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V O L T A G E S A G I N D I C E S a n d
S T A T I S T I C S
b y
F r a n t i e k K i n e
T h e s i s f o r t h e D e g r e e o f M a s t e r o f S c i e n c e
D e c e m b e r 2 0 0 4
D e p a r t m e n t o f E l e c t r i c P o w e r E n g i n e e r i n g
C h a l m e r s U n i v e r s i t y o f T e c h n o l o g y
4 1 2 9 6 G t e b o r g , S w e d e n
I S S N 1 4 0 1 - 6 1 8 4
M . S c . N o . 1 1 3 E
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2/142
i i
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T i t l e
I n d e x o c h s t a t i s t i k f r s p n n i n g s d i p p a r
T i t l e i n e n g l i s h
V o l t a g e S a g I n d i c e s a n d S t a t i s t i c s
F r f a t t a r e / A u t h o r
F r a n t i e k K i n e
U t g i v a r e / P u b l i s h e r
C h a l m e r s T e k n i s k a H g s k o l a
I n s t i t u t i o n e n f r e l t e k n i k
4 1 2 9 6 G t e b o r g , S v e r i g e
I S S N
1 4 0 1 - 6 1 8 4
E x a m e n s a r b e t e / M . S c . T h e s i s N o .
1 1 3 E
m n e / S u b j e c t
P o w e r S y s t e m s
E x a m i n e r s
A s s o c i a t e P r o f . A m b r a S a n n i n o
D a t e
2 0 0 4 - 1 2 - 1 7
T r y c k t a v / P r i n t e d b y
C h a l m e r s t e k n i s k a h g s k o l a
4 1 2 9 6 G T E B O R G
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i v
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A b s t r a c t
V o l t a g e s a g i n d i c e s a r e a w a y o f q u a n t i f y i n g t h e p e r f o r m a n c e o f t h e p o w e r s u p p l y , a s f a r
a s v o l t a g e s a g s a r e c o n c e r n e d . I n d i c e s c a n b e d e n e d f o r i n d i v i d u a l e v e n t s , f o r i n d i v i d u a l
s i t e s , a n d f o r a w h o l e s y s t e m . A s t a n d a r d m e t h o d f o r s i n g l e - e v e n t m e t h o d s i s p a r t o f I E C
s t a n d a r d 6 1 0 0 0 - 4 - 3 0 .
T h i s t h e s i s e m p h a s i z e s t h e i m p o r t a n c e o f v o l t a g e s a g i n d i c e s a n d d i e r e n t m e t h o d s f o r
c a l c u l a t i n g t h r e e - p h a s e v o l t a g e s a g c h a r a c t e r i s t i c s . T h r e e - p h a s e e v e n t s m e a s u r e d i n a
m e d i u m n e t w o r k v o l t a g e o v e r p e r i o d o f o n e m o n t h w e r e a n a l y z e d , r e s u l t s e x a m i n e d a n d
s t a t i s t i c a l l y e v a l u a t e d . A n a l g o r i t h m f o r c a l c u l a t i n g v o l t a g e s a g c h a r a c t e r i s t i c s a n d i n d i c e s
w a s c r e a t e d i n M a t l a b .
A l g o r i t h m d e t e c t s i f t h e e v e n t i s v o l t a g e s a g , i n t e r r u p t i o n o r s w e l l . T w o d i e r e n t m e t h o d s ,
s y m m e t r i c a l c o m p o n e n t m e t h o d a n d s i x - p h a s e r m s m e t h o d , f o r c a l c u l a t i n g s a g t y p e a r e
u s e d i n t h e a l g o r i t h m . S i n g l e - e v e n t c h a r a c t e r i s t i c s a s d u r a t i o n , r e t a i n e d v o l t a g e , v o l t a g e
s a g e n e r g y i n d e x , v o l t a g e s a g s e v e r i t y a n d s a g t y p e a r e c a l c u l a t e d f o r e a c h e v e n t a n d
s u m m a r i z e d i n s y n o p t i c t a b l e .
A f t e r s i n g l e - e v e n t c h a r a c t e r i s t i c r e s u l t s w e r e s a t i s f a c t o r y , s i t e a n d s y s t e m i n d i c e s w e r e
i m p l e m e n t e d i n M a t L a b a n d s o m e s t a t i s t i c s w e r e c a r r i e d o u t .
A l s o v a r i o u s i m p l e m e n t a t i o n i s s u e s w i t h a d e t a i l e d d e s c r i p t i o n o f s y m m e t r i c a l c o m p o n e n t
m e t h o d a n d s i x - p h a s e r m s m e t h o d w e r e w r i t t e n .
K e y w o r d s : p o w e r q u a l i t y , v o l t a g e s a g , s w e l l , i n t e r r u p t i o n , d u r a t i o n , r e t a i n e d v o l t a g e
v
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A c k n o w l e d g e m e n t s
T h a n k s t o P r o f . M a t h B o l l e n a n d A s s o c i a t e P r o f . A m b r a S a n n i n o w h o h e l p e d m e w i t h
m y t h e s i s a s m y s u p e r v i s o r s .
T h a n k s t o m y f a m i l y , t h a t s u p p o r t e d m e d u r i n g m y s t u d i e s a t C h a l m e r s U n i v e r s i t y o f
T e c h n o l o g y .
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C o n t e n t s
1 I n t r o d u c t i o n 1
1 . 1 W h a t i s V o l t a g e S a g ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 . 2 V o l t a g e S a g I n d i c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1 . 3 A i m a n d s t r u c t u r e o f t h i s t h e s i s . . . . . . . . . . . . . . . . . . . . . . . . 2
2 S i n g l e - E v e n t C h a r a c t e r i s t i c s a n d I n d i c e s 4
2 . 1 E x a c t F r e q u e n c y E s t i m a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 . 2 R M S C a l c u l a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 . 3 D u r a t i o n a n d R e t a i n e d V o l t a g e . . . . . . . . . . . . . . . . . . . . . . . . 5
2 . 3 . 1 I n t e r r u p t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 . 3 . 2 S w e l l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 . 4 V o l t a g e - S a g E n e r g y I n d e x . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 . 5 V o l t a g e - S a g S e v e r i t y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 . 6 T h r e e - p h a s e c l a s s i c a t i o n o f a v o l t a g e s a g . . . . . . . . . . . . . . . . . . 9
2 . 6 . 1 V o l t a g e s a g c l a s s i c a t i o n . . . . . . . . . . . . . . . . . . . . . . . . 9
2 . 6 . 2 M e t h o d s f o r e x t r a c t i n g s a g t y p e . . . . . . . . . . . . . . . . . . . . 1 2
3 I m p l e m e n t a t i o n I s s u e s a n d R e s u l t s o f S i n g l e - E v e n t C h a r a c t e r i s t i c s 1 7
3 . 1 I m p l e m e n t a t i o n I s s u e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7
3 . 1 . 1 R e f e r e n c e V o l t a g e . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7
3 . 1 . 2 E x a c t F r e q u e n c y . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8
3 . 1 . 3 R M S C a l c u l a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9
3 . 1 . 4 I m p l e m e n t a t i o n o f t h e T w o M e t h o d s . . . . . . . . . . . . . . . . . 2 0
3 . 2 M a t L a b R e s u l t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1
3 . 2 . 1 R e s u l t s o f S i n g l e - E v e n t C h a r a c t e r i s t i c s . . . . . . . . . . . . . . . . 2 1
3 . 2 . 2 D i e r e n t c a l c u l a t i o n s o f V o l t a g e S a g E n e r g y I n d e x . . . . . . . . . . 2 3
3 . 2 . 3 V o l t a g e S a g S e v e r i t y R e s u l t s . . . . . . . . . . . . . . . . . . . . . . 2 5
3 . 2 . 4 S a g T y p e R e s u l t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 6
3 . 2 . 5 S t a t i s t i c s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 8
4 S i t e I n d i c e s 3 1
4 . 1 S A R F I - X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1
4 . 2 S A R F I - C u r v e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2
4 . 2 . 1 S A R F I - I T I C ( C B E M A ) . . . . . . . . . . . . . . . . . . . . . . . . 3 2
4 . 2 . 2 S A R F I - S E M I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3
4 . 3 V o l t a g e - S a g T a b l e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4
4 . 4 V o l t a g e - s a g e n e r g y m e t h o d . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4
4 . 4 . 1 V o l t a g e - S a g E n e r g y I n d e x . . . . . . . . . . . . . . . . . . . . . . . 3 5
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4 . 4 . 2 A v e r a g e S a g E n e r g y I n d e x . . . . . . . . . . . . . . . . . . . . . . . 3 5
4 . 4 . 3 N u m b e r o f e v e n t p e r s i t e . . . . . . . . . . . . . . . . . . . . . . . . 3 5
4 . 5 V o l t a g e - S a g S e v e r i t y M e t h o d . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5
5 S i t e I n d i c e s R e s u l t s 3 7
5 . 1 S A R F I I n d i c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 7
5 . 2 I E C T a b l e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0
6 S y s t e m I n d i c e s 4 2
6 . 1 S A R F I S y s t e m I n d i c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3
6 . 2 V o l t a g e - S a g T a b l e s f o r a s y s t e m . . . . . . . . . . . . . . . . . . . . . . . . 4 3
6 . 3 V o l t a g e - S a g E n e r g y I n d e x o f a S y s t e m . . . . . . . . . . . . . . . . . . . . 4 3
6 . 4 V o l t a g e - S a g S e v e r i t y S y s t e m I n d e x . . . . . . . . . . . . . . . . . . . . . . 4 4
7 C o n c l u s i o n s 4 5
A M a t l a b C o d e 4 7
A . 1 M a k i n g . m a t F i l e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 7
A . 2 G e n e r a t i n g S y n t h e t i c S a g s . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 7
A . 3 S i t e I n d i c e s a n d F i g u r e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2
B S y n t h e t i c S a g s w i t h C h a r a c t e r i s t i c V o l t a g e V = 0 . 5 p u 8 8
R e f e r e n c e s 9 0
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2 1 I n t r o d u c t i o n
I n t h e F i g . 1 . 1 e x a m p l e o f e v e n t t h a t i s c l a s s i e d a s v o l t a g e s a g , i n t e r r u p t i o n a n d s w e l l
i s s h o w n .
0 2 4 6 8 10 12 14 160
0.2
0.4
0.6
0.8
1
1.2
Time [cycles]
RMSVoltage[pu]
sag threshold = 0.9 pu
interruption threshold = 0.1 pu
swell threshold = 1.1 pu
F i g u r e 1 . 1 : E x a m p l e o f v o l t a g e s a g , i n t e r r u p t i o n a n d s w e l l i n o n e e v e n t
V o l t a g e s a g s c a n b e m i t i g a t e d b y m a n y d i e r e n t e l e c t r i c d e v i c e s , d e p e n d i n g o n t h e
a p p l i c a t i o n , b u t t h a t i s n o t a s u b j e c t t h a t w i l l b e d i s c u s s e d i n t h e f o l l o w i n g c h a p t e r s .
I n t h e f o l l o w i n g c h a p t e r s I w i l l d i s c u s s v o l t a g e s a g i n d i c e s i n m o r e d e t a i l a l o n g w i t h t h e
a n a l y s i s o f t h e m e a s u r e d d a t a .
V o l t a g e s a g s i n t h e e l e c t r i c a l s y s t e m i s s o m e t h i n g w e d o n o t l i k e , b u t w e c a n m a k e
i m p r o v e m e n t s i n t h e s y s t e m t o p r e v e n t t h e m f r o m h a p p e n i n g . T h e r e f o r e t h e r e i s a h i g h
n e e d f o r b e t t e r a n a l y s i s a n d u n d e r s t a n d i n g o f t h e s e e v e n t s .
1 . 2 V o l t a g e S a g I n d i c e s
N o w a d a y s p o w e r p r o v i d e r s a r e b u i l d i n g d a t a b a s e s o f p o w e r q u a l i t y e v e n t s w i t h m e g a b y t e s
t o g i g a b y t e s o f m e a s u r e m e n t s . T h e r e f o r e t h e r e i s a n e e d t o a n a l y s e t h e s e d a t a a c c u r a t e l y
a n d w i t h a h i g h e c i e n c y . V o l t a g e s a g i n d i c e s a r e a g o o d t o o l f o r a n a l y s i n g t h e s e d a t a .
V o l t a g e s a g i n d i c e s a r e a w a y o f q u a n t i f y i n g t h e p e r f o r m a n c e o f t h e p o w e r s u p p l y , a s f a r
a s v o l t a g e s a g s a r e c o n c e r n e d . I n d i c e s c a n b e d e n e d f o r i n d i v i d u a l e v e n t s , f o r i n d i v i d u a l
s i t e s , a n d f o r a w h o l e s y s t e m .
T h e r e c o n t i n u e s t o b e a l a c k o f c o m m o n t e r m i n o l o g y t o a s s e s s u t i l i t y s e r v i c e q u a l i t y
p e r f o r m a n c e , t h e r e f o r e a l s o a n o v e r v i e w o f t h e e x i s t i n g k n o w l e d g e o n v o l t a g e s a g i n d i c e s
t o g e t h e r w i t h v a r i o u s s t a t i s t i c s w i l l b e d i s c u s s e d .
T h e m a i n d o c u m e n t t h a t w i l l b e u s e d t o o b t a i n v o l t a g e s a g i n d i c e s i s V o l t a g e s a g
i n d i c e s - d r a f t 5 , w o r k i n g d o c u m e n t f o r I E E E P 1 5 6 4 [ 2 ] . I n t h i s d o c u m e n t v o l t a g e s a g
i n d i c e s a r e e x p l a i n e d i n a v e r y g o o d m a n n e r , s o o n e c a n u n d e r s t a n d i t .
1 . 3 A i m a n d s t r u c t u r e o f t h i s t h e s i s
T h e a i m s o f t h i s t h e s i s i s r s t l y t o i m p l e m e n t t h e a l g o r i t h m s t o c a l c u l a t e s i t e a n d s y s t e m
i n d i c e s f r o m s a m p l e d v o l t a g e s a c c o r d i n g t o t h e l i s t e d d o c u m e n t s [ 1 ] a n d [ 2 ] i n M a t l a b ,
w i t h w r i t t e n o v e r v i e w o f t h e e x i s t i n g k n o w l e d g e o n v o l t a g e s a g i n d i c e s .
