RAZOG Distance relay - ABB · PDF fileTitle: RAZOG Distance relay Created Date: 7/3/2001 11:04:27 AM
Modeling and Testing of Digital Distance Relay Using Matlab
7
Modeling a n d Testing o f a igital Distance Relay Using MATLAB/SIMULINK Li-Cheng W u , Chih-Wen Liu,Senior Member,jEEE, Ching-Shan Chen,Member,IEEE Department o f Electrical Engineering, National Taiwan University, Taipei, Taiwan Abstract This paper describes modelling a nd testing o f a digital distance relay f o r transmission line protection using MATLAB/SIMULINK. SIMULINK's Power System Blockset (PSB) i s used for detailed modelling o f a power system network a n d fault simulation. MATLAB i s used t o implement programs o f digital distance relaying algorithms a n d t o serve a s main software environment. Th e technique i s a n interactive simulation environment f o r relaying algorithm design a n d evaluation. T h e basic principles o f a digital distance relay a n d some related filtering techniques ar e also described in this paper. A 3 4 5 k V , 1 00 k m transmission line a n d a MHO type distance relay a r e selected a s examples f o r fault simulation a n d relay testing. Some simulation results a re given. Index Terms-Digital relay Digital distance relay Electromagnetic Transient Program (EMTP) Automatic test analysis tool [4]. This tool w a s modelled b y using a graphically Object-Oriented environment approach integrated with t h e digital calculate technology that gives more flexibility t o create simulation system; therefore, w e c a n quickly develop a program o f protective relay algorithms, a n d a model o f protection relays. Because they commonly exist i n t h e same environment that involves communication ability, it i s very easy t o develop a convenient graphical tool for building interactive relay system. T h e above-mentioned excellent advantages that MATLAB/SIMULINK h a s make MATLAB/SIMULINK a convenient a n d interactive tool f o r both numerous analysis a n d direct communications with relay's test program. This paper describes ho w t o u s e MATLAB/SIMULINK f o r automatic, interactive, a n d high performance testing relay system. Some examples a n d simulation results a r e also provided i n t h e paper. I . INTRODUCTION F o r transmission lines protection, choosing a suitable relay type or relay's setting i s essential. Generally speaking, w e m ay make t h e fault analysis a n d t h e test by t h e simulation software, a n d according t o t h e actual system requirement, choose t h e suitable protective relay, but f o r reliability a n d security considerations, t he massive simulations tests a r e usually undertaken. This i s a quite numerous a n d diverse job; therefore, having a superior simulated environment i s important. Th e EMTP [1](Electromagnetic Transient Program) i s t h e simulation tool that i s used t o simulate t h e electromagnetic transient phenomenon, a n d power system faults analysis, a n d it i s o n e o f t h e most widely used programs i n t h e electric utility since 1970. Generally speaking, Protective relay performance has been tested with t h e waveform signals generated b y t h e n o n real-time simulator like EMTP. This approach h a s t h e disadvantage that i t s difficult t o provide real-time test f o r t h e relay algorithm dynamically. I n addition, w e can't finished most test tasks a t t h e same time with t h e tool. I n school a n d industry, simulation tools based o n MATLAB/SIMULINK [2 ] a r e becoming popular f o r engineering applications. T h e MATLAB involves many high instructions a n d tools f o r some systems designing applications a n d developing algorithms a n d t h e SIMULINK provides excellent G UI (Graphical User Interface) interface a n d block module that will allow t h e users to rapidly an d easily build a nd simulate system models a n d executive massive simulation tests a t t h e same time. Furthermore, since t h e MATLAB/SIMULINK contain Power System Block Se t Toolbox [3], t e software t u m into a powerful power systems simulation an d I I . ALGORITHM O F DIGITAL DISTANCE RELAY Digital distance protection i s a universal short-circuit protection. I t s mode o f operation i s based on t h e measurement a n d evaluation o f t h e short-circuit impedance, which i s named by t he algorithm o f digital distance relay. This algorithm i s used t o input signals t o D S P b y discrete voltage a n d discrete current t o judge whether faults occur or not. However, this method i s just a program. MATLAB ha s t he advantage o f conducting massive calculation functions an d i ts program c a n b e easily developed. Therefore, i t i s a very suitable tool o f protective relay designs a n d applications f o r protection engineers. I t can't b e denied that graphics reach o u t t o people better than texts d o . I n addition, we focus n o t only on t h e correction o f relay operations, b u t also on t h e dynamic characteristics o f relay. Therefore, if w e c a n u s e graphics t o show t h e variance o f impedances trace, then t h e software o f interface will become more user-friendly a nd convenient. MATLAB includes excellent graphics capacity multi-dimension o f graphic function, a n d c a n change graphics parameters at t h e same time. Therefore, many graphs c a n b e shown on t h e same window t o make comparison with one another. This paper focuses o n t h e model a n d test o f digital distance relay. Therefore, t h e principles a n d relating techniques o f t h e distance relay will b e discussed first, followed by t h e description o f t h e distance relay practice by MATLAB. Distance relays a r e also named impedance relays. They a r e used t o calculate line impedance by measurement o f voltages a n d currents o n o e single end. F o r example, f o r MH type distance relays, t he relays compare t h e 0-7803-9255-8/05/ 20.00 2005 IEEE 25 3
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Transcript of Modeling and Testing of Digital Distance Relay Using Matlab
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s e t t i n g
i m p e d a n c e w it h
t h e
m e a s u r e m e n t
i m p e d a n c e t o
d e t e r m i n e
i f
t h e f a u l t
i s
i n s i d e o r
o u t s i d e
t h e
p r o t e c t e d
z o n e .
T h e y
i m m e d i a t e l y
r e l e a s e
a
t r i p
s i g n a l
w h e n
t h e
i m p e d a n c e
v a l u e
i s
i n s i d e
t h e
z o n e
1
i m p e d a n c e
c i r c l e
o f
d i s t a n c e
r e l a y .
F o r
s e c u r i t y p r o t e c t i o n
c o n s i d e r a t i o n , t h e
c o n f i r m a t i o n
o f a
f a u l t o c c u r r e n c e w i l l
n o t
b e m a d e
u n t i l
s u c c e s s i v e
t r i p
s i g n a l s
a r e
r e l e a s e d
i n
o n e
s e a s o n .
D i f f e r e n t
f o r m u l a s
s h o u l d b e
a d o p t e d
w h e n
c a l c u l a t i n g t h e
f a u l t
i m p e d a n c e d u e t o d i f f e r e n t f a u l t
t y p e s .
