1 9 7 7 2 8 5 4 , 6

    1 8 7 2 , 6

    4 7 2 7 , 2 8 , 3

    1 9 7 8 2 9 8 7 , 9

    1 8 8 0 , 8

    4 8 6 8 , 7

    3

    1 9 7 9

    2 9 8 7 , 9 2 1 3 0 , 8

    5 1 1 8 , 7 5 , 1

    1 9 8 0

    2 9 8 7 , 9

    2 1 3 0 , 8 5 1 1 8 , 7

    0

    1 9 8 1

    3 1 8 1 , 3

    2 3 5 6 , 3 5 5 3 7 , 6

    8 , 2

    1 9 8 2

    3 5 5 6 , 3 3 0 8 2 , 3

    6 6 3 8 , 6

    1 9 , 9

    1 9 8 3 3 6 9 5 , 8 3 2 3 9 , 3

    6 9 3 5 , 1

    4 , 5

    1 9 8 4 4 5 8 4 , 3

    3 8 7 4 , 8

    1 7 , 5

    8 4 5 9 , 1 2 2

    1 9 8 5

    5 2 4 4 , 3 3 8 7 4 , 8

    1 7 . 5 9 1 1 9 , 1

    7 , 8

    1 9 8 6 6 2 3 5 , 2 3 8 7 7 , 5 1 7 , 5 1 0 1 1 2 , 7

    1 0 , 9

    1 9 8 7

    7 4 8 9 , 3

    5 0 0 3 , 3 1 7 , 5

    1 2 4 9 2 , 6 2 3 , 5

    1 9 8 8

    8 2 9 9 , 8 6 2 1 8 , 3

    1 7 , 5 1 4 5 1 8 , 1

    1 6 , 2

    1 9 8 9 9 2 0 8 , 4

    6 5 9 7 , 3 1 7 , 5 1 5 8 0 5 , 7

    8 , 9

    1 9 9 0 9 5 5 0 , 8

    6 7 6 4 , 3

    1 7 , 5

    1 6 3 1 5 , 1

    3 , 2

    1 9 9 1 1 0 0 9 2 7 1 1 3 , 8

    1 7 , 5

    1 7 2 0 6 , 6

    5 , 5

    1 9 9 2

    1 0 3 3 4

    8 3 7 8 , 7

    1 7 , 5 1 8 7 1 3 , 6 8 , 8

    1 9 9 3

    1 0 6 5 3

    9 6 8 1 , 7 1 7 , 5 2 0 3 3 5 , 1

    8 , 7

    1 9 9 4

    1 0 9 9 2

    9 8 6 4 , 6 1 7 , 5

    2 0 8 5 7 , 3 2 , 6

    1 9 9 5

    1 1 0 8 9 9 8 6 2 , 8 1 7 , 5

    2 0 9 5 1 , 8 0 , 5

    1 9 9 6

    1 1 3 1 2

    9 9 3 4 , 8

    1 7 , 5

    2 1 2 4 6 , 9

    1 , 4

    1 9 9 7

    1 1 7 8 6 1 0 1 0 2

    1 7 , 5 2 1 8 8 9 , 4

    3

    1 9 9 8 1 3 0 2 1

    1 0 3 0 6

    2 6 , 2 2 4 1 8 9

    6 , 7

    1 9 9 9

    1 5 5 5 5

    1 0 5 3 7 2 6 , 2 2 6 1 1 9 , 3

    1 1 , 8

    2 0 0 0

    1 6 0 5 2 1 1 1 7 5 3 6 , 4 2 7 2 6 4 , 1

    4 , 4

    2 0 0 1 1 6 6 2 3 1 1 6 7 2

    3 6 , 4 2 8 3 3 2 , 4

    3 , 9

    2 0 0 2 1 9 3 8 5 1 2 2 4 0

    3 6 . 4

    3 1 8 4 5 . 8 1 1 . 2

    2 0 0 3

    2 2 8 0 9 1 2 5 9 7 3 6 . 4

    3 5 5 8 7 1 1 . 1

    T h e r m a l

    a n d

    H y d r o t h e r m a l

    P l a n t s

    T o t a l

    g e n e r a t i o n ,

    n u m b e r

    o f t h e group s a n d

    i n t e r i o r

    c o n s u m p t i o n

    o f

    t h e p l a n t s

    ar e

    g i v e n

    i n T a b l e

    2 .

    ( 2 0 0 3 -

    summer

    p u a n t l o a d )

    TABLE

    2

    TO TAL

    GENERATION

    BY

    NUMBER OF

    T HE

    GROUPS

    AND

    INTERIOR CO NSUMPTIO N O F T HE

    PLANTS

    P l a n t Name Number

    of G e n e r a t i o n

    I . c o n s u m p t .