S e c o n d l y t o d e v e l o p a m e t h o d f o r c a l c u l a t i n g s i n g l e - e v e n t , s i t e a n d s y s t e m i n d i c e s
b a s e d o n t h r e e - p h a s e c h a r a c t e r i s t i c s u s i n g d o c u m e n t [ 3 ] a s s t a r t i n g p o i n t a n d t o i m p l e m e n t
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14/142
C h a p t e r 2
S i n g l e - E v e n t C h a r a c t e r i s t i c s a n d
I n d i c e s
I n t h i s c h a p t e r m e t h o d s , s e l e c t e d f r o m d o c u m e n t s [ 1 ] a n d [ 2 ] , t h a t h a v e b e e n i m p l e m e n t e d
i n M a t l a b a n d a p p l i e d t o a l a r g e n u m b e r o f e v e n t s . T h e s t a r t i n g p o i n t i s a t i m e - d o m a i n
w a v e f o r m o f a t h r e e - p h a s e v o l t a g e s a m p l e d w i t h k n o w n f r e q u e n c y . F i r s t l y i t i s i m p o r -
t a n t t o c a l c u l a t e R M S v o l t a g e v e r s u s t i m e c h a r a c t e r i s t i c s , c a l c u l a t e r e t a i n e d v o l t a g e a n d
d u r a t i o n o f a v o l t a g e s a g . T h e s e c o n d s t e p i s t o c a l c u l a t e v o l t a g e - s a g e n e r g y i n d e x a n d
v o l t a g e - s a g s e v e r i t y .
2 . 1 E x a c t F r e q u e n c y E s t i m a t i o n
B e f o r e c a l c u l a t i n g s o m e o f t h e s i n g l e - e v e n t c h a r a c t e r i s t i c s , a c c u r a t e f r e q u e n c y o f t h e s i g n a l
i s n e e d e d . A c c o r d i n g t o [ 7 ] , t h i s i s o n l y p o s s i b l e w h e n a t l e a s t t w o c y c l e s o f p r e - e v e n t
w a v e f o r m d a t a a r e a v a i l a b l e . T h e r s t s t e p i s t o e s t i m a t e t h e l e n g t h o f o n e c y c l e o f t h e
p o w e r s y s t e m f r e q u e n c y . A n i n t e g e r n u m b e r o f s a m p l e s w i t h a d u r a t i o n a s c l o s e a s p o s s i b l e
t o 2 0 m s ( f o r a 50
- H z s y s t e m ) i s u s e d f o r t h i s . L e t t h e l e n g t h o f t h i s e s t i m a t i o n b e T
.
T h e i n i t i a l a n g l e 1 o f t h e f u n d a m e n t a l c o m p o n e n t i s d e t e r m i n e d o v e r t h e w i n d o w [0, T]
b y u s i n g a D F T a l g o r i t h m . T h e a n g l e o v e r t h e n e x t " p e r i o d " , [T, 2T]
i s2 . T h e s e c o n d
a n g l e i s o b t a i n e d b y i n c r e a s i n g t h e r s t a n g l e b y 2f T
w i t h f t h e a c t u a l f r e q u e n c y a n d
Tt h e e s t i m a t e d p e r i o d [ 7 ] . T h e a c t u a l f r e q u e n c y c a n b e o b t a i n e d f r o m t h e e x p r e s s i o n :
2 + 2 = 1 + 2f T ( 2 . 1 )
f r o m w h i c h t h e f o l l o w i n g e x p l i c i t e x p r e s s i o n f o r t h e a c t u a l f r e q u e n c y i s o b t a i n e d :
f =1
T
1 +
2 12
( 2 . 2 )
S o m e e v e n t s s t a r t w i t h a v o l t a g e s a g r e c o v e r i n g t o n o m i n a l p o s t - e v e n t v o l t a g e . I n
t h e s e c a s e s t h e p r e - e v e n t w a v e f o r m i s n o t a v a i l a b l e . T o g e t t h e a n g l e s 1 a n d 2 , t h e l a s t
t w o c y c l e s o f t h e p o s t - e v e n t v o l t a g e a r e c o n s i d e r e d i n s t e a d .
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2 . 2 R M S C a l c u l a t i o n 5
2 . 2 R M S C a l c u l a t i o n
T h e I E C p o w e r - q u a l i t y m e a s u r e m e n t s t a n d a r d I E C 6 1 0 0 0 - 4 - 3 0 [ 1 ] p r e s c r i b e s a v e r y p r e c i s e
m e t h o d f o r o b t a i n i n g t h e v o l t a g e m a g n i t u d e a s a f u n c t i o n o f t i m e . T h e r s t s t e p i n t h i s
p r o c e d u r e i s t o o b t a i n t h e r m s v o l t a g e o v e r a w i n d o w w i t h a l e n g t h e x a c t l y e q u a l t o o n e
c y c l e o f t h e p o w e r - f r e q u e n c y . T h e s t a n d a r d d o e s n o t p r e s c r i b e a m e t h o d t o o b t a i n t h e
w i n d o w l e n g t h , b u t i t d o e s s t a t e a n a c c u r a c y r e q u i r e m e n t [ 7 ] .
A c c o r d i n g t o [ 7 ] , t h e c a l c u l a t i o n o f t h i s " o n e - c y c l e r m s v o l t a g e " i s r e p e a t e d e v e r y h a l f
c y c l e ; i n o t h e r w o r d s : t h e w i n d o w i s s h i f t e d o n e h a l f c y c l e i n t i m e . T h i s r e s u l t s i n a
d i s c r e t e f u n c t i o n w i t h a t i m e s t e p e q u a l t o o n e h a l f c y c l e o f t h e p o w e r - s y s t e m f r e q u e n c y .
T h e o n e - c y c l e r m s v o l t a g e c a l c u l a t e d e v e r y h a l f - c y c l e i s o b t a i n e d b y ,
Urms(n) = 1N( n2 +1)N
k=1+nN
2
u(k)2
( 2 . 3 )
w h e r e N
i s n u m b e r o f s a m p l e s p e r c y c l e , u(k)
i s t h e s a m p l e d v o l t a g e w a v e f o r m a n d
k = 1, 2, 3, e t c . T h e r s t v a l u e i s o b t a i n e d o v e r t h e s a m p l e s ( 1 , N ) , t h e n e x t o v e r t h e
s a m p l e s ( 1
2N + 1, 1 1
2N)
, e t c [ 1 ] .
T h e o n e - c y c l e r m s v o l t a g e c a l c u l a t e d e v e r y s a m p l e i s o b t a i n e d b y ,
Urms(n) = 1
N
n
k=nN+1 u(k)2
( 2 . 4 )
w h e r e N
i s n u m b e r o f s a m p l e s p e r c y c l e , u(k)
i s t h e s a m p l e d v o l t a g e w a v e f o r m a n d
k = 1, 2, 3, e t c .
A c c o r d i n g t o [ 7 ] , i n s o m e c a s e s i t m a y b e m o r e a p p r o p r i a t e t o u s e a h a l f - c y c l e w i n d o w
t o c a l c u l a t e t h e r m s v o l t a g e . T h e m a i n a d v a n t a g e o f u s i n g a h a l f - c y c l e w i n d o w , c o m p a r e d
t o a o n e - c y c l e w i n d o w , i s a f a s t e r t r a n s i t i o n f r o m t h e p r e - f a u l t v o l t a g e t o t h e d u r i n g - f a u l t
v o l t a g e a n d f r o m t h e d u r i n g f a u l t v o l t a g e t o t h e p o s t - f a u l t v o l t a g e .
T h e h a l f - c y c l e r m s v o l t a g e c a l c u l a t e d e v e r y s a m p l e i s o b t a i n e d b y ,
Urms 12(n) = 1
N
nk=nN+1
u(k)2( 2 . 5 )
w h e r e N
i s n u m b e r o f s a m p l e s p e r h a l f - c y c l e , u(k)
i s t h e s a m p l e d v o l t a g e w a v e f o r m a n d
k = 1, 2, 3, e t c .
2 . 3 D u r a t i o n a n d R e t a i n e d V o l t a g e
A c c o r d i n g t o [ 7 ] v o l t a g e s a g s a r e d e s c r i b e d b y t w o m a i n i n d i c e s : d u r a t i o n a n d r e t a i n e d
v o l t a g e .
T h e d u r a t i o n o f a v o l t a g e s a g i s t h e a m o u n t o f t i m e d u r i n g w h i c h t h e v o l t a g e m a g n i t u d e
i s b e l o w t h e s a g t h r e s h o l d . T h e s a g t h r e s h o l d i s t y p i c a l l y c h o s e n a s 90%
o f t h e n o m i n a l
v o l t a g e m a g n i t u d e . I n a t h r e e p h a s e s y s t e m , t h e d u r a t i o n o f t h e v o l t a g e s a g i s t h e t i m e
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6 2 S i n g l e - E v e n t C h a r a c t e r i s t i c s a n d I n d i c e s
d u r i n g w h i c h a t l e a s t o n e o f t h e r m s v o l t a g e s i s b e l o w t h e t h r e s h o l d . T h e v o l t a g e s a g
s t a r t s w h e n a t l e a s t o n e o f t h e r m s v o l t a g e s d r o p s b e l o w t h e s a g - s t a r t i n g t h r e s h o l d . T h e
s a g e n d s w h e n a l l t h r e e r m s v o l t a g e s h a v e r e c o v e r e d a b o v e t h e s a g - e n d i n g t h r e s h o l d [ 7 ] .
2 3 4 5 6 7 8 9 10 11 120.8
0.85
0.9
0.95
1
1.05
threshold
duration
Time [cycles]
RMSVoltage[pu]
F i g u r e 2 . 1 : C a l c u l a t i o n o f d u r a t i o n o f t h e v o l t a g e s a g .
T h i s m e a n s t h a t t h e d u r a t i o n o f t h e v o l t a g e s a g i s t h e t i m e b e t w e e n t h e s t a r t o f
t h e v o l t a g e s a g a n d e n d o f t h e v o l t a g e s a g . D u r a t i o n c a n b e t h e n c a l c u l a t e d a s t h e
d i e r e n c e b e t w e e n t h e t i m e w h e n a l l t h r e e r m s v o l t a g e s h a v e r e c o v e r e d a b o v e t h e s a g -
e n d i n g t h r e s h o l d a n d t h e t i m e w h e n a t l e a s t o n e o f t h e r m s v o l t a g e s d r o p s b e l o w t h e
s a g - s t a r t i n g t h r e s h o l d . F i g u r e 2 . 1 i l l u s t r a t e s h o w t h e d u r a t i o n i s c a l c u l a t e d , w h e r e t h e
r m s v o l t a g e i s c a l c u l a t e d o v e r o n e h a l f - c y c l e a n d u p d a t e d e v e r y s a m p l e .
T h e r e t a i n e d v o l t a g e o f t h e v o l t a g e s a g i s t h e l o w e s t r m s v o l t a g e i n a n y o f t h e t h r e e
p h a s e s . T o b e a b l e t o r e p r e s e n t r e t a i n e d v o l t a g e i n p e r u n i t , i t i s i m p o r t a n t t o s a y t h a t
t h e r e f e r e n c e v o l t a g e i s c h o s e n a s t h e p r e - e v e n t v o l t a g e . T h e r e a s o n w h y p r e - e v e n t v o l t a g e
i s c h o s e n , i s t h a t t h e n o m i n a l v o l t a g e i s d i e r e n t f o r e v e r y l e t h a t i s a n a l y s e d .
2 . 3 . 1 I n t e r r u p t i o n
A c c o r d i n g t o I E C s t a n d a r d i n [ 1 ] , t h e i n t e r r u p t i o n s t a r t s w h e n a l l t h r e e r m s v o l t a g e s d r o p
b e l o w t h e t h r e s h o l d a n d e n d s w h e n a t l e a s t o n e o f t h e m r i s e s a b o v e t h e t h r e s h o l d . T h e
i n t e r r u p t i o n t h r e s h o l d i s t y p i c a l l y c h o s e n
10%o f t h e n o m i n a l v o l t a g e . T h e d u r a t i o n o f t h e
i n t e r r u p t i o n i s t h e t i m e d u r i n g w h i c h a l l t h e t h r e e r m s v o l t a g e s a r e b e l o w t h e i n t e r r u p t i o n
t h r e s h o l d . I f t h e v o l t a g e i s z e r o i n a l l t h r e e p h a s e s t h e e v e n t i s c l a s s i e d a s a v o l t a g e s a g
a n d a s a n i n t e r r u p t i o n .
2 . 3 . 2 S w e l l
A v o l t a g e s w e l l c a n b e c h a r a c t e r i z e d i n t h e s a m e w a y a s a v o l t a g e s a g . T h e d u r a t i o n o f a
s w e l l e q u a l s t h e a m o u n t o f t i m e t h e r m s v o l t a g e i s a b o v e t h e s w e l l t h r e s h o l d . T h e s w e l l
s t a r t s w h e n a t l e a s t o n e o f t h e r m s v o l t a g e s r i s e s a b o v e t h e s w e l l - s t a r t i n g t h r e s h o l d . T h e
s w e l l e n d s w h e n a l l t h r e e r m s v o l t a g e s h a v e r e c o v e r e d b e l o w t h e s w e l l - e n d i n g t h r e s h o l d .
T h e r e t a i n e d v o l t a g e i s t h e h i g h e s t v a l u e o f t h e r m s v o l t a g e s . T h e r e c o m m e n d e d v a l u e
f o r t h e s w e l l t h r e s h o l d i s 110%
o f t h e d e c l a r e d v o l t a g e o r o f t h e s l i d i n g - r e f e r e n c e v o l t a g e .
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2 . 4 V o l t a g e - S a g E n e r g y I n d e x 7
2 . 4 V o l t a g e - S a g E n e r g y I n d e x
A c c o r d i n g t o [ 2 ] , t h e v o l t a g e s a g e n e r g y Evs i s d e n e d a s :
Evs = T0
1 U(t)Unom
2dt( 2 . 6 )
w h e r e U(t)
i s t h e r m s v o l t a g e d u r i n g t h e e v e n t a n d Unom i s t h e n o m i n a l v o l t a g e . T h e
i n t e g r a t i o n i s t a k e n o v e r t h e d u r a t i o n o f t h e e v e n t , e . g . f o r a l l t h e v a l u e s o f t h e r m s v o l t a g e
b e l o w t h e t h r e s h o l d . T h e v o l t a g e - s a g e n e r g y h a s t h e u n i t o f t i m e .