T a b l e 1
i n d i c a t e s c a l c u l a t i o n
f o r m u l a
f o r
a l l
o f
t h e
f a u l t
t y p e s [ 5 ] .
A n y
t h r e e - p h a s e f a u l t s c a n
b e
d e t e c t e d
f r o m
e v e r y f o r m u l a i n T a b l e
1 .
I n o r d e r t o r e d u c e
c a l c u l a t i o n
b u r d e n ,
we
d e s i g n
a f a u l t
d e t e c t o r a n d
f a u l t
t y p e s e l e c t o r .
T h e
f a u l t d e t e c t o r c a n
j u d g e w h i c h
f a u l t t y p e
i t
i s a n d t h e n
c a l c u l a t e f a u l t
i m p e d a n c e
b y
s e l e c t i n g
a
s u i t a b l e
f o r m u l a
f r o m T a b l e 1 . I f
we d o n ' t u s e f a u l t
t y p e
j u d g m e n t
f i r s t ,
t h e n
t h e d i s t a n c e
r e l a y
o f
p r o g r a m s
m u s t b e
c a l c u l a t e d
b y
a l l
t h e
s i x
f o r m u l a s
i n
t a b l e 1 a t
t h e s a m e
t i m e ,
w h i c h
c a u s e s
m u c h c a l c u l a t i o n
b u r d e n .
' I a b l e
I
f a u l t
i m p e d a n c e c a l c u l a t i o n f o r m u l a
o n i d i f f i e r e n 1 c e
f a u l t s
F a u l t T y p e F o r m u l a
A G
V A / ( 1 A + 3 k ] o )
B G
V B / ( I B + 3 k I o )
CG
V c / ( I c + 3 k I o )
A B
o r
AB G
( V A - V B ) /
( I A - I B )
BC
o r
BCG
( V B - V c ) /
( I B - I C )
CA o r
CAG
( V c - V A ) /
( I C - I A )
W h e r e
A
-
B
a n d C
i n d i c a t e s n u m b e r
o f
p h a s e ,
G i s
g r o u n d
f a u l t
, V a n d I
a r e p h a so r o f
v o l t a g e
a n d
c u r r e n t ,
k = ( Z o - Z 1 ) / Z 1
Z o
a n d
Z 1
a r e
l i n e
o f
i m p e d a n c e
z e r o - s e q u e n c e , p o s i t i v e - s e q u e n c e
r e s p e c t i v e l y .
l o
i s
z e r o - s e q u e n c e
c u r r e n t .
When t h e d i s t a n c e
r e l a y s
r e c e i v e d i s c r e t e
v o l t a g e
a n d
c u r r e n t
s i g n a l ,
i t
h a s t o
c o n v e r t t h e m
t o
p h a s o r .
T h e
D i s c r e t e
F o u r i e r T r a n s f o r m
( D F T ) i s t h e m o s t
p o p u l a r
m e t h o d
t o
e s t i m a t e
f u n d a m e n t a l
p h a s o r s
f o r
d i g i t a l
r e l a y i n g .
T h e
f u l l - c y c l e
DFT
i s
d e s c r i b e d
a s
f o l l o w i n g
e q u a t i o n
1 ) :
N - 1
X
Xke
i j 2 ( 1 )
N
k
W h e r e
X
i s
c o m p l e x
p h a s o r ,
X k i s
t h e
s a m p l e
d i s c r e t e
d a t a
o f
t h e
s i g n a l ,
a n d
N
i s
t h e
n u m b e r o f
s a m p l e s p e r
c y c l e .
E q u a t i o n
( 1 ) i s t h e
f o r m u l a o f
f u l l - c y c l e D F T .
When a
s i g n a l i s
s a m p l e d
w i t h
3 2
s a m p l e s
p e r
c y c l e ,
a s
a n
e x a m p l e ,
t h e n
MATLAB DFT
p r o g r a m
c a n b e
w r i t t e n
a s
f o l l o w s :
I n
a d d i t i o n ,
w h e n
a
f a u l t
occurs on
t r a n s m i s s i o n
l i n e s ,
t h e v o l t a g e a n d
c u r r e n t
s i g n a l s ar e
s e v e r e l y d i s t o r t e d .
T h e s e
s i g n a l s may
c o n t a i n
d e c a y i n g
d c
c o m p o n e n t s ,
s u b s y s t e m
f r e q u e n c y t r a n s i e n t s ,
h i g h
f r e q u e n c y
o s c i l l a t i o n
q u a n t i t i e s , a n d e t c .
T h e
h i g h e r
f r e q u e n c y
components
c an
b e
e l i m i n a t e d
u s i n g
l o w
p a s s a n t i - a l i a s i n g
f i l t e r s
w it h
a p p r o p r i a t e
c u t - o f f
f r e q u e n c y ,
b u t
t h e
a n t i - a l i a s i n g
f i l t e r s
c a n n o t remove
d e c a y i n g
d c
c o m p o n e n t s
a n d
r e j e c t
l o w
f r e q u e n c y c o m p o n e n t s .
T h i s
m a k e s t h e
p h a s o r s
v e r y
d i f f i c u l t t o b e
q u i c k l y
e s t i m a t e d
a n d
a f f e c t s
t h e
p e r f o r m a n c e
o f
d i g i t a l r e l a y i n g . T h e r e f o r e ,
we
u s u a l l y
u s e
t h e m i m i c
f i l t e r t o
r e m o v e d
t h e d c - o f f s e t
c o m p o n e n t s
[ 6 ] .
T h e
m i m i c f i l t e r
c a n b e
d e v e l o p e d
b y d i g i t a l
m e t h o d .
H e r e ,
we
w a n t
t o
p a s s
t h e
f u n d a m e n t a l f r e q u e n c y
s i g n a l
( 6 0 H z )
b y
t h e
f i l t e r .
T h e n ,
a s s u m i n g
t h e
g a i n
K
e q u a l s
I
a n d
t h e
s a m p l e s f r e q u e n c y
i s
f 5
( f 5
=
I
I
T
) , f i n a l l y ,
we o b t a i n a
f o r m u l a
( 2 )
| K ( 1
J T f 5 )
K l T f
c o s
T ,
+
j K t f s
s i n
T=1
( 2 )
W h e r e
o
=
2 *
n
* 6 0 ,
T
i s
t i m e
c o n s t a n t
f o r
u s e r
d e f i n i t i o n .