    G r o u p s

    M W ) M W )

    Ada

    DG

    2 3 3 0

    5

    A l t i n k a y a

    2 2 6 2

    A m b a r l i

    8 1 0 0 0

    2 5

    A t a t u i r k

    5 1 3 2 0

    B i r e c i k H e s

    4

    4 1 6

    B u r s a DG

    2

    3 7 0 5

    C a t a l a n

    3

    1 5 6

    a y i r h a n

    3 3 4 0 4 6

    E l b i s t a n

    1 3 0 0 2 7

    G e b z e DG

    6 1 4 0 0 2 1

    G 6 k q e k a y a

    2

    1 6 7

    a s a n U g u r l u

    2

    2 0 0

    H a m i t a b a t 6

    6 2 0 1 0

    I z m i r

    DG

    6

    1 4 6 9

    2 0

    K a r a k a y a

    3 8 4 0

    K e b a n

    7 1 1 2 5

    K e m e r k o y 1

    2 0 0

    1 8

    K e m e r k o y

    2 3 6

    O y m a p i n a r

    2

    2 5 0

    S e y i t o m e r

    2 2 9 0 2 8

    Soma

    6

    6 4 0 6 4

    S u g o z u i

    2 1 1 1 2 8 0

    U n i m a r

    3

    4 5 2

    7

    Y a t a g a n

    2

    3 9 0

    4 0

    Y e n i k o y 2

    3 3 0 3 3

    O t o p r . + M o b i l

    1 6 3 1

    R e g u l a t e d s t a i r c u r v e u s i n g

    2 0 0 2 l o a d d a t a i s s h o w n

    i n

    f i g u r e 1 .

    xI 0

    .

    ol i c a

    . m . c

    . c a

    X

    ~

    T i m e

    F i g

    1

    S t a i r

    c u r v e

    f o r

    2 0 0 2

    l o a d

    v a l u e s

    R e a c t a n c e , I m p e d a n c e

    a n d

    C a p a c i t a n c e

    V a l u e s

    o f

    t h e

    s y s t e m

    T h e

    i n t e r c o n n e c t e d

    p o w e r

    s y s t e m

    o f

    T u r k e y

    w h i c h

    c o n s i s t s

    o f

    3 0

    g e n e r a t i o n

    a n d

    3 5

    l o a d

    b u s e s ,

    t o t a l i n g

    6 5

    b u s e s c o n n e c t e d

    e a c h o t h e r

    w i t h

    3 8 0 - k V

    p o w e r

    t r a n s m i s s i o n

    l i n e s . T h e

    s y s t e m

    i s s h o w n

    i n

    t h e

    F i g u r e

    2 . B u s c o d e s a r e

    g i v e n

    i n

    t h e

    T a b l e

    3 .

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    TABLE 3

    BUS C OD ES F OR T HE

    SYSTEM

    The

    lengths

    of the transmission lines and number of the

    b u n d l e d

    c o n d u c t o r s

    ar e

    g i v e n

    i n

    T a b l e

    4

    f o r

    a

    f e w s e l e c t e d

    one s.

    TABLE

    4

    PARAMETERS

    FOR

    A

    FEW

    SELECTED LINES

    B u s t o

    L e n g t h s

    o f

    T y p e

    o f Number o f

    T y p e

    o f h e

    b u s l i n e

    ( k m )

    p i l l a r b o u n d e d

    i n d .

    c o n d u c t o r

    1

    - 4

    1 5 3

    3ABC

    3 C a r d i n a l

    1 - 3 9 9 0

    A 2

    C a r d i n a l

    3 - 3 9 8 7

    A 2

    C a r d i n a l

    2 - 3 9 8 5

    S 1 S 2 3 C a r d i n a l

    2 - 5

    4 8

    PH

    3

    P h e a s a n t

    6 - 7

    3 1 . 9 5 7

    4A1 2

    R a i l

    U s i n g

    t h e

    d a t a

    g i v e n

    i n T a b l e

    4 ,

    R,X

    a n d B / 2

    v a l u e s

    ar e

    c a l c u l a t e d a n d some s e le c te d v a l u es f o r

    t h i s

    p a r a m e t e r s

    ar e

    g i v e n

    i n

    T a b l e 5 .

    TABLE

    5

    SELECTED VALUES

    FOR

    R , X

    AND

    B / 2

    B u s

    t o

    R

    X

    B / 2

    b u s

    ( p . u )

    ( p . u ) ( p . u )

    1

    - 4

    0 . 0 0 2 4 4 4 0 . 0 2 8 0 8 2

    0 . 4 6 1 2 9 0 5

    1

    - 3 9 0 . 0 0 2 1 6 5

    0 . 0 2 0 0 0 1 0 . 2 2 2 0 9 8

    3 - 3 9

    0 . 0 0 2 0 8 0

    0 . 0 1 9 2 2 1

    0 . 2 5 3 3

    2 - 3 9 0 . 0 0 1 3 6 4

    0 . 0 1 6 2 3 4

    0 . 2 4 8 3 2 6 5

    2 - 5 0 . 0 0 0 5 7 7 0 . 0 0 8 6 2 8

    0 . 1 4 8 3 5 2

    6 7 0 . 0 0 0 7 6 9 0 . 0 0 7 1 1 9

    0 . 0 7 8 7 0 5

    I V . POWER FLOW ANALYSIS

    U s i n g d a t a t a k e n f r o m

    T E I A S , power

    f l o w

    a n a l y s i s

    i s

    m a d e

    f o r t h e g i v e n s y s t e m . T h e

    p r i n c i p a l

    i n f o r m a t i o n

    o b t a i n e d

    f r o m

    t h i s s t u d y

    i s

    t h e m a g n i t u d e

    a n d t h e

    p h a s e

    a n g l e

    o f

    t h e v o l t a g e a t e a c h b u s a n d t h e r e a l a n d t h e r ea c t iv e

    power

    f l o w i n g

    i n

    e a c h l i n e .