S u b s t i t u t i n g E q . 2 . 5 i n E q . 2 . 6 , w e o b t a i n a n e x p r e s s i o n w i t h t h e h a l f - c y c l e r m s
v o l t a g e t h a t c a n b e i m p l e m e n t e d i n M a t l a b :
Evs =1
2fo
N
n=11 Urms 1
2(n)
Unom 2
( 2 . 7 ) w h e r e
fo i s t h e f r e q u e n c y a n d t h e s u m i s t a k e n o v e r t h e w h o l e d u r a t i o n o f t h e e v e n t , e . g .
f o r a l l v a l u e s o f t h e r m s v o l t a g e b e l o w t h e t h r e s h o l d .
I n c a s e o n l y r e t a i n e d v o l t a g e a n d d u r a t i o n o f a n e v e n t a r e a v a i l a b l e , t h e r m s v o l t a g e i s
a s s u m e d c o n s t a n t o v e r t h e d u r a t i o n o f t h e e v e n t . T h i s r e s u l t s i n t h e f o l l o w i n g e x p r e s s i o n
f o r t h e v o l t a g e s a g e n e r g y :
Evs =
1
U
Unom
2 T
( 2 . 8 )
w i t h T
t h e d u r a t i o n a n d U
t h e r e t a i n e d v o l t a g e o f t h e e v e n t .
T h e v o l t a g e - s a g e n e r g y i s t h e d u r a t i o n o f a n i n t e r r u p t i o n l e a d i n g t o t h e s a m e l o s s o f
e n e r g y f o r a n i m p e d a n c e l o a d a s t h e v o l t a g e s a g [ 2 ] .
F o r m u l t i - c h a n n e l e v e n t s ( e . g . t h r e e - p h a s e s y s t e m s ) t h e v o l t a g e - s a g e n e r g y i s d e n e d
a s t h e s u m o f t h e v o l t a g e - s a g e n e r g y i n t h e i n d i v i d u a l c h a n n e l s ( p h a s e s ) .
Evs = Evsa + Evsb + Evsc ( 2 . 9 )
V o l t a g e s w e l l e n e r g y c a n b e d e n e d a n a l o g o u s t o v o l t a g e - s a g e n e r g y a s f o l l o w s :
Evs = T0
U(t)Unom
2 1dt ( 2 . 1 0 ) w h e r e
U(t)i s t h e r m s v o l t a g e d u r i n g t h e e v e n t a n d
Unom i s t h e n o m i n a l v o l t a g e . T h e
i n t e g r a t i o n i s t a k e n o v e r t h e d u r a t i o n o f t h e s w e l l , i . e . f o r a l l v a l u e s o f t h e r m s v o l t a g e
t h a t e x c e e d t h e s w e l l t h r e s h o l d ( t y p i c a l l y 110%
) .
S u b s t i t u t i n g E q . 2 . 5 i n E q . 2 . 1 0 , w e o b t a i n a n e x p r e s s i o n w i t h t h e h a l f - c y c l e r m s
v o l t a g e
Evs =1
2fo
N
n=1Urms 12
(n)
Unom 2
1 ( 2 . 1 1 )
w h e r e fo i s t h e f r e q u e n c y a n d t h e s u m i s t a k e n o v e r t h e w h o l e d u r a t i o n o f t h e s w e l l , e . g .
f o r a l l v a l u e s o f t h e r m s v o l t a g e a b o v e t h e t h r e s h o l d [ 2 ] .
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8 2 S i n g l e - E v e n t C h a r a c t e r i s t i c s a n d I n d i c e s
2 . 5 V o l t a g e - S a g S e v e r i t y
T h e v o l t a g e s a g s e v e r i t y i s a c c o r d i n g t o [ 2 ] c a l c u l a t e d f r o m t h e r e t a i n e d v o l t a g e ( i n p u )
a n d t h e d u r a t i o n o f a v o l t a g e s a g i n c o m b i n a t i o n w i t h a r e f e r e n c e c u r v e :
Se =1 U
1 Ucurve(d) ( 2 . 1 2 )
w h e r e U
i s t h e r e t a i n e d v o l t a g e , d
i s t h e d u r a t i o n o f t h e e v e n t a n d Ucurve(d) i s t h e r e t a i n e d
v o l t a g e o f t h e r e f e r e n c e c u r v e f o r t h e s a m e d u r a t i o n . S E M I c u r v e , a s s h o w n i n F i g s . 2 . 2
a n d 2 . 3 , i s r e c o m m e n d e d a s t h e r e f e r e n c e . S E M I c u r v e c a n b e f o u n d i n S E M I s t a n d a r d
F - 4 7 a n d i n [ 2 1 ] . S E M I i s t h e S e m i c o n d u c t o r E q u i p m e n t a n d M a t e r i a l s I n t e r n a t i o n a l
G r o u p . C o n s t r u c t i o n o f C B E M A c u r v e c a n b e f o u n d i n [ 1 7 ] a n d [ 2 0 ] . M o r e i n f o r m a t i o n
c a n b e a l s o f o u n d a c c o r d i n g t o [ 2 ] i n t h e I E E E O r a n g e b o o k [ 1 4 ] .
F i g u r e 2 . 2 : O v e r l a y o f C B E M A a n d S E M I c u r v e s [ 2 1 ] .
F r o m F i g . 2 . 3 i t c a n b e o b s e r v e d , t h a t a s t h e d u r a t i o n o f t h e e v e n t g e t s l o n g e r a n d
t h e r e t a i n e d v o l t a g e l o w e r , t h e v o l t a g e - s a g s e v e r i t y i n d e x i n c r e a s e d . F o r a n e v e n t
o n t h e r e f e r e n c e c u r v e t h e v o l t a g e - s a g s e v e r i t y e q u a l s o n e ,
a b o v e t h e r e f e r e n c e c u r v e t h e v o l t a g e - s a g s e v e r i t y i s l e s s t h a n o n e ,
b e l o w t h e r e f e r e n c e c u r v e t h e v o l t a g e - s a g s e v e r i t y i s g r e a t e r t h a n o n e ,
w i t h r e t a i n e d v o l t a g e a b o v e t h e v o l t a g e - s a g t h r e s h o l d
(90%)t h e v o l t a g e - s a g s e v e r i t y
i s e q u a l t o z e r o .
U s i n g t h e S E M I c u r v e a s a r e f e r e n c e g i v e s t h e a l g o r i t h m f o r c a l c u l a t i n g t h e v o l t a g e - s a g
s e v e r i t y f r o m t h e r e t a i n e d v o l t a g e U
a n d t h e d u r a t i o n d
r e p o r t e d i n T a b l e 2 . 1 :
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2 . 6 T h r e e - p h a s e c l a s s i c a t i o n o f a v o l t a g e s a g 9
F i g u r e 2 . 3 : V o l t a g e - s a g s e v e r i t y w i t h r e f e r e n c e t o t h e S E M I c u r v e [ 2 ] .
Ucurve d , d u r a t i o n r a n g e Se , v o l t a g e - s a g s e v e r i t y c a l c u l a t i o n
0.0p u d
20m s
Se =(1U)
(10.0)= (1U)
1= 1 U
0.5p u
20m s
3 0 0 / 0 . 0 2 ) ;
9 3 V e c t D u r 2 = f i n d ( D u r < 0 . 5 ) ;
9 4 V e c t N o H C = f i n d ( D u r > 0 . 5 ) ;
9 5
9 6 D u r H C = D u r ( V e c t N o H C ) ;
9 7 R e t H C = R e t ( V e c t N o H C ) ;
9 8
9 9 H a l f C y c l e s = R e t ( V e c t D u r 2 ) ;
1 0 0 H c = l e n g t h ( f i n d ( H a l f C y c l e s < 0 . 9 ) ) ;
1 0 1 R e t _ l e n g t h = l e n g t h ( R e t ) ;
1 0 2
1 0 3 % 7 f i l e s a r e o n l y s w e l l s , n o t s a g s = > S a r f i 1 1 0 i s n o t e q u a l t o S a r f i 1 1 0 A + C + D = > t h e y d o n o t h a v e d i p t y p e d e f i n e d
1 0 4 [ S a r f i 1 1 0 , S a r f i 1 1 0 A , S a r f i 1 1 0 C , S a r f i 1 1 0 D ] = S a r f i X ( D u r _ S w e l l A l l , R e t _ S w e l l A l l , D i p T y p e S w e l l s , 1 . 1 ) ; % o n l y s w e l l s w i t h d u r g r e a t e r
1 0 5 [ S a r f i 9 0 , S a r f i 9 0 A , S a r f i 9 0 C , S a r f i 9 0 D ] = S a r f i X ( D u r , R e t , D i p T y p e , 0 . 9 ) ;
1 0 6[ S a r f i 7 0 , S a r f i 7 0 A , S a r f i 7 0 C , S a r f i 7 0 D ] = S a r f i X ( D u r , R e t , D i p T y p e , 0 . 7 ) ;
1 0 7 [ S a r f i 5 0 , S a r f i 5 0 A , S a r f i 5 0 C , S a r f i 5 0 D ] = S a r f i X ( D u r , R e t , D i p T y p e , 0 . 5 ) ;
1 0 8 [ S a r f i 1 0 , S a r f i 1 0 A , S a r f i 1 0 C , S a r f i 1 0 D ] = S a r f i X ( D u r , R e t , D i p T y p e , 0 . 1 ) ;
1 0 9
1 1 0 [ S a r f i _ I T I C , S a r f i _ S E M I ] = S a r f i C u r v e ( D u r _ S e c , R e t ) ;
1 1 1
1 1 2 [ S a r f i _ I T I C _ A N o P e r , S a r f i _ I T I C _ A , S a r f i _ S E M I _ A N o P e r , S a r f i _ S E M I _ A ] = S a r f i C u r v e T y p e ( D u r _ S e c , R e t , v e c t D i p T y p e A , S a r f i _ I T I C , S a r f i
1 1 3 [ S a r f i _ I T I C _ C N o P e r , S a r f i _ I T I C _ C , S a r f i _ S E M I _ C N o P e r , S a r f i _ S E M I _ C ] = S a r f i C u r v e T y p e ( D u r _ S e c , R e t , v e c t D i p T y p e C , S a r f i _ I T I C , S a r f i
1 1 4 [ S a r f i _ I T I C _ D N o P e r , S a r f i _ I T I C _ D , S a r f i _ S E M I _ D N o P e r , S a r f i _ S E M I _ D ] = S a r f i C u r v e T y p e ( D u r _ S e c , R e t , v e c t D i p T y p e D , S a r f i _ I T I C , S a r f i
1 1 5
1 1 6 S a r f i _ I T I C _ t e s t = S a r f i _ I T I C _ A N o P e r + S a r f i _ I T I C _ C N o P e r + S a r f i _ I T I C _ D N o P e r ;
1 1 7S a r f i _ S E M I _ t e s t = S a r f i _ S E M I _ A N o P e r + S a r f i _ S E M I _ C N o P e r + S a r f i _ S E M I _ D N o P e r ;
1 1 8
1 1 9 i f S a r f i _ I T I C _ t e s t = = S a r f i _ I T I C
1 2 0 d i s p ( ' c o r r e c t ' )
1 2 1e l s e
1 2 2 d i s p ( ' i n c o r r e c t ' )
1 2 3 e n d
1 2 4 i f S a r f i _ S E M I _ t e s t = = S a r f i _ S E M I
1 2 5d i s p ( ' c o r r e c t ' )
1 2 6 e l s e
1 2 7 d i s p ( ' i n c o r r e c t ' )
1 2 8 e n d
1 2 9
1 3 0 % % p e r c e n t a g e :
1 3 1 % S a r f i _ I T I C _ A p e r c e n t = ( S a r f i _ I T I C _ A / S a r f i _ I T I C ) * 1 0 0 ;
1 3 2 % S a r f i _ I T I C _ C p e r c e n t = ( S a r f i _ I T I C _ C / S a r f i _ I T I C ) * 1 0 0 ;
1 3 3 % S a r f i _ I T I C _ D p e r c e n t = ( S a r f i _ I T I C _ D / S a r f i _ I T I C ) * 1 0 0 ;
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7 4 A M a t l a b C o d e
1 3 4 %
1 3 5 % S a r f i _ I T I C _ A = [ n u m 2 s t r ( S a r f i _ I T I C _ A ) ' ( ' n u m 2 s t r ( r o u n d n ( S a r f i _ I T I C _ A p e r c e n t , - 1 ) ) ' % ) ' ] ;
1 3 6 % S a r f i _ I T I C _ C = [ n u m 2 s t r ( S a r f i _ I T I C _ C ) ' ( ' n u m 2 s t r ( r o u n d n ( S a r f i _ I T I C _ C p e r c e n t , - 1 ) ) ' % ) ' ] ;
1 3 7 % S a r f i _ I T I C _ D = [ n u m 2 s t r ( S a r f i _ I T I C _ D ) ' ( ' n u m 2 s t r ( r o u n d n ( S a r f i _ I T I C _ D p e r c e n t , - 1 ) ) ' % ) ' ] ;
1 3 8
1 3 9
1 4 0 c l e a r ( ' V e c t D u r 1 ' , ' V e c t D u r 2 ' , ' V e c t N o H C ' , ' S a r f i _ I T I C _ t e s t ' , ' S a r f i _ S E M I _ t e s t ' ) ;
1 4 1 c l e a r ( ' H a l f C y c l e s ' , ' H c ' , ' D i p T y p e S w e l l s ' ) ;
1 4 2
1 4 3 % = = = % S a r f i - X c a l c u l a t i o n ( S y m m . C o m p . m e t h o d ) : = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
1 4 4
1 4 5 v e c t D i p T y p e S _ A = s t r m a t c h ( ' A ' , D i p T y p e S ) ;
1 4 6 v e c t D i p T y p e S _ C = s t r m a t c h ( ' C ' , D i p T y p e S ) ;
1 4 7 v e c t D i p T y p e S _ D = s t r m a t c h ( ' D ' , D i p T y p e S ) ;
1 4 8
1 4 9 [ S a r f i S 1 1 0 , S a r f i S 1 1 0 A , S a r f i S 1 1 0 C , S a r f i S 1 1 0 D ] = S a r f i X ( D u r _ S w e l l A l l , R e t _ S w e l l A l l , D i p T y p e S S w e l l s , 1 . 1 ) ;