T o
s o l v e
e q u a t i o n
( 2 )
c a n
g e t
t h e
g a i n
K
K
=
s q r t (
I
W h e r e
M=1
+
T f 5
-
t f s
c o s (
)
f s
2
*n*60
N=cf
s i n (
)
. f s
( 3 )
4 - 1 )
4 - 2 )
When we u s e
m i m i c
f i l t e r
t o r e m o v e
t h e
d c - o f f s e t
c o m p o n e n t s ,
MATLAB
p r o g r a m
i s
d e s c r i b e d a s
f o l l o w s :
t = 2 * 1 / 6 0 ;
a s s u m e d t i m e
c o n s t a n t
=
2
c y c l e s
f s
=
3 2 * 6 0 ;
s a m p l i n g
f r e q u e n c y
M=1
+ t * f s - t * f s * c o s ( 2 * p i * 6 0 / f s ) ;
N = t * f s
* s i n ( 2
* p i
* 6 0 / f s ) ;
K = s q r t ( l / ( M ^ 2 + N ^ 2 ) ) ;
b = [ K * ( l + t * f s )
- K * t * f s ] ;
a = [ ] ] ;
i a
m f = f i l t e r ( b , a ,
i a ) ;
A s
s h o w n i n
t h e a b o v e
e q u a t i o n ,
t h e
c u r r e n t i a
i s
t h r o u g h t h e m i m i c
f i l t e r i n
o r d e r t o
r e m o v e t h e
d c - o f f s e t
c o m p o n e n t s .
F i n a l l y ,
we
g e t a
f u n d a m e n t a l
f r e q u e n c y
w a v e i a
m f .
F r o m
t h e
a b o v e
d i s c u s s i o n ,
we k n o w
t h a t
MATLAB
c a n
e a s i l y
f i n i s h a l l o f
a l g o r i t h m s
f o r p r o t e c t i v e
r e l a y s .
W i t h
t h e
a d v a n t a g e
t h a t
SIMULINK c a n
e a s i l y
s i m u l a t e
p o w e r s y s t e m
f a u l t s ,
t h e d e s i g n
a n d t h e
t e s t
o f
p r o t e c t i v e
r e l a y s
c an b e
a c h i e v e d
w i t h e a s e .
I t s m a j o r
c h a r a c t e r i s t i c
o f i n t e g r a t i n g
s y s t e m f a u l t
s i m u l a t i o n a n d
p r o t e c t i o n
r e l a y
a l g o r i t h m s i n
a s o f t w a r e
s y s t e m
c a n
e n h a n c e
t h e
e f f i c i e n c y
o f
p r o t e c t i o n
r e l a y
t e s t .
I I I .
POWER
SYSTEM
ESTABLISHMENT
A N D
SIMULATION
I n o r d e r
t o
g e t
e x a c t
s i m u l a t i o n
r e s u l t s , we
m u s t
e s t a b l i s h
a c c u r a t e n e t w o r k
m o d e l .
S I M U L I N K / P o w e r
S y s t e m B l o c k s e t
( P S B ) i s
u s e d
t o
c r e a t e
p o w e r
s y s t e m
m o d e l
f o r
s i m u l a t i o n . W i t h
t h e
u p d a t e d
v e r s i o n s
o f
M A T L A B / S I M U L I N K ,
t h e m o d e l
d e v e l o p m e n t o f
p o w e r
s y s t e m
c o m p o n e n t s
i s o n w a r d
t o
p e r f e c t i o n .
D u e t o
t h e
254
N
=
3 2 ;
X=
0 ;
f o r
k
I : N
X
=
X
+
x ( k ) * e x p ( j
* 2 * p i / 3 2 * ( k - 1 ) ) ;
e n d
X
=
X * 2 / N ;
8/11/2019 Modeling and Testing of Digital Distance Relay Using Matlab
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f a s t
d e v e l o p m e n t
o f
n e w
t e c h n o l o g i e s ,
w h i c h
i m p r o v e t h e
p o w e r
t r a n s f e r
e f f i c i e n c y
a n d
t h e
o p t i m u m
u t i l i z a t i o n
o f
s y s t e m
c a p a b i l i t y ,
p o w e r
e l e c t r o n i c
e q u i p m e n t
l i k e
TCSC
UPFC
S T A T C O M . . .
a n d
s o
o n
m a y b e
w i d e l y
u s e d i n
p o w e r
s y s t e m s I n t h e
f u t u r e .
T h u s , t h e
s e l e c t i o n
a n d
t h e s e t t i n g o f
p r o t e c t i v e r e l a y
s h o u l d
b e
e v a l u a t e d
a n d
t e s t e d
t h o r o u g h l y
[ 7 ] .
H e r e , SIMULINK
i n c l u d e s
v a r i a n t
b a s i c
p o w e r
c o m p o n e n t s , w h i c h c a n
b e
u s e d a l o n e
o r i n
c o m b i n a t i v e u se
t o
f i n i s h a l l
k i n d s
o f
p o w e r
s y s t e m
n e t w o r k
s i m u l a t i o n s .
I t
i s
v e r y
e a s y
t o
c r e a t e
p o w e r
s y s t e m i n
SIMULINK
e n v i r o n m e n t , w h i c h a l l o w s
u s e r s t o b u i l d
a m o d e l
b y
s i m p l e
c l i c k
a n d
d r a g
p r o c e d u r e s . B e c a u s e
a l l
o f
t h e
e l e c t r i c a l p a r t s o f
t h e s i m u l a t i o n
i n t e r a c t w i t h
t h e
S I M L L I N K S
e x t e n s i v e
m o d e l l i n g
l i b r a r y , i t i s n o t
j u s t
p o s s i b l e
t o
e a s i l y
d r a w t h e
p o w e r
s y s t e m
n e t w o r k ,
b u t a l s o
t o i n c l u d e i t s
i n t e r a c t i o n s
w i t h
e v e r y
e l e c t r i c a l
c o m p o n e n t .
I n
a d d i t i o n ,
t h e s i m u l a t i o n
s y s t e m
o f
b l o c k
c o m p o n e n t
c a n
s e t
r e l a t i o n
e l e c t r i c a l
p a r a m e t e r s
f r o m
MATLAB
c o m m a n d s .
O n e
t h i n g
s h o u l d b e
n o t e d
i s
t h a t
SIMULINK
i s more
s u i t a b l e f o r a
s m a l l
s y s t e m
f o r
s i m u l a t e d
t e s t s .