    F i r s t ,

    b u s

    t y p e s o f t h e

    s y s t e m

    ar e

    d e f i n e d . H a m i t a b a t b u s i s c h o s e n

    s l a c k

    b u s .

    T h e b u s

    a d m i t t a n c e

    m at ri x o f

    t h e s y s t e m

    i s

    c o m p o s e d

    u s i n g

    R , X ,

    B / 2 d a t a . T h e m a t r i x i s

    a

    sparse

    m a t r i x .

    D i m e n s i o n

    o f

    t h e

    m a t r i x

    i s

    6 5 x 6 5 . I n

    f i g u r e 3

    s h o w s t h e

    n u m b e r o f d i f f e r e n t zero s f o r

    s y s t e m .

    0

    10

    2 0

    30

    40

    50

    60

    0

    1

    0 2 0 3 0 4 0

    5 0

    6 0

    n z

    2 4 9

    F i g .

    3 : T h e n u m b er of d i f f e r e n t

    zero s f o r s y s t e m

    i n

    t h e

    b u s a d m i t t a n c e

    m a t r i x .

    T h e

    c o n v e r g e

    g r a p h i c s o f t h e AP

    a n d

    AQ

    ar e

    s h o w n i n

    t h e

    F i g u r e

    4 .

    A f t e r

    t h e s i x t i e t h

    i t e r a t i o n ,

    AP a n d

    AQ

    v a l u e s

    c onv e rge

    t o v a l u e o f 0 . 0 2 .

    _3

    -

    D D

    m

    3 0

    _

    60

    OS

    .

    0 . +

    - 0 . -

    1 0

    X

    30

    4 X

    a

    l e t r i o

    F i g .

    4 : T h e

    converge g r a p h i c s

    o f

    t h e

    AP a n d

    AQ

    R es ul ts o f t h e

    power

    f l o w

    a n a l y s i s

    ar e shown

    i n

    t a b l e 6 .

    B u s B u s B u s

    B u s Na m e

    B u s

    Name

    B u s

    Na m e

    1

    H a m i t a b a t

    2 3

    E r e g l i _ 2

    4 5

    I z m i r _ D G K C

    2 H a b i b l e r 2 4

    C a r s a m b a

    4 6

    I U i k l a r

    3 I k i t e l l i

    2 5

    T i r e b o l u

    4 7

    Y a t a g a n

    4 A l i b e y k o y 2 6

    K a y a b a s i

    4 8

    Y e n i k o y

    5 P a s a k o y 2 7 D e c e k o 4 9

    K e m e r k y y

    6

    U m r a n i y e

    2 8

    E r z u r u m

    5 0

    O . P n a r

    7 T . O r e n

    2 9 H o r a s a n

    5 1

    G . A n t e p 2

    8

    K a r a b i g a

    3 0

    O z l u c e

    5 2

    S . O m e r

    9

    B

    a l i k e s i r

    2

    3 1

    D . B a k i r

    5 3

    G o k c e k a y a

    1 0

    A l i a g a _ 2

    3 2 B a t m a n 5 4

    AdaTM

    1 1

    U z u n d e r e 3 3

    S . U r f a 5 5

    G e b z e ( a d a l )

    1 2 V a r s a k 3 4

    K e b a n _ 2

    5 6

    A d a _ 2

    1 3 A d a n a

    3 5

    D e n i z l i

    5 7

    O s m a n c a

    1 4 E r z i n

    3 6

    S . S e h i r

    5 8

    B i r e c i k

    1 5 A n d i r i n

    3 7

    C a y i r h a n

    5 9 A t a t u r k

    1 6

    K o n y a

    3 8

    A l t i n k a y a

    6 0

    K a r a k a y a

    1 7

    G o l b a s i 3 9 U n i m a r

    6 1

    E l b B

    1 8

    T e m e l l i

    4 0

    A m b a r l i 6 2

    E l b A

    1 9

    Y . H i s a r

    4 1 B u r s a N . G

    6 3 H . U g u r l u

    2 0 K a p a s i t o r

    4 2

    B.

    I n d .

    6 4

    K a n g a l

    2 1 A n k a r a 4 3 T . S a l t 6 5

    K e b a n

    1

    2 2 K u r s u n l u

    4 4

    S o m a _ B

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    2 3 8

    H a m i t a b a t 1

    3 9

    Am

    I z m i r

    D G K Q

    4 5

    U z u n d e r e

    1 1

    Y . K o y

    4 8

    3

    n b a r l i

    4 0

    AdaT.M

    5 4

    8

    2 5

    2 8

    K a y a b a , i

    2 6

    K e

    K e b a n 2

    3 4

    El b

    A

    |