1 5 0 [ S a r f i S 9 0 , S a r f i S 9 0 A , S a r f i S 9 0 C , S a r f i S 9 0 D ] = S a r f i X ( D u r , R e t , D i p T y p e S , 0 . 9 ) ;
1 5 1 [ S a r f i S 7 0 , S a r f i S 7 0 A , S a r f i S 7 0 C , S a r f i S 7 0 D ] = S a r f i X ( D u r , R e t , D i p T y p e S , 0 . 7 ) ;
1 5 2[ S a r f i S 5 0 , S a r f i S 5 0 A , S a r f i S 5 0 C , S a r f i S 5 0 D ] = S a r f i X ( D u r , R e t , D i p T y p e S , 0 . 5 ) ;
1 5 3 [ S a r f i S 1 0 , S a r f i S 1 0 A , S a r f i S 1 0 C , S a r f i S 1 0 D ] = S a r f i X ( D u r , R e t , D i p T y p e S , 0 . 1 ) ;
1 5 4
1 5 5 [ S a r f i S _ I T I C _ A N o P e r , S a r f i S _ I T I C _ A , S a r f i S _ S E M I _ A N o P e r , S a r f i S _ S E M I _ A ] = S a r f i C u r v e T y p e ( D u r _ S e c , R e t , v e c t D i p T y p e S _ A , S a r f i _ I T I C
1 5 6[ S a r f i S _ I T I C _ C N o P e r , S a r f i S _ I T I C _ C , S a r f i S _ S E M I _ C N o P e r , S a r f i S _ S E M I _ C ] = S a r f i C u r v e T y p e ( D u r _ S e c , R e t , v e c t D i p T y p e S _ C , S a r f i _ I T I C
1 5 7 [ S a r f i S _ I T I C _ D N o P e r , S a r f i S _ I T I C _ D , S a r f i S _ S E M I _ D N o P e r , S a r f i S _ S E M I _ D ] = S a r f i C u r v e T y p e ( D u r _ S e c , R e t , v e c t D i p T y p e S _ D , S a r f i _ I T I C
1 5 8
1 5 9 S a r f i S _ I T I C _ t e s t = S a r f i S _ I T I C _ A N o P e r + S a r f i S _ I T I C _ C N o P e r + S a r f i S _ I T I C _ D N o P e r ;
1 6 0 S a r f i S _ S E M I _ t e s t = S a r f i S _ S E M I _ A N o P e r + S a r f i S _ S E M I _ C N o P e r + S a r f i S _ S E M I _ D N o P e r ;
1 6 1
1 6 2 i f S a r f i S _ I T I C _ t e s t = = S a r f i _ I T I C
1 6 3 d i s p ( ' c o r r e c t ' )
1 6 4 e l s e
1 6 5 d i s p ( ' i n c o r r e c t ' )
1 6 6 e n d
1 6 7 i f S a r f i S _ S E M I _ t e s t = = S a r f i _ S E M I
1 6 8 d i s p ( ' c o r r e c t ' )
1 6 9 e l s e
1 7 0 d i s p ( ' i n c o r r e c t ' )
1 7 1e n d
1 7 2
1 7 3 c l e a r ( ' v e c t D i p T y p e S _ A ' , ' v e c t D i p T y p e S _ C ' , ' v e c t D i p T y p e S _ D ' , ' S a r f i S _ I T I C _ t e s t ' , ' S a r f i S _ S E M I _ t e s t ' , ' D i p T y p e S S w e l l s ' ) ;
1 7 4
1 7 5% = = = = = = = % s a r f i t a b l e : % = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
1 7 6 S a r f i _ r o w 1 = { ' ' ' T o t a l n u m b e r o f e v e n t s ' ' S A R F I _ 1 1 0 * ' ' S A R F I _ 9 0 * * ' ' S A R F I _ 7 0 * * ' ' S A R F I _ 5 0 * * ' ' S A R F I _ 1 0 * * ' ' S A R F I _ I T I C ( C B E
1 7 7 S a r f i _ r o w 2 = { ' C o u n t o f e v e n t s ' n u m 2 s t r ( R e t _ l e n g t h ) n u m 2 s t r ( S a r f i 1 1 0 ) n u m 2 s t r ( S a r f i 9 0 ) n u m 2 s t r ( S a r f i 7 0 ) n u m 2 s t r ( S a r f i 5 0 ) n
1 7 8 S a r f i _ r o w 3 = { ' E v e n t s p e r 3 0 d a y s ' n u m 2 s t r ( R e t _ l e n g t h ) n u m 2 s t r ( S a r f i 1 1 0 ) n u m 2 s t r ( S a r f i 9 0 ) n u m 2 s t r ( S a r f i 7 0 ) n u m 2 s t r ( S a r f i 5 0
1 7 9S a r f i _ r o w 4 = { ' C o u n t o f e v e n t s f o r T y p e A ( S i x R M S m e t h o d ) ' n u m 2 s t r ( R e t _ l e n g t h ) n u m 2 s t r ( S a r f i 1 1 0 A ) n u m 2 s t r ( S a r f i 9 0 A ) n u m 2 s
1 8 0 S a r f i _ r o w 5 = { ' C o u n t o f e v e n t s f o r T y p e C ( S i x R M S m e t h o d ) ' n u m 2 s t r ( R e t _ l e n g t h ) n u m 2 s t r ( S a r f i 1 1 0 C ) n u m 2 s t r ( S a r f i 9 0 C ) n u m 2 s
1 8 1 S a r f i _ r o w 6 = { ' C o u n t o f e v e n t s f o r T y p e D ( S i x R M S m e t h o d ) ' n u m 2 s t r ( R e t _ l e n g t h ) n u m 2 s t r ( S a r f i 1 1 0 D ) n u m 2 s t r ( S a r f i 9 0 D ) n u m 2 s
1 8 2 S a r f i _ r o w 7 = { ' ' , ' ' , ' ' , ' ' , ' ' , ' ' , ' ' , ' ' , ' ' } ;
1 8 3 S a r f i _ r o w 8 = { ' C o u n t o f e v e n t s f o r T y p e A ( S y m m . C o m p . m e t h o d ) ' n u m 2 s t r ( R e t _ l e n g t h ) n u m 2 s t r ( S a r f i S 1 1 0 A ) n u m 2 s t r ( S a r f i S 9 0 A )
1 8 4 S a r f i _ r o w 9 = { ' C o u n t o f e v e n t s f o r T y p e C ( S y m m . C o m p . m e t h o d ) ' n u m 2 s t r ( R e t _ l e n g t h ) n u m 2 s t r ( S a r f i S 1 1 0 C ) n u m 2 s t r ( S a r f i S 9 0 C )
1 8 5 S a r f i _ r o w 1 0 = { ' C o u n t o f e v e n t s f o r T y p e D ( S y m m . C o m p . m e t h o d ) ' n u m 2 s t r ( R e t _ l e n g t h ) n u m 2 s t r ( S a r f i S 1 1 0 D ) n u m 2 s t r ( S a r f i S 9 0 D )
1 8 6 S a r f i _ r o w 1 1 = { ' * i n S a r f i _ 1 1 0 7 e v e n t s a r e o n l y s w e l l s = > D i p T y p e i s n o t d e f i n e d f o r t h e m ' , ' ' , ' ' , ' ' , ' ' , ' ' , ' ' , ' ' , ' ' } ;
1 8 7 S a r f i _ r o w 1 2 = { ' * * o n l y e v e n t s w i t h d u r a t i o n b e t w e e n 0 . 5 c y c l e a n d 5 m i n u t e s a r e t a k e n i n t o a c c o u n t ' , ' ' , ' ' , ' ' , ' ' , ' ' , ' ' , ' ' , '
1 8 8
1 8 9 S a r f i T a b l e = [ S a r f i _ r o w 1 ; S a r f i _ r o w 2 ; S a r f i _ r o w 3 ; S a r f i _ r o w 4 ; S a r f i _ r o w 5 ; S a r f i _ r o w 6 ;
1 9 0S a r f i _ r o w 7 ; S a r f i _ r o w 8 ; S a r f i _ r o w 9 ; S a r f i _ r o w 1 0 ; S a r f i _ r o w 1 1 ; S a r f i _ r o w 1 2 ] ;
1 9 1
1 9 2 s a v e ( ' R e s u l t s \ S t a t i s t i c P l o t s \ S a r f i T a b l e . m a t ' , ' S a r f i T a b l e ' ) ;
1 9 3
1 9 4% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
1 9 5
1 9 6 c l e a r ( ' R e t _ l e n g t h ' , ' S a r f i 1 1 0 ' , ' S a r f i 9 0 ' , ' S a r f i 7 0 ' , ' S a r f i 5 0 ' , ' S a r f i 1 0 ' , ' S a r f i _ I T I C ' , ' S a r f i _ S E M I ' ) ;
1 9 7 c l e a r ( ' S a r f i 1 1 0 A ' , ' S a r f i 9 0 A ' , ' S a r f i 7 0 A ' , ' S a r f i 5 0 A ' , ' S a r f i 1 0 A ' , ' S a r f i _ I T I C _ A ' , ' S a r f i _ S E M I _ A ' ) ;
1 9 8c l e a r ( ' S a r f i 1 1 0 C ' , ' S a r f i 9 0 C ' , ' S a r f i 7 0 C ' , ' S a r f i 5 0 C ' , ' S a r f i 1 0 C ' , ' S a r f i _ I T I C _ C ' , ' S a r f i _ S E M I _ C ' ) ;
1 9 9 c l e a r ( ' S a r f i 1 1 0 D ' , ' S a r f i 9 0 D ' , ' S a r f i 7 0 D ' , ' S a r f i 5 0 D ' , ' S a r f i 1 0 D ' , ' S a r f i _ I T I C _ D ' , ' S a r f i _ S E M I _ D ' ) ;
2 0 0 c l e a r ( ' S a r f i S 1 1 0 ' , ' S a r f i S 9 0 ' , ' S a r f i S 7 0 ' , ' S a r f i S 5 0 ' , ' S a r f i S 1 0 ' , ' S a r f i S _ I T I C ' , ' S a r f i S _ S E M I ' ) ;
2 0 1 c l e a r ( ' S a r f i S 1 1 0 A ' , ' S a r f i S 9 0 A ' , ' S a r f i S 7 0 A ' , ' S a r f i S 5 0 A ' , ' S a r f i S 1 0 A ' , ' S a r f i S _ I T I C _ A ' , ' S a r f i S _ S E M I _ A ' ) ;
2 0 2c l e a r ( ' S a r f i S 1 1 0 C ' , ' S a r f i S 9 0 C ' , ' S a r f i S 7 0 C ' , ' S a r f i S 5 0 C ' , ' S a r f i S 1 0 C ' , ' S a r f i S _ I T I C _ C ' , ' S a r f i S _ S E M I _ C ' ) ;
2 0 3 c l e a r ( ' S a r f i S 1 1 0 D ' , ' S a r f i S 9 0 D ' , ' S a r f i S 7 0 D ' , ' S a r f i S 5 0 D ' , ' S a r f i S 1 0 D ' , ' S a r f i S _ I T I C _ D ' , ' S a r f i S _ S E M I _ D ' ) ;
2 0 4 c l e a r ( ' S a r f i _ I T I C _ A N o P e r ' , ' S a r f i _ S E M I _ A N o P e r ' , ' S a r f i _ I T I C _ C N o P e r ' , ' S a r f i _ S E M I _ C N o P e r ' ) ;
2 0 5 c l e a r ( ' S a r f i _ I T I C _ D N o P e r ' , ' S a r f i _ S E M I _ D N o P e r ' ) ;
2 0 6 c l e a r ( ' S a r f i S _ I T I C _ A N o P e r ' , ' S a r f i S _ S E M I _ A N o P e r ' , ' S a r f i S _ I T I C _ C N o P e r ' , ' S a r f i S _ S E M I _ C N o P e r ' ) ;
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A . 3 S i t e I n d i c e s a n d F i g u r e s 7 5
2 0 7 c l e a r ( ' S a r f i S _ I T I C _ D N o P e r ' , ' S a r f i S _ S E M I _ D N o P e r ' ) ;
2 0 8
2 0 9 c l e a r ( ' S a r f i _ r o w 1 ' , ' S a r f i _ r o w 2 ' , ' S a r f i _ r o w 3 ' , ' S a r f i _ r o w 4 ' , ' S a r f i _ r o w 5 ' , ' S a r f i _ r o w 6 ' )
2 1 0 c l e a r ( ' S a r f i _ r o w 7 ' , ' S a r f i _ r o w 8 ' , ' S a r f i _ r o w 9 ' , ' S a r f i _ r o w 1 0 ' , ' S a r f i _ r o w 1 1 ' , ' S a r f i _ r o w 1 2 ' ) ;
2 1 1
2 1 2 % = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
2 1 3 % = = = = % T a b l e o f m o s t c o m m o n v a l u e s o f d u r a t i o n a n d r e t a i n e d v o l t a g e f o r d i f f e r e n t d i p t y p e s % = = = = = = %
2 1 4
2 1 5 D u r T y p e A = D u r _ S e c ( v e c t D i p T y p e A ) ;
2 1 6 D u r T y p e C = D u r _ S e c ( v e c t D i p T y p e C ) ;
2 1 7 D u r T y p e D = D u r _ S e c ( v e c t D i p T y p e D ) ;
2 1 8
2 1 9 R e t T y p e A = R e t ( v e c t D i p T y p e A ) ;
2 2 0 R e t T y p e C = R e t ( v e c t D i p T y p e C ) ;
2 2 1R e t T y p e D = R e t ( v e c t D i p T y p e D ) ;
2 2 2
2 2 3 c l e a r ( ' v e c t D i p T y p e A ' , ' v e c t D i p T y p e C ' , ' v e c t D i p T y p e D ' ) ;
2 2 4
2 2 5% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = %
2 2 6 % c a l c u l a t i o n o f p r o b a b i l i t y m a t c h i n g o f D i p T y p e c a l c u l a t e d b y b o t h m e t h o d s
2 2 7 m a t c h i n g _ p r o b a b i l i t y = ( l e n g t h ( m a t c h _ n o n 0 ) . / ( j + 1 ) ) . * 1 0 0 ;
2 2 8 d i s p ( [ [ ' m a t c h i n g _ p r o b a b i l i t y = ' n u m 2 s t r ( m a t c h i n g _ p r o b a b i l i t y ) ] ' % ' ] )
2 2 9
2 3 0 c l e a r ( ' m a t c h i n g _ p r o b a b i l i t y ' , ' m a t c h _ n o n 0 ' )
2 3 1
2 3 2 % % = = = = = = = = = = = = = = = = = f i n d i n g i f V < F : = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
2 3 3 % v e c t 1 = f i n d ( V > F ) ;
2 3 4 %
2 3 5 % v e c t 2 = f i n d ( V _ s > F _ s ) ;
2 3 6 % l e n g t h ( v e c t 2 ) ;
2 3 7 %
2 3 8 % v e c t 3 = f i n d ( F _ s - V _ s < - 0 . 0 0 5 ) ;
2 3 9 % l e n g t h ( v e c t 3 ) ;
2 4 0 %
2 4 1 % N = l e n g t h ( v e c t 2 ) - l e n g t h ( v e c t 3 ) ;
2 4 2 %
2 4 3 % f o r n = N + 1 : l e n g t h ( v e c t 2 )
2 4 4% V e c t 3 ( n ) = v e c t 3 ( n - N ) ;
2 4 5 % e n d
2 4 6 % V e c t 3 ( 1 : N ) = 1 ;
2 4 7 %
2 4 8% % t o m a k e t h e t i m e v e c t o r s a m e d i m e n s i o n % ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !
2 4 9 % f o r g = 1 : l e n g t h ( V e c t 3 )
2 5 0 % V e c t o r 3 ( g , 1 ) = V e c t 3 ( 1 , g ) ;
2 5 1 % e n d
2 5 2%
2 5 3 % F i l e _ o f _ V e c t 2 = F i l e ( v e c t 2 ) ;
2 5 4 % F i l e _ o f _ V e c t 3 = F i l e ( V e c t o r 3 ) ;
2 5 5 %
2 5 6 % F i l e _ a l l = [ F i l e _ o f _ V e c t 2 , F i l e _ o f _ V e c t 3 ] ;
2 5 7 % = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
2 5 8
2 5 9 % p l o t t i n g f i g u r e s
2 6 0
2 6 1 f i g u r e ( 1 )
2 6 2 % a x e s ( ' Y S c a l e ' , ' l o g ' ) ,
2 6 3s e m i l o g x ( D u r , R e t , ' k * ' ) , g r i d o n , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , x l a b e l ( ' D u r a t i o n [ c y c l e s ] ' ) , y l a b e l ( ' R e t a i n e d v o l t a g e [ p u ] ' ) , y l i m (
2 6 4 , x l i m ( [ 0 7 5 0 ] ) ,
2 6 5 t i t l e ( ' R e t a i n e d v o l t a g e v s . d u r a t i o n ' ) ,
2 6 6 % s e t ( g c a , ' Y S c a l e ' , ' l o g ' )
2 6 7l i n e ( [ 1 1 ] , [ 0 0 . 5 ] ) , l i n e ( [ 1 1 0 ] , [ 0 . 5 0 . 5 ] ) ,
2 6 8 l i n e ( [ 1 0 1 0 ] , [ 0 . 5 0 . 7 ] ) , l i n e ( [ 1 0 2 5 ] , [ 0 . 7 0 . 7 ] ) ,
2 6 9 l i n e ( [ 2 5 2 5 ] , [ 0 . 7 0 . 8 ] ) , l i n e ( [ 2 5 5 0 0 ] , [ 0 . 8 0 . 8 ] ) ,
2 7 0 l i n e ( [ 5 0 0 5 0 0 ] , [ 0 . 8 0 . 9 ] ) , l i n e ( [ 5 0 0 1 0 0 0 ] , [ 0 . 9 0 . 9 ] ) ;
2 7 1
2 7 2 % p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 0 1 _ R e t D u r C y c . e p s ;
2 7 3
2 7 4 f i g u r e ( 2 )
2 7 5s e m i l o g x ( D u r _ S e c , R e t , ' k * ' ) , g r i d o n , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , y l i m ( [ 0 1 ] ) , x l i m ( [ 0 7 5 0 * 0 . 0 2 ] ) ,
2 7 6 x l a b e l ( ' D u r a t i o n [ s e c o n d s ] ' ) , y l a b e l ( ' R e t a i n e d v o l t a g e [ p u ] ' ) ,
2 7 7 t i t l e ( ' R e t a i n e d v o l t a g e v s . d u r a t i o n ' ) ,
2 7 8 l i n e ( [ 0 . 0 2 0 . 0 2 ] , [ 0 0 . 5 ] ) , l i n e ( [ 0 . 0 2 0 . 2 ] , [ 0 . 5 0 . 5 ] ) ,
2 7 9 l i n e ( [ 0 . 2 0 . 2 ] , [ 0 . 5 0 . 7 ] ) , l i n e ( [ 0 . 2 0 . 5 ] , [ 0 . 7 0 . 7 ] ) ,
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7 6 A M a t l a b C o d e
2 8 0 l i n e ( [ 0 . 5 0 . 5 ] , [ 0 . 7 0 . 8 ] ) , l i n e ( [ 0 . 5 1 0 ] , [ 0 . 8 0 . 8 ] ) ,
2 8 1 l i n e ( [ 1 0 1 0 ] , [ 0 . 8 0 . 9 ] ) , l i n e ( [ 1 0 2 0 ] , [ 0 . 9 0 . 9 ] ) ;
2 8 2
2 8 3 % p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 0 2 _ R e t D u r S e c . e p s ;
2 8 4
2 8 5 C o r e l a t i o n = c o r r c o e f ( D u r , R e t ) ;
2 8 6
2 8 7 f i g u r e ( 3 )
2 8 8 c d f p l o t ( ( D u r ) ) , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , t i t l e ( ' P r o b a b i l i t y d i s t r i b u t i o n o f D u r a t i o n ' ) , x l a b e l ( ' D u r a t i o n [ c y c l e s ] ' ) ;
2 8 9
2 9 0 % p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 0 3 _ D u r P r o b . e p s ;
2 9 1
2 9 2 f i g u r e ( 4 )
2 9 3 n o r m p l o t ( ( R e t ) ) , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , t i t l e ( ' P r o b a b i l i t y d i s t r i b u t i o n o f R e t a i n e d v o l t a g e ' ) , x l a b e l ( ' R e t a i n e d v o l t a g e [ p u ] '
2 9 4
2 9 5 % p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 0 4 _ R e t P r o b . e p s ;
2 9 6
2 9 7 f i g u r e ( 5 )
2 9 8p l o t ( E v s _ D u r R e t , E v s , ' r * ' ) , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , t i t l e ( ' V o l t a g e S a g E n e r g y I n d e x R e s u l t s [ c y c l e s ] ' ) ,
2 9 9 x l a b e l ( ' V o l t a g e S a g E n e r g y I n d e x c a l c . f r o m D u r & R e t ' ) ,
3 0 0 y l a b e l ( ' V o l t a g e S a g E n e r g y I n d e x c a l c . f r o m I n t e g r a l ' ) , g r i d o n
3 0 1
3 0 2% p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 0 5 a _ E v s . e p s
3 0 3
3 0 4 f i g u r e ( 1 9 )
3 0 5 s e m i l o g x ( R e t , E v s _ D u r R e t , ' b X ' , R e t , E v s , ' g + ' ) , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) ,
3 0 6 x l i m ( [ 0 1 ] ) , t i t l e ( ' V o l t a g e S a g E n e r g y I n d e x R e s u l t s [ c y c l e s ] ' ) , x l a b e l ( ' R e t a i n e d v o l t a g e [ p u ] ' ) ,
3 0 7 y l a b e l ( ' V o l t a g e S a g E n e r g y I n d e x ' ) , l e g e n d ( ' E v s _ { D u r R e t } ' , ' E v s _ { i n t e g r a l } ' ) , g r i d o n
3 0 8
3 0 9 % p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 0 5 b _ R e t E v s . e p s
3 1 0
3 1 1 f i g u r e ( 6 )
3 1 2 s e m i l o g x ( E v s , S e , ' * ' ) , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) ,
3 1 3 t i t l e ( ' V o l t a g e - S a g S e v e r i t y v s . V o l t a g e - s a g E n e r g y I n d e x ' ) , x l a b e l ( ' V o l t a g e - s a g E n e r g y I n d e x [ c y c l e s ] ' ) ,
3 1 4 y l a b e l ( ' V o l t a g e - S a g S e v e r i t y [ p u ] ' ) , g r i d o n ;
3 1 5
3 1 6 % p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 0 6 _ E v s V S _ S e . e p s
3 1 7
3 1 8 f i g u r e ( 7 )
3 1 9 s e m i l o g x ( D u r H C , R e t H C , ' k * ' ) , g r i d o n , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , y l i m ( [ 0 1 ] ) , x l i m ( [ 0 7 5 0 ] ) ,
3 2 0 x l a b e l ( ' D u r a t i o n [ c y c l e s ] ' ) , y l a b e l ( ' R e t a i n e d v o l t a g e [ p u ] ' ) ,
3 2 1t i t l e ( ' R e t a i n e d v o l t a g e v s . d u r a t i o n f o r a l l s a g s w i t h d u r a t i o n > 1 0 m s ( S E M I c u r v e ) ' ) ,
3 2 2 l i n e ( [ 1 1 ] , [ 0 0 . 5 ] ) , l i n e ( [ 1 1 0 ] , [ 0 . 5 0 . 5 ] ) ,
3 2 3 l i n e ( [ 1 0 1 0 ] , [ 0 . 5 0 . 7 ] ) , l i n e ( [ 1 0 2 5 ] , [ 0 . 7 0 . 7 ] ) ,
3 2 4 l i n e ( [ 2 5 2 5 ] , [ 0 . 7 0 . 8 ] ) , l i n e ( [ 2 5 5 0 0 ] , [ 0 . 8 0 . 8 ] ) ,
3 2 5l i n e ( [ 5 0 0 5 0 0 ] , [ 0 . 8 0 . 9 ] ) , l i n e ( [ 5 0 0 1 0 0 0 ] , [ 0 . 9 0 . 9 ] ) ;
3 2 6
3 2 7 % p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 0 7 _ R e t D u r C y c N o H C . e p s
3 2 8
3 2 9 f i g u r e ( 8 )
3 3 0 s e m i l o g x ( D u r T y p e A , R e t T y p e A , ' k * ' ) , g r i d o n , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) ,
3 3 1 y l i m ( [ 0 1 ] ) , x l i m ( [ 1 0 ^ - 3 7 5 0 * 0 . 0 2 ] ) , x l a b e l ( ' D u r a t i o n [ s e c o n d s ] ' ) , y l a b e l ( ' R e t a i n e d v o l t a g e [ p u ] ' ) ,
3 3 2 t i t l e ( ' R e t a i n e d v o l t a g e v s . d u r a t i o n f o r D i p t y p e A ( S E M I c u r v e r e f e r e n c e ) ' ) ,
3 3 3 l i n e ( [ 0 . 0 2 0 . 0 2 ] , [ 0 0 . 5 ] ) , l i n e ( [ 0 . 0 2 0 . 2 ] , [ 0 . 5 0 . 5 ] ) ,
3 3 4 l i n e ( [ 0 . 2 0 . 2 ] , [ 0 . 5 0 . 7 ] ) , l i n e ( [ 0 . 2 0 . 5 ] , [ 0 . 7 0 . 7 ] ) ,
3 3 5 l i n e ( [ 0 . 5 0 . 5 ] , [ 0 . 7 0 . 8 ] ) , l i n e ( [ 0 . 5 1 0 ] , [ 0 . 8 0 . 8 ] ) ,
3 3 6l i n e ( [ 1 0 1 0 ] , [ 0 . 8 0 . 9 ] ) , l i n e ( [ 1 0 2 0 ] , [ 0 . 9 0 . 9 ] ) ;
3 3 7
3 3 8 % p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 0 8 _ R e t D u r A _ S E M I . e p s
3 3 9
3 4 0f i g u r e ( 9 )
3 4 1 s e m i l o g x ( D u r T y p e C , R e t T y p e C , ' k * ' ) , g r i d o n , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) ,
3 4 2 y l i m ( [ 0 1 ] ) , x l i m ( [ 0 7 5 0 * 0 . 0 2 ] ) , x l a b e l ( ' D u r a t i o n [ s e c o n d s ] ' ) , y l a b e l ( ' R e t a i n e d v o l t a g e [ p u ] ' ) ,
3 4 3 t i t l e ( ' R e t a i n e d v o l t a g e v s . d u r a t i o n f o r D i p t y p e C ( S E M I c u r v e r e f e r e n c e ) ' ) ,
3 4 4l i n e ( [ 0 . 0 2 0 . 0 2 ] , [ 0 0 . 5 ] ) , l i n e ( [ 0 . 0 2 0 . 2 ] , [ 0 . 5 0 . 5 ] ) ,
3 4 5 l i n e ( [ 0 . 2 0 . 2 ] , [ 0 . 5 0 . 7 ] ) , l i n e ( [ 0 . 2 0 . 5 ] , [ 0 . 7 0 . 7 ] ) ,
3 4 6 l i n e ( [ 0 . 5 0 . 5 ] , [ 0 . 7 0 . 8 ] ) , l i n e ( [ 0 . 5 1 0 ] , [ 0 . 8 0 . 8 ] ) ,
3 4 7 l i n e ( [ 1 0 1 0 ] , [ 0 . 8 0 . 9 ] ) , l i n e ( [ 1 0 2 0 ] , [ 0 . 9 0 . 9 ] ) ;
3 4 8
3 4 9 % p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 0 9 _ R e t D u r C _ S E M I . e p s
3 5 0
3 5 1
3 5 2 f i g u r e ( 1 0 )
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3 5 3 s e m i l o g x ( D u r T y p e D , R e t T y p e D , ' k * ' ) , g r i d o n , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) ,
3 5 4 y l i m ( [ 0 1 ] ) , x l i m ( [ 0 7 5 0 * 0 . 0 2 ] ) , x l a b e l ( ' D u r a t i o n [ s e c o n d s ] ' ) , y l a b e l ( ' R e t a i n e d v o l t a g e [ p u ] ' ) ,
3 5 5 t i t l e ( ' R e t a i n e d v o l t a g e v s . d u r a t i o n f o r D i p t y p e D ( S E M I c u r v e r e f e r e n c e ) ' ) ,
3 5 6 l i n e ( [ 0 . 0 2 0 . 0 2 ] , [ 0 0 . 5 ] ) , l i n e ( [ 0 . 0 2 0 . 2 ] , [ 0 . 5 0 . 5 ] ) ,
3 5 7 l i n e ( [ 0 . 2 0 . 2 ] , [ 0 . 5 0 . 7 ] ) , l i n e ( [ 0 . 2 0 . 5 ] , [ 0 . 7 0 . 7 ] ) ,
3 5 8 l i n e ( [ 0 . 5 0 . 5 ] , [ 0 . 7 0 . 8 ] ) , l i n e ( [ 0 . 5 1 0 ] , [ 0 . 8 0 . 8 ] ) ,