E x e c u t i o n
s p e e d
o f t h e
s i m u l a t i o n
s y s t e m
w i l l
b e c o m e s l o w
w h e n
s i m u l a t i n g s y s t e m
i s
l a r g e . L u c k i l y ,
t h e
p r o t e c t i v e
r e l a y s
a r e
f o r
p r o t e c t i o n
o f
o n e
a r t i c l e
o f
e l e c t r i c a l
e q u i p m e n t ,
s o
we
j u s t
f o c u s
o n
p r o t e c t e d
e q u i p m e n t .
O t h e r
c o m p o n e n t s
c a n
b e
m a d e i n
e q u i v a l e n t
v a l u e .
T h e r e f o r e ,
b y
r e d u c i n g
t h e
c o m p l e x i t y
o f
t h e
s i m u l a t i o n
s y s t e m , t h e
s i m u l a t i o n
s y s t e m
r e s u l t w i l l
b e i n
h i g h
p e r f o r m a n c e .
Z s
ZR
s
r e l a y
F i g .
1 .
O n e - l i n e
d i a g r a m
o f
s i m u l a t i o n
s y s t e m
F i g .
2 .
S I M U L I N K / P o w e r
S y s t e m
B l o c k
c o n s t r u c t s
t h e
s i m u l a t i o n
s y s t e m s
d i a g r a m
2 5 5
v s _
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S u b s y b m
I m e s k )
Pa
disle
1 3 0
f a - t _ l t _ m
1 3 1 6 0
- l
I I
_m
f i g
i 6 o ;
F i g . 3 .
M a i n
w i n d o w
a n d p a r a m e t e r
i n t e r f a c e
f o r
s i m u l a t i o n s y s t e m s
T h i s s e c t i o n
d e s c r i b e s
t h e p e r f o r m a n c e t e s t
a n d
v e r i f i c a t i o n
o f t r a n s m i s s i o n
l i n e p r o t e c t i o n o f
d i s t a n c e
r e l a y s
u s i n g MATLAB/SIMULINK.
How t o us e
SIMULINK o f
t h e
PSB t o
b u i l d
t r a n s m i s s i o n l i n e s
s y s t e m s
m o d e l w i l l
b e d i s c u s s e d as f o l l o w s .
W i t h
r e f e r e n c e
t o F i g . I O n e - l i n e
d i a g r a m
o f s i m u l a t i o n
s y s t e m ,
we can
e s t a b l i s h t h e
s i m u l a t i o n s y s t e m d i a g r a m i n F i g .
2 .
T h e
s i m u l a t i o n system o f e a c h
e n d source can b e r e p l a c e d
b y
t h e T h e v e n i n e q u i v a l e n t
c i r c u i t s .
H o w e v e r ,
we
can
c o m p l e t e l y f i n i s h
a l l o f
t h e
t e s t c i r c u i t s
w i t h
t h e
us e
o f t h e
source
a n d
t h e
m o d e l o f c o u p l in g
component. E a c h
e l e m e n t
v a l u e o f
t h e
t e s t
s y s t e m
can
b e
s e t b y
power
f l o w
d a t a
a n d s h o r t - c i r c u i t
c a p a c i t y
d a t a . G e n e r a l l y
s p e a k i n g ,
we n e e d t o
g e t v o l t a g e s
a n d
c u r r e n t
s i g n a l d a t a b y c u r r e n t
t r a n s f o r m e r ( C T )
a n d
v o l t a g e
t r a n s f o r m e r ( V T ) as s h o w n
i n F i g . 2 CTS
a n d VTS
r e s p e c t i v e l y
b e c a u s e d i s t a n c e
r e l a y s
n e e d t h r e e - p h a s e v o l t a g e s
a n d
t h r e e - p h a s e c u r r e n t s
f o r t h e i m p e d a n c e c a l c u l a t i o n .
T h e d e s i g n o f d i g i t a l
d i s t a n c e
r e l a y s o f a l g o r i t h m
i s b a s e d
on t h e
component o f
f u n d a m e n t a l f r e q u e n c y
( 6 0 H z ) . When
power
s y s t e m s
f a u l t
occurs,
t h e
s i g n a l s
may c o n t a i n h i g h f r eq ue n c y
c o m p o n e n t s . T h e s e h i g h e r f r e q u e n c y components
must
b e
e l i m i n a t e d ,
so we a d o p t a n a l o g u e l o w
pass f i l t e r s o f b l o c k
i n t h e
s i m u l a t i o n
s y s t e m s
i n
SIMULINK. T h is b l o c k can
b e
d e f i n e d
as
f i l t e r o f t y p e s ( L o w pass, B a n d pass, a n d
H i g h
p a s s ) , o r d e r , a n d
c u t - o f f f r e q u e n c y e t c .
b y u s e r .
T h e s e
are
e x c e l l e n t
c h a r a c t e r i s t i c s .
I n a d d i t i o n ,
SIMULINK p r o v i d e s
some
o p t i o n s
l i k e r e a l - t i m e d i s p l a y ,
s t o r i n g d a t a i n WORKSPACE
a n d h a r d d i s k
a f t e r t h e
s i g n a l s d a t a i s r e l e a s e d
b y f i l t e r .
As
s h o w n i n F i g . 2 , we
c a p t u r e s i g n a l s a n d s t o r e
t h e m i n
WO R K SPACE
f r o m
t h e
s i m u l a t i o n
s y s t e m s ,
w h i c h
i s p r o v i d e d
f o r
u s i n g
i n p u t
o f
d i s t a n c e
r e l a y
a l g o r i t h m .
A b o u t
t r a n s m i s s i o n
l i n e s
m o d e l ,
SIMULINK
p r o v i d e s
P i a n d d i s t r i b u t i o n m o d e l ,
w h i c h can
s e t s p a r a m e t e r s
as n u m b e r s o f
p h a s e ,
f r e q u e n c y , r e s i s t a n c e ,
i n d u c t a n c e , c a p a c i t o r ,
a n d l i n e
l e n g t h
e t c . T h i s
p a p e r
u s e s
d i s t r i b u t i o n
m o d e l
f o r
t r a n s m i s s i o n l i n e
m o d e l
o f t h e
p o w e r s y s t e m s
s i m u l a t i o n .
I n
F i g . 2 ,
t h e
b l o c k f o r
f a u l t
t y p e s e l e c t i o n
a n d f a u l t
r e s i s t a n c e s
s e t t i n g a r e l o c a t e d
b e l o w
t w o
d i s t r i b u t i o n m o d e l
b l o c k s .
H e r e ,
we h a v e f i n i s h e d t h e p o w e r s y s t e m s i m u l a t i o n
m o d e l
a s s h o w n
i n
F i g . 2 , b u t
t h e g r a p h i c s h o w n i n
w i n d o w i s a
b i t
m e s s y .
T h u s
t h e
SUBSYSTEM b l o c k
i s
u s e d b y c o v e r i n g a l l
o f
b l o c k s
t o p r o d u c e
a
s i n g l e
b l o c k ,
a s
s h o w n
i n
F i g .
3 .
F a u l t
s i m u l a t i o n
b l o c k .
I f
we
d o u b l e
c l i c k t h e b l o c k ,
t h e
i n t e r a c t i v e i n t e r f a c e
w i n d o w
o n
r i g h t
s i d e
o f
F i g .
3 . w i l l
b e
s h o w n a g a i n ,
i n
w h i c h t h e i n t e r f a c e
w i n d o w
c a n r e n e w
s o m e
p a r a m e t e r s
f o r n e x t t i m e
s i m u l a t i o n
w h e n t h e
s i m u l a t i o n i s f i n i s h e d .
I n
a d d i t i o n ,
we
c a n s i m u l a t e m a n y c a s e s a t t h e s a m e
t i m e .
A s
d i s c u s s e d
a b o v e , t h e
p r o t e c t i v e
r e l a y
s i m u l a t i o n
s y s t e m
h a s
b e c o m e
a
s y s t e m
o f
e a s y u s e a n d w i t h e f f i c i e n c y .
4 3 7
MATLAB
WORKSPACE
I
F i g .
4 .
P r o t e c t i v e
r e l a y
t e s t systems
b a s e d onMATLAB/SIMULINK
H e r e , w h e n
we
com p are
MATLAB/SIMULINK
w i t h
E M T P / A T P ,
we
w i l l
see w h i c h on e
i s b e t t e r f o r t h e
p r o t e c t i v e r e l a y s i m u l a t i o n
s y s t e m s . T h e
f o l l o w i n g i t e m s
s u m m a r i z e
t h e i r most i m p o r t a n t d i f f e r e n c e s
i n
p r o t e c t i o n
s y s t e m s s i m u l a t i o n :
1 .
T h e EMTP/
ATP
i s
s p e c i f i c
s o f t w a r e t o s i m u l a t e
power s y s t e m t r a n s i e n t
p r o b l e m ,
w h e r e a s
t h e
MATLAB/SIMULINK
can
b e
u s e d
t o s i m u l a t e
power
s y s t e m
f a u l t s
a n d
p r o t e c t i v e
r e l a y a l g o r i t h m
a t t h e
s a m e t i m e .
2 . ATP/EMTP i s d e s i g n e d
t o s i m u l a t e
t h e p h y s i c a l
processes
o f
t r a n s m i s s i o n
l i n e s a n d t r a n s f o r m e r s
q u i c k l y
a n d
i n
a
c o n v e n i e n t
way b u t
2 5 6
MATLAB
P o w e r S y s t e m s o f
F a u l t
S i m u l a t i o n o f M a i n P r o g r a m s
S I M U J L I N K - B a s e d
S i m u l a t i o n S y s t e m s
. n= -
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MATLAB/SIMULINK o f f e r s m o r e
p o s s i b i l i t i e s
i n
p o w e r
e l e c t r o n i c s , s i g n a l
p r o c e s s i n g
a n d
c o n t r o l .
3 .
U s e r s c a n
e a s i l y c r e a t e new
r e l a y
m o d e l
w i t h
M A T L A B / S I M U L I N K ,
w h e r e a s EMTP/ ATP
d o e s n ' t
h a v e
s u c h
c a p a c i t y .
4 .
MATLAB/SIMULINK
e n c o m p a s s e s
b e t t e r
g r a p h i c
f u n c t i o n
t o o l s
t h a n EMTP/ATP
o f
P C P L O T ,
PLOTXY
a n d
s o o n .
T h e r e f o r e ,
t h i s
p a p e r
s e l e c t s
MATLAB/SIMULINK
f o r
i n t e r a c t i v e
a u t o m a t i c
r e l a y
t e s t
s y s t e m s .
I V .
INTERACTIVE
RELAY
TEST
SYSTEMS
B a s e d o n t h e
d i s c u s s i o n m a d e i n t h e
p r e v i o u s
t w o
s e c t i o n s ,
we
c a n
e s t a b l i s h
i n t e r a c t i v e
r e l a y
t e s t
s y s t e m s
b a s e d
o n
MATLAB/SIMULINK
a s s h o w n i n
F i g .
4 .
W e
c a n u s e
M A T L A B
t o
w r i t e m a i n
p r o g r a m
f o r
p r o t e c t i v e
r e l a y t e s t . T h e m a i n
p r o g r a m
c a n n o t
o n l y
s t a r t
f a u l t
s i m u l a t i o n
s y s t e m s
w i t h
SIMULINK
b u t
a l s o
g i v e
c o m m a n d s a n d
p a r a m e t e r s
t o r e n e w
s i m u l a t i o n
s y s t e m s
a t
t h e
s a m e
t i m e . A s
i n d i c a t e d
i n
F i g .
3 ,
we
c a n
c h a n g e
p a r a m e t e r s
o f
s i m u l a t i o n
s y s t e m s
i n c l u d i n g
f a u l t
l o c a t i o n s ,
f a u l t
r e s i s t a n c e s ,
f a u l t
t i m e ,
a n d
f a u l t
t y p e s
e t c . ,
a n d
t h e n
t h e m a i n
p r o g r a m
w i l l
e x e c u t e
s e t t i n g
a n d
c h a n g e
v a l u e .
F i n a l l y
t h e m a i n
p r o g r a m
c o n t r o l s
SIMULINK e x e c u t i o n
d y n a m i c
o f
s i m u l a t i o n a s
s h o w n o n
F i g .
2 .
A f t e r
t h e
s i m u l a t i o n
i s
f i n i s h e d ,
t h e s i m u l a t i o n
r e s u l t
d a t a
w i l l
b e
s t o r e d i n
WO RKSPACE o r h a r d
d i s k ,
a n d i t s
w a v e f o r m
c a n
b e
s h o w n
d i r e c t l y
o n s c r e e n
t h r o u g h
u s e r ' s
c o m m a n d .
S o
f a r
we
h a v e
f i n i s h e d
f a u l t s i m u l a t i o n
t a s k ,
a n d t h e n
g o t
r e l a t e d
i n p u t
d a t a
f o r
p r o t e c t i v e
r e l a y a l g o r i t h m .