3 5 9 l i n e ( [ 1 0 1 0 ] , [ 0 . 8 0 . 9 ] ) , l i n e ( [ 1 0 2 0 ] , [ 0 . 9 0 . 9 ] ) ;
3 6 0
3 6 1 % p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 1 0 _ R e t D u r D _ S E M I . e p s
3 6 2
3 6 3 f i g u r e ( 1 1 )
3 6 4 s e m i l o g x ( D u r T y p e A , R e t T y p e A , ' k * ' ) , g r i d o n , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) ,
3 6 5 y l i m ( [ 0 1 ] ) , x l i m ( [ 1 0 ^ - 3 7 5 0 * 0 . 0 2 ] ) , x l a b e l ( ' D u r a t i o n [ s e c o n d s ] ' ) , y l a b e l ( ' R e t a i n e d v o l t a g e [ p u ] ' ) ,
3 6 6 t i t l e ( ' R e t a i n e d v o l t a g e v s . d u r a t i o n f o r D i p t y p e A ( I T I C c u r v e r e f e r e n c e ) ' ) ,
3 6 7l i n e ( [ 0 . 0 2 0 . 0 2 ] , [ 0 0 . 7 ] ) , l i n e ( [ 0 . 0 2 0 . 5 ] , [ 0 . 7 0 . 7 ] ) ,
3 6 8 l i n e ( [ 0 . 5 0 . 5 ] , [ 0 . 7 0 . 8 ] ) , l i n e ( [ 0 . 5 1 0 ] , [ 0 . 8 0 . 8 ] ) ,
3 6 9 l i n e ( [ 1 0 1 0 ] , [ 0 . 8 0 . 9 ] ) , l i n e ( [ 1 0 2 0 ] , [ 0 . 9 0 . 9 ] ) ;
3 7 0
3 7 1% p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 1 1 _ R e t D u r A _ I T I C . e p s
3 7 2
3 7 3
3 7 4 f i g u r e ( 1 2 )
3 7 5s e m i l o g x ( D u r T y p e C , R e t T y p e C , ' k * ' ) , g r i d o n , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , y l i m ( [ 0 1 ] ) , x l i m ( [ 0 7 5 0 * 0 . 0 2 ] ) ,
3 7 6 x l a b e l ( ' D u r a t i o n [ s e c o n d s ] ' ) , y l a b e l ( ' R e t a i n e d v o l t a g e [ p u ] ' ) ,
3 7 7 t i t l e ( ' R e t a i n e d v o l t a g e v s . d u r a t i o n f o r D i p t y p e C ( I T I C c u r v e r e f e r e n c e ) ' ) ,
3 7 8 l i n e ( [ 0 . 0 2 0 . 0 2 ] , [ 0 0 . 7 ] ) , l i n e ( [ 0 . 0 2 0 . 5 ] , [ 0 . 7 0 . 7 ] ) ,
3 7 9 l i n e ( [ 0 . 5 0 . 5 ] , [ 0 . 7 0 . 8 ] ) , l i n e ( [ 0 . 5 1 0 ] , [ 0 . 8 0 . 8 ] ) ,
3 8 0 l i n e ( [ 1 0 1 0 ] , [ 0 . 8 0 . 9 ] ) , l i n e ( [ 1 0 2 0 ] , [ 0 . 9 0 . 9 ] ) ;
3 8 1
3 8 2 % p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 1 2 _ R e t D u r C _ I T I C . e p s
3 8 3
3 8 4 f i g u r e ( 1 3 )
3 8 5 s e m i l o g x ( D u r T y p e D , R e t T y p e D , ' k * ' ) , g r i d o n , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , y l i m ( [ 0 1 ] ) ,
3 8 6 x l i m ( [ 0 7 5 0 * 0 . 0 2 ] ) , x l a b e l ( ' D u r a t i o n [ s e c o n d s ] ' ) , y l a b e l ( ' R e t a i n e d v o l t a g e [ p u ] ' ) ,
3 8 7 t i t l e ( ' R e t a i n e d v o l t a g e v s . d u r a t i o n f o r D i p t y p e D ( I T I C c u r v e r e f e r e n c e ) ' ) ,
3 8 8 l i n e ( [ 0 . 0 2 0 . 0 2 ] , [ 0 0 . 7 ] ) , l i n e ( [ 0 . 0 2 0 . 5 ] , [ 0 . 7 0 . 7 ] ) ,
3 8 9 l i n e ( [ 0 . 5 0 . 5 ] , [ 0 . 7 0 . 8 ] ) , l i n e ( [ 0 . 5 1 0 ] , [ 0 . 8 0 . 8 ] ) ,
3 9 0l i n e ( [ 1 0 1 0 ] , [ 0 . 8 0 . 9 ] ) , l i n e ( [ 1 0 2 0 ] , [ 0 . 9 0 . 9 ] ) ;
3 9 1
3 9 2 % p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 1 3 _ R e t D u r D _ I T I C . e p s
3 9 3
3 9 4
3 9 5 f i g u r e ( 1 4 )
3 9 6 s e m i l o g x ( D u r _ S w e l l , R e t _ S w e l l , ' k * ' , D u r _ S w e l l S a g s , R e t _ S w e l l S a g s , ' r * ' ) , g r i d o n , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , x l i m ( [ 0 7 5 0 * 0 . 0 2 ] ) ,
3 9 7 x l a b e l ( ' D u r a t i o n [ s e c o n d s ] ' ) , y l a b e l ( ' R e t a i n e d v o l t a g e [ p u ] ' ) , l e g e n d ( ' S w e l l s ' , ' S a g s ' )
3 9 8t i t l e ( ' R e t a i n e d v o l t a g e v s . d u r a t i o n o f S w e l l s & S a g s ( I T I C c u r v e r e f e r e n c e ) ' ) ,
3 9 9 % f = g n a m e ( ' c a s e s ' ) ;
4 0 0 % s e t ( f , ' F o n t s i z e ' , 1 7 ) ;
4 0 1
4 0 2 % f o r q = 1 6 : 2 0
4 0 3 % t e x t ( D u r _ S w e l l ( q ) + 0 . 0 0 1 , R e t _ S w e l l ( q ) , n u m 2 s t r ( q - 1 5 ) , ' F o n t s i z e ' , 1 8 )
4 0 4 % t e x t ( D u r _ S w e l l S a g s ( q ) + 0 . 0 0 5 , R e t _ S w e l l S a g s ( q ) , n u m 2 s t r ( q - 1 5 ) , ' C o l o r ' , ' r ' , ' F o n t s i z e ' , 1 8 )
4 0 5 % e n d
4 0 6 % s a g r e f e r e n c e :
4 0 7 l i n e ( [ 0 . 0 2 0 . 0 2 ] , [ 0 0 . 7 ] ) , l i n e ( [ 0 . 0 2 0 . 5 ] , [ 0 . 7 0 . 7 ] ) ,
4 0 8 l i n e ( [ 0 . 5 0 . 5 ] , [ 0 . 7 0 . 8 ] ) , l i n e ( [ 0 . 5 1 0 ] , [ 0 . 8 0 . 8 ] ) ,
4 0 9l i n e ( [ 1 0 1 0 ] , [ 0 . 8 0 . 9 ] ) , l i n e ( [ 1 0 2 0 ] , [ 0 . 9 0 . 9 ] ) ;
4 1 0 % s w e l l r e f e r e n c e :
4 1 1 l i n e ( [ 0 . 0 0 3 0 . 0 0 3 ] , [ 1 . 4 1 . 2 ] ) , l i n e ( [ 0 . 0 0 3 0 . 5 ] , [ 1 . 2 1 . 2 ] ) ,
4 1 2 l i n e ( [ 0 . 5 0 . 5 ] , [ 1 . 2 1 . 1 ] ) , l i n e ( [ 0 . 5 2 0 ] , [ 1 . 1 1 . 1 ] ) ;
4 1 3
4 1 4 % p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 1 4 _ R e t D u r S w e l l s . e p s
4 1 5
4 1 6 % f i g u r e ( 2 0 )
4 1 7% s e m i l o g x ( D u r _ S w e l l A l l , R e t _ S w e l l A l l , ' k * ' , D u r _ S w e l l S a g s , R e t _ S w e l l S a g s , ' r * ' ) , g r i d o n , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , x l i m ( [ 0 7 5 0 * 0 .
4 1 8 % x l a b e l ( ' D u r a t i o n [ s e c o n d s ] ' ) , y l a b e l ( ' R e t a i n e d v o l t a g e [ p u ] ' ) , l e g e n d ( ' S w e l l s ' , ' S a g s ' )
4 1 9 % t i t l e ( ' R e t a i n e d v o l t a g e v s . d u r a t i o n o f S w e l l s & S a g s ( I T I C c u r v e r e f e r e n c e ) ' ) ,
4 2 0 % % s a g r e f e r e n c e :
4 2 1% l i n e ( [ 0 . 0 2 0 . 0 2 ] , [ 0 0 . 7 ] ) , l i n e ( [ 0 . 0 2 0 . 5 ] , [ 0 . 7 0 . 7 ] ) ,
4 2 2 % l i n e ( [ 0 . 5 0 . 5 ] , [ 0 . 7 0 . 8 ] ) , l i n e ( [ 0 . 5 1 0 ] , [ 0 . 8 0 . 8 ] ) ,
4 2 3 % l i n e ( [ 1 0 1 0 ] , [ 0 . 8 0 . 9 ] ) , l i n e ( [ 1 0 2 0 ] , [ 0 . 9 0 . 9 ] ) ;
4 2 4 % % s w e l l r e f e r e n c e :
4 2 5 % l i n e ( [ 0 . 0 0 3 0 . 0 0 3 ] , [ 1 . 4 1 . 2 ] ) , l i n e ( [ 0 . 0 0 3 0 . 5 ] , [ 1 . 2 1 . 2 ] ) ,
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4 9 9 l i n e ( [ 1 0 1 0 ] , [ 0 . 8 0 . 9 ] ) , l i n e ( [ 1 0 2 0 ] , [ 0 . 9 0 . 9 ] ) ;
5 0 0 s e t ( g c f , ' C u r r e n t A x e s ' , A X ( 2 ) )
5 0 1 s e t ( g c a , ' Y D i r ' , ' r e v e r s e ' ) , y l i m ( [ 0 5 ] )
5 0 2
5 0 3 % p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 1 8 _ D u r S e c S e . e p s ;
5 0 4
5 0 5 c l e a r ( ' A X ' , ' H 1 ' , ' H 2 ' ) ;
5 0 6
5 0 7 f i g u r e ( 2 1 )
5 0 8 n o r m p l o t ( R e t T y p e A ) , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , t i t l e ( ' P r o b a b i l i t y d i s t r i b u t i o n o f R e t a i n e d v o l t a g e f o r s a g t y p e A ' ) , x l a b e l ( ' R e t a
5 0 9
5 1 0 p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 1 9 _ R e t P r o b A . e p s ;
5 1 1
5 1 2 f i g u r e ( 2 2 )
5 1 3n o r m p l o t ( R e t T y p e C ) , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , t i t l e ( ' P r o b a b i l i t y d i s t r i b u t i o n o f R e t a i n e d v o l t a g e f o r s a g t y p e C ' ) , x l a b e l ( ' R e t a
5 1 4
5 1 5 p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 2 0 _ R e t P r o b C . e p s ;
5 1 6
5 1 7f i g u r e ( 2 3 )
5 1 8 n o r m p l o t ( R e t T y p e D ) , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , t i t l e ( ' P r o b a b i l i t y d i s t r i b u t i o n o f R e t a i n e d v o l t a g e f o r s a g t y p e D ' ) , x l a b e l ( ' R e t a
5 1 9
5 2 0 p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 2 1 _ R e t P r o b D . e p s ;
5 2 1
5 2 2 f i g u r e ( 2 4 )
5 2 3 n o r m p l o t ( D u r T y p e A ) , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , t i t l e ( ' P r o b a b i l i t y d i s t r i b u t i o n o f D u r a t i o n f o r s a g t y p e A ' ) , x l a b e l ( ' D u r a t i o n [ c y
5 2 4
5 2 5 p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 2 2 _ D u r P r o b A . e p s ;
5 2 6
5 2 7 f i g u r e ( 2 5 )
5 2 8 n o r m p l o t ( D u r T y p e C ) , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , t i t l e ( ' P r o b a b i l i t y d i s t r i b u t i o n o f D u r a t i o n f o r s a g t y p e C ' ) , x l a b e l ( ' D u r a t i o n [ c y
5 2 9
5 3 0 p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 2 3 _ D u r P r o b C . e p s ;
5 3 1
5 3 2 f i g u r e ( 2 6 )
5 3 3 n o r m p l o t ( D u r T y p e D ) , s e t ( g c a , ' F o n t s i z e ' , 1 4 ) , t i t l e ( ' P r o b a b i l i t y d i s t r i b u t i o n o f D u r a t i o n f o r s a g t y p e D ' ) , x l a b e l ( ' D u r a t i o n [ c y
5 3 4
5 3 5 p r i n t - d e p s c R e s u l t s \ S t a t i s t i c P l o t s \ 2 4 _ D u r P r o b D . e p s ;
5 3 6
5 3 7
5 3 8 c l e a r ( ' D u r _ S w e l l ' , ' R e t _ S w e l l ' , ' D u r _ S w e l l S a g s ' , ' R e t _ S w e l l S a g s ' , ' D u r _ S w e l l A l l ' , ' R e t _ S w e l l A l l ' ) ;
5 3 9 c l e a r ( ' D u r _ S w e l l s O N L Y ' , ' R e t _ S w e l l s O N L Y ' , ' v e c t S t a t u s S ' ) ;