A s f a r a s
t h e d i s t a n c e
r e l a y s
i n
t h i s
p a p e r
a r e
c o n c e m e d ,
we n e e d
t o
g e t
t h r e e - p h a s e
v o l t a g e s
a n d
t h r e e - p h a s e
c u r r e n t s
f r o m
S
t e r m i n a l
( F i g . 1 . ) .
I n
t h e n e x t
s t e p ,
i n p u t t h e s i m u l a t i o n
r e s u l t d a t a
t o
p r o t e c t i v e
r e l a y
a l g o r i t h m b y MATLAB
t o
d i s t i n g u i s h
w h e t h e r
t h e
c i r c u i t
b r e a k e r
( C . B . )
a c t i o n
o c c u r s
o r
n o t
f r o m
p l a n l o g i c .
When
t h e
f a u l t
i m p e d a n c e
i s
c a l c u l a t e d
a n d
i t
i s
s a t i s f i e d i n t h e
p r o t e c t i o n
z o n e
1 , t h e
p r o t e c t i v e
r e l a y o p e r a t i o n
t h e n
r e l e a s e s
t r i p s i g n a l t o
C . B .
w i t h o u t
a d d i t i o n a l
d e l a y . H e r e ,
MATLAB
c a n
e a s i l y
s h o w
i m p e d a n c e t r a c e o n
s c r e e n
f o r
u s e r ' s
v e r i f i c a t i o n ,
a n d
s t o r e
t h e
t e s t
r e c o r d s .
S o
f a r
we
h a v e
o n l y
f i n i s h e d o n e
f a u l t
c a s e f o r
v e r i f i c a t i o n
r e l a y
a c t i o n . A f t e r
t h i s
t e s t
i s
f i n i s h e d ,
t h e
m a i n
p r o g r a m
c a n
a u t o m a t i c a l l y c h a n g e
p a r a m e t e r s
a g a i n
t o e x e c u t e
s i m u l a t i o n s , t e s t s ,
a n d
r e c o r d s
c o n t i n u a l l y .
W i t h
t h e
i n c l u s i o n o f
t h e
l o o p
f u n c t i o n a n d
t h e
m o d i f i c a t i o n
o f
s y s t e m
p a r a m e t e r s ,
t h e m a i n
p r o g r a m c a n
f i n i s h
h u n d r e d s
a n d
t h o u s a n d s
o f
c a s e
t e s t s
a t
t h e
s a m e
t i m e
t o
m e e t
t h e
p u r p o s e o f
h a v i n g
a u t o m a t i c
t e s t s
f o r
p r o t e c t i v e
r e l a y s .
T h e
r e a s o n
w h y
t h i s
f u n c t i o n
i s s o
p o w e r f u l
i s
t h a t
we
i n t e g r a t e MATLAB/SIMULINK
i n t o
o n e
s i n g l e e n v i r o n m e n t a n d
m a k e
u s e o f
i t s
e a s y
c o m m u n i c a t i o n
f u n c t i o n .
I n
a d d i t i o n
t o t h e
a b o v e - m e n t i o n e d
a d v a n t a g e o f
a u t o m a t i c
p r o t e c t i v e
r e l a y
t e s t s ,
M A T L A B
c a n
e m p o w e r
u s
t o
m o d i f y
a n d
a d j u s t
t h e
p r o b l e m s
t h a t
t h e i n i t i a l
r e l a y
d e s i g n may h a v e .
W i t h
t h e
p o w e r f u l
g r a p h i c f u n c t i o n
b y
M A T L A B
we
c a n
u s e
t h e
p r o g r a m
t o o b t a i n
e a s i l y o u t p u t
s i g n a l
v a l u e s a n d
w a v e f o r m s
f o r
r e l a y
a l g o r i t h m s
v e n r f i c a t i o n . I f
t h e
r e l a y a l g o r i t h m
i s
b a d ,
t h e n
m o d i f y
i t
i m m e d i a t e l y .
I t
i s
v e r y
c o n v e n i e n t
f o r
d e s i g n i n g
p r o t e c t i v e
r e l a y
a s
w e l l a s
f o r
c h e c k i n g
w h e t h e r
t h e
s e t t i n g
o f
t h e
i n t e r a c t i v e
r e l a y
t e s t
e n v i r o n m e n t
i s
a p p r o p r i a t e .
V . EXAMPLE
Now t h a t
t h e
t h e o r y
a n d
t h e
s t r u c t u r e
o f
t h e
i n t e r a c t i v e
r e l a y
t e s t
s y s t e m
a r e
p r e s c r i b e d , t h e
f o l l o w i n g
b e g i n s
w i t h a n
e x a m p l e
o f
a
p o w e r
t r a n s m i s s i o n
l i n e
o f
f a u l t
s i m u l a t i o n
t o
t e s t
r e l a y o p e r a t i o n . F i g .
1
d e p i c t s
t h e
3 4 5
k V ,
6 0 Hz
s i m u l a t e d
s y s t e m o n e - l i n e
d i a g r a m . F i g .
2
i s
t h e
s i m u l a t e d
s y s t e m
m o d e l
b y
S I M U L I N K . T h e
o t h e r
r e l a t e d
p a r a m e t e r s
o f
t h e s i m u l a t e d
s y s t e m a r e
s h o w n
i n
T a b l e 2 .
Z o n e
1
i s
s e t t i n g
80 o f
t h e
t o t a l
l i n e
l e n g t h .
T h i s
e x a m p l e
u s e s
MHO
t y p e
t o
e x p l a i n
t h e
r e l a y
o p e r a t i o n
p e r f o r m a n c e . T h e m i m i c
f i l t e r s w it h t im e c o n s t a n t
2
c y c l e s ,
t h e
p h a s e
d i f f e r e n c e
b e t w e e n
E S a n d ER i s
1 5
d e g r e e s ,
a n d
t h e
s a m p l i n g f r e q u e n c y
i s
1 9 2 0
H z . T h e
t r a n s m i s s i o n
l i n e
l e n g t h
i s
1 0 0 k m .
T h e
p h a s o r i s
e s t i m a t e d
b y
f u l l - c y c l e
D F T .
T a b l e
2
T h e
p a r a m e t e r s
o f
t h e s i m u l a t i o n
t r a n s m i s s i o n
s y s t e m
F i r s t , In o r d e r
t o
prove d i g i t a l
d i s t a n c e
r e l a y o f
p e r f o r m a n c e ,
an
i n t e m a l
f a u l t i s
a p p l i e d
t o t h e power
s y s t e m
w i t h
t h e
p h a s e
A
t o
g r o u n d
f a u l t , t h e f a u l t
r e s i s t a n c e i s 1
o h m ,
t h e
f a u l t
a n g l e i s
zero
d e g r e e ( r e f e r
t o
S t e r m i n a l
o f
p h a s e
A
v o l t a g e s
w a v e f o r m ), a n d t h e
f a u l t i s
l o c a t e d
s i x t y k i l o m e t e r s
f o r m S
t e r m i n a l .
T h e r e f o r e ,
t h e
f a u l t
c u r r e n t s
w i l l i n c l u d e
d c - o f f s e t
c o m p o n e n t s .
F i g .
5
s h o w s t h e
p h a s e
A
c u r r e n t
w a v e f o r m ,
t h e
p h a s e
A
v o l t a g e
w a v e f o r m , a n d
t h e
i m p e d a n c e
t r a c e
f o r
t h e s i n g l e p h a s e t o
g r o u n d f a u l t .
J u d g i n g
f r o m
F i g . 5 - ( a )
a n d
( b ) ,
f i l t e r s
can
b e
e l i m i n a t e d
h i g h
f r e q u e n c y
components
f o r m
t h e f a u l t
w a v e f o r m ,
b u t
r e s u l t
i n
s i g n a l s
t i m e
d e l a y .
T h e r e f o r e , t h e
c u t o f f
h i g h
f r e q u e n c y c a n ' t
b e
s e t t o o
l o w ,
o t h e r w i s e ,
t h e
r e l a y
o p e r a t i o n t i m e
can b e
a f f e c t e d .
As s h o w n
i n
F i g .
5 t h e
m i m i c
f i l t e r can
e f f e c t i v e l y
remove
t h e
d e c a y i n g
d c
c o m p o n e n t .
I f
t h e f i l t e r
i s
no
us e i n
t h e
r e l a y a l g o r i t h m , t h e n t h e
c u r r e n t p h a s o r
r e s u l t s i n u n s t a b l e
p h e n o m e n o n a n d t h e
i m p e d a n c e t r a c e
w i l l
b e
o s c i l l a t e d . T h e
r e l a y may
m a l f u n c t i o n
w h e n
some
257
V o l t a g e
R a t i n g :
3 4 5
kV
S y s t e m f r e q u e n c y : 6 0
Hz
E q u i v a l e n t
V o l t a g e
Pe r U n i t :
E S = 1 / Z 5 ( p . u . ) , E R
= 1 Z 0 ( p . u . )
E q u i v a l e n t
S o u r c e
I m p e d a n c e :
z s i
= 0 . 2 3 8
+
5 . 7 2 ( Q ) ,
Z s o
2 . 7 3 8 + 1
0 ( Q )
Z R I
= 0 . 2 3 8 + 6 . 1 9 ( Q ) ,
Z R 0
= 0 . 8 3 3 + 5 . 1 2 ( Q )
L e n g t h
o f
T r a n s m i s s i o n
L i n e : 1 0 0
km
L i n e
C o n s t a n t :
R o
=
0 . 2 7 5 ( Q ) ,
L o
=
3 . 7 2 5 ( m H ) ,
C 0
=
6 . 7 1
l ( n F )
R I
=
0 . 0 2 7 5 ( Q ) ,
L I
=
1 . 3 4 5 ( m H ) , C l
=
9 . 4 8 3 ( n F )
F i l t e r :
2
O r d e r o f
B u t t e r w o r t h
Lo w P a s s
F i l t e r H i g h
C u t - O f f
F r e q u e n c y
3 6 0 ( H z )
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f a u l t s
o c c u r i n n e a r
p r o t e c t i o n z o n e
m a r g i n .
I n
o t h e r
w o r d s ,
t h i s
i s
m a i n r e a s o n
w h y
we w a n t t o r e m o v e
t h e
d e c a y i n g
d c
c o m p o n e n t .
X
1 . ,
0
1 0
2 0
3 0
4 0
5 0
6 0
l i m e
( m s )
. ^
} ~ ~ ~ ~ ~ ~ ~ ~
0 1 0 2 0
3 0
t i f e
5 1 0
3
2 . 2 5
X
51
2
a
0
1 0
2 C 3 0
t i m e
6 0 0 0 1
I~~~~
z
.
4 O . -
F
2 0 0 0
-.
0
0
1 0 2 0
3 0
t i r
t 4 2
X ,
- 2 0 0
2 0
4 0 5 0
6 0
a d o p t s
f u l l - c y c l e
DFT
a l g o r i t h m .
F i n a l l y ,
t h e z o n e
1
f a u l t
o f
i m p e d a n c e
t r a c e i s
s h o w n
i n
F i g . 5 - e ) .
D u e
t o t h e
d i a g r a m
w e
c a n f i n d t h e
i m p e d a n c e
t r a c e
i n c l u d e d
b y
zone
1 ; t h e r e f o r e ,
t h e
r e l a y
r e l e a s e s a
t r i p
s i g n a l
t o C . B b e c a u s e
t h e
r e l a y
d e t e c t s t h e f a u l t
b e l o n g i n g
t o z o n e
1 .
B e l o w i s
a
p h a s e
A- B
f a u l t t e s t
c a s e .
T h e f a u l t
l o c a t i o n , n i n e t y
k i l o m e t e r s
f o r m
S
t e r m i n a l ,
i s
i n
z o n e
2 ,
s o
i t
w o n t
a f f e c t
t h e
p r o t e c t i v e
r e l a y .
T h e
z o n e
2
u s u a l l y
g i v e s
a
t i m e
d e l a y
a b o u t
t w e n t y c y c l e s
a s
T P C s
( T w a i n
P o w e r
C o m p a n y )
p o w e r
n e t w o r k s .
T h e
F i g .
6
s h o w s
t h e
i m p e d a n c e
t r a c e
e x c l u d e d
i n
z o n e
1 ,
s o t h e
r e l a y
o p e r a t e d
w i t h
a t i m e
d e l a y .
T h e a b o v e
t w o c a s e s a r e
i l l u s t r a t e d t o
e x p l a i n p r o t e c t i v e
r e l a y s
o f
o p e r a t i o n
a n d
t e s t
b y
MATLAB/SIMULINK. I n
f a c t ,
we
c a n
a p p l y
a u t o m a t i c
m o d e
f o r more
p r o t e c t i v e
r e l a y
t e s t .
V I .