5 4 0c l e a r ( ' D u r T y p e A ' , ' D u r T y p e C ' , ' D u r T y p e D ' , ' R e t T y p e A ' , ' R e t T y p e C ' , ' R e t T y p e D ' ) ;
5 4 1 c l e a r ( ' F i l e ' , ' D u r ' , ' R e t ' , ' E v s _ D u r R e t ' , ' E v s _ a ' , ' E v s _ b ' , ' E v s _ c ' , ' S e ' , ' D i p T y p e ' , ' V ' , ' F ' ) ;
5 4 2 c l e a r ( ' D i p T y p e S ' , ' V _ s ' , ' F _ s ' , ' E v s _ a l l ' , ' E v s ' , ' D i p T y p e _ a l l ' , ' D u r H C ' , ' R e t H C ' , ' j ' , ' C o r e l a t i o n ' ) ;
5 4 3 c l e a r ( ' D u r _ S e c ' , ' q ' )
5 4 4
SarfiX.m
1 f u n c t i o n [ S a r f i , S a r f i _ A , S a r f i _ C , S a r f i _ D ] = S a r f i X ( D u r , R e t , D i p T y p e , t h r e s h o l d )
2
3 % = = = % S a r f i - X c a l c u l a t i o n : = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
4
5 v e c t D i p T y p e A = s t r m a t c h ( ' A ' , D i p T y p e ) ;
6 v e c t D i p T y p e C = s t r m a t c h ( ' C ' , D i p T y p e ) ;
7 v e c t D i p T y p e D = s t r m a t c h ( ' D ' , D i p T y p e ) ;
8
9 i f ( t h r e s h o l d = = 0 . 9 ) % | | t h r e s h o l d = = 1 . 1 )
1 0
1 1 D u r T y p e A = D u r ( v e c t D i p T y p e A ) ;
1 2D u r T y p e C = D u r ( v e c t D i p T y p e C ) ;
1 3 D u r T y p e D = D u r ( v e c t D i p T y p e D ) ;
1 4
1 5 D u r T y p e A _ N o H C = f i n d ( D u r T y p e A > 0 . 5 ) ;
1 6D u r T y p e C _ N o H C = f i n d ( D u r T y p e C > 0 . 5 ) ;
1 7 D u r T y p e D _ N o H C = f i n d ( D u r T y p e D > 0 . 5 ) ;
1 8
1 9 V e c t N o H C = f i n d ( D u r > 0 . 5 ) ;
2 0R e t H C = R e t ( V e c t N o H C ) ;
2 1 R e t H C _ T y p e A = R e t H C ( D u r T y p e A _ N o H C ) ;
2 2 R e t H C _ T y p e C = R e t H C ( D u r T y p e C _ N o H C ) ;
2 3 R e t H C _ T y p e D = R e t H C ( D u r T y p e D _ N o H C ) ;
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A . 3 S i t e I n d i c e s a n d F i g u r e s 8 1
SarfiCurve.m
1 f u n c t i o n [ S a r f i _ I T I C , S a r f i _ S E M I ] = S a r f i C u r v e ( D u r _ S e c , R e t )
2
3 % = = = = = = = % S a r f i - c u r v e c a l c u l a t i o n : % = = = = = = = = = = = = = = = =
4 % = % S a r f i - I T I C ( C B E M A ) = = = = = = = = = = = = = = = = = = = = = = = = = = =
5 % = % U _ i t i c < 0 . 7 p u % = = = % 0 . 0 2 < d < = 0 . 5 0 0 % = = = = =
6 v e c t D u r _ I T I C _ 1 = f i n d ( 0 . 0 2 < D u r _ S e c & D u r _ S e c < = 0 . 5 0 0 ) ;
7 R e t _ I T I C _ 1 = R e t ( v e c t D u r _ I T I C _ 1 ) ;
8 v e c t R e t _ I T I C _ 1 = f i n d ( R e t _ I T I C _ 1 < 0 . 7 ) ;
9 S a r f i _ I T I C 1 = l e n g t h ( R e t _ I T I C _ 1 ( v e c t R e t _ I T I C _ 1 ) ) ;
1 0
1 1
1 2 % = % U _ i t i c < 0 . 8 p u % = = = % 0 . 5 0 0 < d < = 1 0 % = = = = =
1 3v e c t D u r _ I T I C _ 2 = f i n d ( 0 . 5 0 0 < D u r _ S e c & D u r _ S e c < = 1 0 ) ;
1 4 R e t _ I T I C _ 2 = R e t ( v e c t D u r _ I T I C _ 2 ) ;
1 5 v e c t R e t _ I T I C _ 2 = f i n d ( R e t _ I T I C _ 2 < 0 . 8 ) ;
1 6 S a r f i _ I T I C 2 = l e n g t h ( R e t _ I T I C _ 2 ( v e c t R e t _ I T I C _ 2 ) ) ;
1 7
1 8 % = % U _ i t i c < 0 . 9 p u % = = = % 1 0 < d % = = = = =
1 9 v e c t D u r _ I T I C _ 3 = f i n d ( 1 0 < D u r _ S e c ) ;
2 0 R e t _ I T I C _ 3 = R e t ( v e c t D u r _ I T I C _ 3 ) ;
2 1v e c t R e t _ I T I C _ 3 = f i n d ( R e t _ I T I C _ 3 < 0 . 9 ) ;
2 2 S a r f i _ I T I C 3 = l e n g t h ( R e t _ I T I C _ 3 ( v e c t R e t _ I T I C _ 3 ) ) ;
2 3
2 4 S a r f i _ I T I C = S a r f i _ I T I C 1 + S a r f i _ I T I C 2 + S a r f i _ I T I C 3 ;
2 5
2 6 % = % S a r f i - S E M I = = = = = = = = = =
2 7
2 8 % = % U _ s e m i < 0 . 5 p u % = = = % 0 . 0 2 < d < = 0 . 2 0 0 % = = = = =
2 9 v e c t D u r _ S E M I _ 1 = f i n d ( 0 . 0 2 < D u r _ S e c & D u r _ S e c < = 0 . 2 0 0 ) ;
3 0 R e t _ S E M I _ 1 = R e t ( v e c t D u r _ S E M I _ 1 ) ;
3 1 v e c t R e t _ S E M I _ 1 = f i n d ( R e t _ S E M I _ 1 < 0 . 5 ) ;
3 2 S a r f i _ S E M I 1 = l e n g t h ( R e t _ S E M I _ 1 ( v e c t R e t _ S E M I _ 1 ) ) ;
3 3
3 4 % = % U _ s e m i < 0 . 7 p u % = = = % 0 . 2 0 0 < d < = 0 . 5 0 0 % = = = = =
3 5 v e c t D u r _ S E M I _ 2 = f i n d ( 0 . 2 0 0 < D u r _ S e c & D u r _ S e c < = 0 . 5 0 0 ) ;
3 6R e t _ S E M I _ 2 = R e t ( v e c t D u r _ S E M I _ 2 ) ;
3 7 v e c t R e t _ S E M I _ 2 = f i n d ( R e t _ S E M I _ 2 < 0 . 7 ) ;
3 8 S a r f i _ S E M I 2 = l e n g t h ( R e t _ S E M I _ 2 ( v e c t R e t _ S E M I _ 2 ) ) ;
3 9
4 0% = % U _ s e m i < 0 . 8 p u % = = = % 0 . 5 0 0 < d < = 1 0 % = = = = =
4 1 v e c t D u r _ S E M I _ 3 = f i n d ( 0 . 5 0 0 < D u r _ S e c & D u r _ S e c < = 1 0 ) ;
4 2 R e t _ S E M I _ 3 = R e t ( v e c t D u r _ S E M I _ 3 ) ;
4 3 v e c t R e t _ S E M I _ 3 = f i n d ( R e t _ S E M I _ 3 < 0 . 8 ) ;
4 4S a r f i _ S E M I 3 = l e n g t h ( R e t _ S E M I _ 3 ( v e c t R e t _ S E M I _ 3 ) ) ;
4 5
4 6 % = % U _ s e m i < 0 . 9 p u % = = = % 1 0 < d % = = = = =
4 7 v e c t D u r _ S E M I _ 4 = f i n d ( 1 0 < D u r _ S e c ) ;
4 8 R e t _ S E M I _ 4 = R e t ( v e c t D u r _ S E M I _ 4 ) ;
4 9 v e c t R e t _ S E M I _ 4 = f i n d ( R e t _ S E M I _ 4 < 0 . 9 ) ;
5 0 S a r f i _ S E M I 4 = l e n g t h ( R e t _ S E M I _ 4 ( v e c t R e t _ S E M I _ 4 ) ) ;
5 1
5 2 S a r f i _ S E M I = S a r f i _ S E M I 1 + S a r f i _ S E M I 2 + S a r f i _ S E M I 3 + S a r f i _ S E M I 4 ;
SarfiCurveType.m
1
2f u n c t i o n [ S a r f i _ I T I C T y p e , S a r f i _ I T I C T y p e P e r c e n t , S a r f i _ S E M I T y p e , S a r f i _ S E M I T y p e P e r c e n t ] = S a r f i C u r v e T y p e ( D u r _ S e c , R e t , v e c t D i p T y
3
4 % = = = = = = = % S a r f i - c u r v e c a l c u l a t i o n : % = = = = = = = = = = = = = = = =
5 D u r _ S e c T y p e = D u r _ S e c ( v e c t D i p T y p e ) ;
6R e t _ T y p e = R e t ( v e c t D i p T y p e ) ;
7 l e n g t h t y p e = l e n g t h ( D u r _ S e c T y p e ) ;
8 % = % S a r f i - I T I C ( C B E M A ) = = = = = = = = = = = = = = = = = = = = = = = = = = =
9 % = % U _ i t i c < 0 . 7 p u % = = = % 0 . 0 2 < d < = 0 . 5 0 0 % = = = = =
1 0v e c t D u r _ I T I C _ 1 = f i n d ( 0 . 0 2 < D u r _ S e c T y p e & D u r _ S e c T y p e < = 0 . 5 0 0 ) ;
1 1 R e t _ I T I C _ 1 = R e t _ T y p e ( v e c t D u r _ I T I C _ 1 ) ;
1 2 v e c t R e t _ I T I C _ 1 = f i n d ( R e t _ I T I C _ 1 < 0 . 7 ) ;
1 3 S a r f i _ I T I C 1 = l e n g t h ( R e t _ I T I C _ 1 ( v e c t R e t _ I T I C _ 1 ) ) ;
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8 2 A M a t l a b C o d e
1 4
1 5 % = % U _ i t i c < 0 . 8 p u % = = = % 0 . 5 0 0 < d < = 1 0 % = = = = =
1 6 v e c t D u r _ I T I C _ 2 = f i n d ( 0 . 5 0 0 < D u r _ S e c T y p e & D u r _ S e c T y p e < = 1 0 ) ;
1 7 R e t _ I T I C _ 2 = R e t _ T y p e ( v e c t D u r _ I T I C _ 2 ) ;
1 8 v e c t R e t _ I T I C _ 2 = f i n d ( R e t _ I T I C _ 2 < 0 . 8 ) ;
1 9 S a r f i _ I T I C 2 = l e n g t h ( R e t _ I T I C _ 2 ( v e c t R e t _ I T I C _ 2 ) ) ;
2 0
2 1 % = % U _ i t i c < 0 . 9 p u % = = = % 1 0 < d % = = = = =
2 2 v e c t D u r _ I T I C _ 3 = f i n d ( 1 0 < D u r _ S e c T y p e ) ;
2 3 R e t _ I T I C _ 3 = R e t _ T y p e ( v e c t D u r _ I T I C _ 3 ) ;
2 4 v e c t R e t _ I T I C _ 3 = f i n d ( R e t _ I T I C _ 3 < 0 . 9 ) ;
2 5 S a r f i _ I T I C 3 = l e n g t h ( R e t _ I T I C _ 3 ( v e c t R e t _ I T I C _ 3 ) ) ;
2 6
2 7 S a r f i _ I T I C T y p e = S a r f i _ I T I C 1 + S a r f i _ I T I C 2 + S a r f i _ I T I C 3 ;
2 8
2 9 % i n p e r c e n t a g e
3 0 S a r f i _ I T I C _ T y p e P e r c e n t = ( S a r f i _ I T I C T y p e / S a r f i _ I T I C ) * 1 0 0 ;
3 1 S a r f i _ I T I C T y p e P e r c e n t = [ n u m 2 s t r ( S a r f i _ I T I C T y p e ) ' ( ' n u m 2 s t r ( r o u n d n ( S a r f i _ I T I C _ T y p e P e r c e n t , - 1 ) ) ' % ) ' ] ;
3 2
3 3 % = % S a r f i - S E M I = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
3 4
3 5 % = % U _ s e m i < 0 . 5 p u % = = = % 0 . 0 2 < d < = 0 . 2 0 0 % = = = = =
3 6v e c t D u r _ S E M I _ 1 = f i n d ( 0 . 0 2 < D u r _ S e c T y p e & D u r _ S e c T y p e < = 0 . 2 0 0 ) ;
3 7 R e t _ S E M I _ 1 = R e t _ T y p e ( v e c t D u r _ S E M I _ 1 ) ;
3 8 v e c t R e t _ S E M I _ 1 = f i n d ( R e t _ S E M I _ 1 < 0 . 5 ) ;
3 9 S a r f i _ S E M I 1 = l e n g t h ( R e t _ S E M I _ 1 ( v e c t R e t _ S E M I _ 1 ) ) ;
4 0
4 1 % = % U _ s e m i < 0 . 7 p u % = = = % 0 . 2 0 0 < d < = 0 . 5 0 0 % = = = = =
4 2 v e c t D u r _ S E M I _ 2 = f i n d ( 0 . 2 0 0 < D u r _ S e c T y p e & D u r _ S e c T y p e < = 0 . 5 0 0 ) ;
4 3 R e t _ S E M I _ 2 = R e t _ T y p e ( v e c t D u r _ S E M I _ 2 ) ;
4 4 v e c t R e t _ S E M I _ 2 = f i n d ( R e t _ S E M I _ 2 < 0 . 7 ) ;
4 5 S a r f i _ S E M I 2 = l e n g t h ( R e t _ S E M I _ 2 ( v e c t R e t _ S E M I _ 2 ) ) ;
4 6
4 7 % = % U _ s e m i < 0 . 8 p u % = = = % 0 . 5 0 0 < d < = 1 0 % = = = = =
4 8 v e c t D u r _ S E M I _ 3 = f i n d ( 0 . 5 0 0 < D u r _ S e c T y p e & D u r _ S e c T y p e < = 1 0 ) ;
4 9 R e t _ S E M I _ 3 = R e t _ T y p e ( v e c t D u r _ S E M I _ 3 ) ;
5 0 v e c t R e t _ S E M I _ 3 = f i n d ( R e t _ S E M I _ 3 < 0 . 8 ) ;
5 1S a r f i _ S E M I 3 = l e n g t h ( R e t _ S E M I _ 3 ( v e c t R e t _ S E M I _ 3 ) ) ;
5 2
5 3 % = % U _ s e m i < 0 . 9 p u % = = = % 1 0 < d % = = = = =
5 4 v e c t D u r _ S E M I _ 4 = f i n d ( 1 0 < D u r _ S e c T y p e ) ;
5 5R e t _ S E M I _ 4 = R e t _ T y p e ( v e c t D u r _ S E M I _ 4 ) ;
5 6 v e c t R e t _ S E M I _ 4 = f i n d ( R e t _ S E M I _ 4 < 0 . 9 ) ;
5 7 S a r f i _ S E M I 4 = l e n g t h ( R e t _ S E M I _ 4 ( v e c t R e t _ S E M I _ 4 ) ) ;
5 8
5 9S a r f i _ S E M I T y p e = S a r f i _ S E M I 1 + S a r f i _ S E M I 2 + S a r f i _ S E M I 3 + S a r f i _ S E M I 4 ;
6 0
6 1 % i n p e r c e n t a g e
6 2 S a r f i _ S E M I _ T y p e P e r c e n t = ( S a r f i _ S E M I T y p e / S a r f i _ S E M I ) * 1 0 0 ;
6 3 S a r f i _ S E M I T y p e P e r c e n t = [ n u m 2 s t r ( S a r f i _ S E M I T y p e ) ' ( ' n u m 2 s t r ( r o u n d n ( S a r f i _ S E M I _ T y p e P e r c e n t , - 1 ) ) ' % ) ' ] ;
IECTable.m
1 f u n c t i o n [ T a b l e ] = I E C T a b l e ( D u r _ S e c , R e t )
2
3 % p u t t i n g d u r a n d r e t a i n e d v o l t a g e i n o n e m a t r i x
4D u r R e t = [ D u r _ S e c , R e t ] ;
5
6 % = = = = = = = = = m a k i n g V o l t a g e - S a g T A B L E b a s e d o n I E C 6 1 0 0 0 - 4 - 1 1
7 % = = t a b l e _ ? 1 = = = = = D u r _ S e c < 0 . 1 = = = = = = = = = = = =
8% = = t a b l e _ 1 1
9 v e c t D u r 0 _ 0 1 = f i n d ( D u r _ S e c < 0 . 1 ) ;
1 0 R e t 0 _ 0 1 = R e t ( v e c t D u r 0 _ 0 1 ) ;
1 1 v e c t R e t 0 _ 0 1 = f i n d ( R e t 0 _ 0 1 > = 0 . 8 ) ;
1 2t a b l e _ 1 1 = l e n g t h ( R e t 0 _ 0 1 ( v e c t R e t 0 _ 0 1 ) ) ;
1 3 % = = t a b l e _ 2 1
1 4 v e c t R e t 0 _ 0 1 = f i n d ( 0 . 7 < R e t 0 _ 0 1 & R e t 0 _ 0 1 < = 0 . 8 ) ;
1 5 t a b l e _ 2 1 = l e n g t h ( R e t 0 _ 0 1 ( v e c t R e t 0 _ 0 1 ) ) ;
1 6% = = t a b l e _ 3 1
1 7 v e c t R e t 0 _ 0 1 = f i n d ( 0 . 6 < R e t 0 _ 0 1 & R e t 0 _ 0 1 < = 0 . 7 ) ;
1 8 t a b l e _ 3 1 = l e n g t h ( R e t 0 _ 0 1 ( v e c t R e t 0 _ 0 1 ) ) ;
1 9 % = = t a b l e _ 4 1
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8 6 A M a t l a b C o d e
2 3 9 t e s t 6 = ' f a l s e ' ;
2 4 0 e n d
2 4 1 % = = = t a b l e _ ? 7 : = = = = = = 2 0 < = D u r _ S e c < 6 0 = = = = = = = = = = =
2 4 2 v e c t D u r 2 0 _ 6 0 = f i n d ( 2 0 < = D u r _ S e c & D u r _ S e c < 6 0 ) ;
2 4 3 R e t 2 0 _ 6 0 = R e t ( v e c t D u r 2 0 _ 6 0 ) ;
2 4 4 % = = t a b l e _ 1 7
2 4 5 v e c t R e t 2 0 _ 6 0 = f i n d ( R e t 2 0 _ 6 0 > = 0 . 8 ) ;
2 4 6 t a b l e _ 1 7 = l e n g t h ( R e t 2 0 _ 6 0 ( v e c t R e t 2 0 _ 6 0 ) ) ;
2 4 7 % = = t a b l e _ 2 7
2 4 8 v e c t R e t 2 0 _ 6 0 = f i n d ( 0 . 7 < R e t 2 0 _ 6 0 & R e t 2 0 _ 6 0 < = 0 . 8 ) ;
2 4 9 t a b l e _ 2 7 = l e n g t h ( R e t 2 0 _ 6 0 ( v e c t R e t 2 0 _ 6 0 ) ) ;
2 5 0 % = = t a b l e _ 3 7
2 5 1 v e c t R e t 2 0 _ 6 0 = f i n d ( 0 . 6 < R e t 2 0 _ 6 0 & R e t 2 0 _ 6 0 < = 0 . 7 ) ;
2 5 2 t a b l e _ 3 7 = l e n g t h ( R e t 2 0 _ 6 0 ( v e c t R e t 2 0 _ 6 0 ) ) ;
2 5 3% = = t a b l e _ 4 7
2 5 4 v e c t R e t 2 0 _ 6 0 = f i n d ( 0 . 5 < R e t 2 0 _ 6 0 & R e t 2 0 _ 6 0 < = 0 . 6 ) ;
2 5 5 t a b l e _ 4 7 = l e n g t h ( R e t 2 0 _ 6 0 ( v e c t R e t 2 0 _ 6 0 ) ) ;
2 5 6 % = = t a b l e _ 5 7
2 5 7v e c t R e t 2 0 _ 6 0 = f i n d ( 0 . 4 < R e t 2 0 _ 6 0 & R e t 2 0 _ 6 0 < = 0 . 5 ) ;
2 5 8 t a b l e _ 5 7 = l e n g t h ( R e t 2 0 _ 6 0 ( v e c t R e t 2 0 _ 6 0 ) ) ;
2 5 9 % = = t a b l e _ 6 7
2 6 0 v e c t R e t 2 0 _ 6 0 = f i n d ( 0 . 3 < R e t 2 0 _ 6 0 & R e t 2 0 _ 6 0 < = 0 . 4 ) ;
2 6 1t a b l e _ 6 7 = l e n g t h ( R e t 2 0 _ 6 0 ( v e c t R e t 2 0 _ 6 0 ) ) ;
2 6 2 % = = t a b l e _ 7 7
2 6 3 v e c t R e t 2 0 _ 6 0 = f i n d ( 0 . 2 < R e t 2 0 _ 6 0 & R e t 2 0 _ 6 0 < = 0 . 3 ) ;
2 6 4 t a b l e _ 7 7 = l e n g t h ( R e t 2 0 _ 6 0 ( v e c t R e t 2 0 _ 6 0 ) ) ;
2 6 5 % = = t a b l e _ 8 7
2 6 6 v e c t R e t 2 0 _ 6 0 = f i n d ( 0 . 1 < R e t 2 0 _ 6 0 & R e t 2 0 _ 6 0 < = 0 . 2 ) ;
2 6 7 t a b l e _ 8 7 = l e n g t h ( R e t 2 0 _ 6 0 ( v e c t R e t 2 0 _ 6 0 ) ) ;
2 6 8 % = = t a b l e _ 9 7
2 6 9 v e c t R e t 2 0 _ 6 0 = f i n d ( R e t 2 0 _ 6 0 < = 0 . 1 ) ;
2 7 0 t a b l e _ 9 7 = l e n g t h ( R e t 2 0 _ 6 0 ( v e c t R e t 2 0 _ 6 0 ) ) ;
2 7 1 % t r u e - f a l s e t e s t ; c h e c k i n g
2 7 2 t a b l e X 7 = t a b l e _ 1 7 + t a b l e _ 2 7 + t a b l e _ 3 7 + t a b l e _ 4 7 + t a b l e _ 5 7 + t a b l e _ 6 7 + t a b l e _ 7 7 + t a b l e _ 8 7 + t a b l e _ 9 7 ;
2 7 3 i f ( t a b l e X 7 = = l e n g t h ( R e t 2 0 _ 6 0 ) )
2 7 4 % d i s p ( ' t r u e ' )
2 7 5 t e s t 7 = ' t r u e ' ;
2 7 6e l s e
2 7 7 % d i s p ( ' f a l s e ' )
2 7 8 t e s t 7 = ' f a l s e ' ;
2 7 9 e n d
2 8 0% = = = t a b l e _ ? 8 : = = = = = = 6 0 < = D u r _ S e c < 3 0 0 = = = = = = = = = = =
2 8 1 v e c t D u r 6 0 _ 3 0 0 = f i n d ( 6 0 < = D u r _ S e c & D u r _ S e c < 3 0 0 ) ;
2 8 2 R e t 6 0 _ 3 0 0 = R e t ( v e c t D u r 6 0 _ 3 0 0 ) ;
2 8 3 % = = t a b l e _ 1 8
2 8 4v e c t R e t 6 0 _ 3 0 0 = f i n d ( R e t 6 0 _ 3 0 0 > = 0 . 8 ) ;
2 8 5 t a b l e _ 1 8 = l e n g t h ( R e t 6 0 _ 3 0 0 ( v e c t R e t 6 0 _ 3 0 0 ) ) ;
2 8 6 % = = t a b l e _ 2 8
2 8 7 v e c t R e t 6 0 _ 3 0 0 = f i n d ( 0 . 7 < R e t 6 0 _ 3 0 0 & R e t 6 0 _ 3 0 0 < = 0 . 8 ) ;
2 8 8 t a b l e _ 2 8 = l e n g t h ( R e t 6 0 _ 3 0 0 ( v e c t R e t 6 0 _ 3 0 0 ) ) ;
2 8 9 % = = t a b l e _ 3 8
2 9 0 v e c t R e t 6 0 _ 3 0 0 = f i n d ( 0 . 6 < R e t 6 0 _ 3 0 0 & R e t 6 0 _ 3 0 0 < = 0 . 7 ) ;
2 9 1 t a b l e _ 3 8 = l e n g t h ( R e t 6 0 _ 3 0 0 ( v e c t R e t 6 0 _ 3 0 0 ) ) ;
2 9 2 % = = t a b l e _ 4 8
2 9 3 v e c t R e t 6 0 _ 3 0 0 = f i n d ( 0 . 5 < R e t 6 0 _ 3 0 0 & R e t 6 0 _ 3 0 0 < = 0 . 6 ) ;
2 9 4 t a b l e _ 4 8 = l e n g t h ( R e t 6 0 _ 3 0 0 ( v e c t R e t 6 0 _ 3 0 0 ) ) ;
2 9 5% = = t a b l e _ 5 8
2 9 6 v e c t R e t 6 0 _ 3 0 0 = f i n d ( 0 . 4 < R e t 6 0 _ 3 0 0 & R e t 6 0 _ 3 0 0 < = 0 . 5 ) ;
2 9 7 t a b l e _ 5 8 = l e n g t h ( R e t 6 0 _ 3 0 0 ( v e c t R e t 6 0 _ 3 0 0 ) ) ;
2 9 8 % = = t a b l e _ 6 8
2 9 9v e c t R e t 6 0 _ 3 0 0 = f i n d ( 0 . 3 < R e t 6 0 _ 3 0 0 & R e t 6 0 _ 3 0 0 < = 0 . 4 ) ;
3 0 0 t a b l e _ 6 8 = l e n g t h ( R e t 6 0 _ 3 0 0 ( v e c t R e t 6 0 _ 3 0 0 ) ) ;
3 0 1 % = = t a b l e _ 7 8
3 0 2 v e c t R e t 6 0 _ 3 0 0 = f i n d ( 0 . 2 < R e t 6 0 _ 3 0 0 & R e t 6 0 _ 3 0 0 < = 0 . 3 ) ;
3 0 3t a b l e _ 7 8 = l e n g t h ( R e t 6 0 _ 3 0 0 ( v e c t R e t 6 0 _ 3 0 0 ) ) ;
3 0 4 % = = t a b l e _ 8 8
3 0 5 v e c t R e t 6 0 _ 3 0 0 = f i n d ( 0 . 1 < R e t 6 0 _ 3 0 0 & R e t 6 0 _ 3 0 0 < = 0 . 2 ) ;
3 0 6 t a b l e _ 8 8 = l e n g t h ( R e t 6 0 _ 3 0 0 ( v e c t R e t 6 0 _ 3 0 0 ) ) ;
3 0 7% = = t a b l e _ 9 8
3 0 8 v e c t R e t 6 0 _ 3 0 0 = f i n d ( R e t 6 0 _ 3 0 0 < = 0 . 1 ) ;
3 0 9 t a b l e _ 9 8 = l e n g t h ( R e t 6 0 _ 3 0 0 ( v e c t R e t 6 0 _ 3 0 0 ) ) ;
3 1 0 % t r u e - f a l s e t e s t ; c h e c k i n g
3 1 1 t a b l e X 8 = t a b l e _ 1 8 + t a b l e _ 2 8 + t a b l e _ 3 8 + t a b l e _ 4 8 + t a b l e _ 5 8 + t a b l e _ 6 8 + t a b l e _ 7 8 + t a b l e _ 8 8 + t a b l e _ 9 8 ;
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A . 3 S i t e I n d i c e s a n d F i g u r e s 8 7
3 1 2 i f ( t a b l e X 8 = = l e n g t h ( R e t 2 0 _ 6 0 ) )
3 1 3 % d i s p ( ' t r u e ' )
3 1 4 t e s t 8 = ' t r u e ' ;
3 1 5 e l s e
3 1 6 % d i s p ( ' f a l s e ' )
3 1 7 t e s t 8 = ' f a l s e ' ;
3 1 8 e n d
3 1 9
3 2 0 % A l l T e s t :
3 2 1 T e s t = { t e s t 1 t e s t 2 t e s t 3 t e s t 4 t e s t 5 t e s t 6 t e s t 7 t e s t 8 } ;
3 2 2 T a b l e _ t e s t = t a b l e X 1 + t a b l e X 2 + t a b l e X 3 + t a b l e X 4 + t a b l e X 5 + t a b l e X 6 + t a b l e X 7 + t a b l e X 8 ;
3 2 3
3 2 4 i f T a b l e _ t e s t = = l e n g t h ( R e t )
3 2 5 d i s p ( ' c o r r e c t ' )
3 2 6e l s e
3 2 7 d i s p ( ' i n c o r r e c t ' )
3 2 8 e n d
3 2 9
3 3 0% M a k i n g t h e t a b l e
3 3 1 T a b l e _ r o w 1 = { ' R e t a i n e d v o l t a g e [ p u ] ' ' d < 0 . 1 ' ' 0 . 1 < = d < 0 . 2 5 ' ' 0 . 2 5 < = d < 0 . 5 0 ' ' 0 . 5 0 < = d < 1 . 0 ' ' 1 . 0 &