CONCLUSION
m s )
T h i s
p a p e r
d e s c r i b e s t h e
a u t o m a t e d
p r o t e c t i v e
r e l a y
t e s t
s y s t e m
b a s e d
on
M A T L A B / S I M U L I N K .
T h e
s y s t e m
c o m b i n e s
MATLAB
w i t h
SIMULINK f o r t h e
u s e o f
MATLAB f o r
m a i n
c o n t r o l
p r o g r a m s
a n d
c a r r y o u t
r e l a y
a l g o r i t h m s , a n d
t h e u s e
o f
SIMULINK o f PSB
f o r
p o w e r
1- 1
s y s t e m
c o n s t r u c t e d
t o o l s .
D u e
t o
t h a t f a c t t h a t
b o t h
MATLAB
a n d SIMULINK
a r e i n
t h e
s a m e
e n v i r o n m e n t
Z 5 0 6 0
c o m m u n i c a t i o n s
a n d
c o n v e n i e n t
t e s t s
c a n
b e
m a d e
e a s i l y .
( M s )
E s p e c i a l l y
s i n c e t h e MATLAB
h a s
p o w e r f u l
c a p a b i l i t i e s
i t
f o r
n u m e r i c a l
r o b u s t
a n d
g r a p h i c
f u n c t i o n .
I n
a d d i t i o n , t h e
SIMULINK
h a s
p o w e r f u l
c a p a b i l i t i e s
f o r
GUI
i n t e r f a c e
a n d
m o r e a n d
m o r e
m o d e l l i n g f o r
t h e
g e n e r a t i o n ,
t r a n s m i s s i o n ,
a n d
d i s t r i b u t i o n o f
e l e c t r i c a l
p o w e r
e t c . . .
T h e s e
a d v a n t a g e s c a n
h e l p p r o t e c t i o n
e n g i n e e r
e f f e c t i v e l y
e n h a n c e t h e
p e r f o r m a n c e
o f t h e
d i g i t a l p r o t e c t i v e
r e l a y
v >
w
d e s i g n ,
s e l e c t i o n ,
a n d e l e c t
s e t t i n g .
I t s
a b i l i t y
o f
m a s s i v e
4 0
5 0 6 0
m e )
t e s t s
a n d
r e s u l t
r e c o r d s i s
e x c e l l e n t
a n d
c o n v e n i e n t
f o r
- - - - - - - - - - - - - - - -
s a v i n g t i m e
a n d
c o s t s .
4 0 6 0
8 0
1 0 0 1 2 0
1 4 0
R e s i s t a n c e
( o h m )
e )
F i g .
5 .
T h e
v o l t a g e s
t h e c u r r e n t
a n d
t h e
i m p e d a n c e
t r a c e i n
i n t e r n a l
f a u l t
- 2 0
0
2 0
4 0
6 0
8 0
0 0
1 2 0
1 4 0
R e s i s t a n c e
( o h m )
F i 1 , .
6 .
T h e
i m p e d a n c e
t r a c e i n z o n e
2
f a u l t
T h e
F i g .
5 - ( c )
a n d
( d )
i n d i c a t e t h e
p h a s o r
e s t i m a t i o n
r e s u l t s
using
c o n v e n t i o n a l
f u l l - c y c l e DFT
a f t e r t h e
v o l t a g e
a n d
t h e c u r r e n t
s i g n a l s pass f i l t e r s . I f
we
want
t o
g e t b e t t e r
accuracy
f o r
t h e
p h a s o r
v a l u e s ,
a t
l e a s t one
c y c l e o f
t h e
c o m p u t a t i o n
t i m e
s h o u l d
b e
a d o p t e d
b e c a u s e
t h i s pa per
V I I .
REFERENCES
[ 1 ] A l t e m a t i v e T r a n s i e n t
P r o g r a m R u l e
B o o k , E u r o p e a n
EMTP
C e n t e r ,
1 9 8 7 .
[ 2 ]
T h e M a t h
W o r k s ,
I n c . , U s i n g
MATLAB .
1 9 9 9 .
[ 3 ]
T h e M a t h
W o r k s , I n c . ,
P o w e r
S y s t e m
B l o c k s e t
U s e r s
G u i d e ,
1 9 9 9 .
[ 4 ]
G . S y b i l l e
a n d
L . - H .
H o a n g , D i g i t a l S i m u l a t i o n o f
P o w e r
S y s t e m s
a n d
P o w e r
E l e c t r o n i c s
u s i n g t h e
MATLAB/SIMULINK
P o w e r
S y s t e m
B l o c k s e t ,
I E E E / P E S
W i n t e r
M e e t i n g , 2 0 0 0 ,
p p .
2 9 7 3 - 2 9 8 2 .
[ 5 ]
T .
S .
S i d h u ,
D . S .
G h o t r a ,
a n d M . S .
S a c h d e v , A
F a s t
D i s t a n c e
R e l a y
U s i n g
A d a p t i v e
D a t a
Window
F i l t e r s ,
I E E E / P E S
Summer
M e e t i n g ,
J u l y 2 0 0 0 , p p .
1 4 0 7 - 1 4 1 2 .
[ 6 ]
G . B e n m o u y a l ,
R e m o v a l
o f
D e c a y i n g DC i n
C u r r e n t
W a v e f o r m s
U s i n g
D i g i t a l M i m i c F i l t e r i n g , I E E E
T r a n s .
o n
P o w e r
D e l i v e r y ,
V o l .
1 0 ,
N o .
2 ,
A p r i l 1 9 9 5 ,
p p . 6 2 1 - 6 3 0 .
[ 7 ]
K . E l - A r r o u d i .
G .
J o o s ,
a n d
D T .
M c G i l l i s ,
' O p e r a t i o n o f
I m p e d a n c e
P r o t e c t i o n R e l a y s
W i t h t h e
STATCOM ,
I E E E
T r a n s .
o n P o w e r
D e l i v e r y ,
V o l .
1 7 ,
N o .
2 , A p r i l 2 0 0 2
p p . 3 8 1 - 3 8 7 .
L i - C h e n g
Wu
r e c e i v e d
h i s B . S
a n d
M . S .
d e g r e e s i n
e l e c t r i c a l
e n g i n e e r i n g f r o m
N a t i o n a l T a i w a n
U n i v e r s i t y
o f
S c i e n c e
a n d
T e c h n o l o g y , T a i p e i ,
T a i w a n ,
i n 1 9 9 7 a nd
1 9 9 9 ,
r e s p e c t i v e l y .
He
i s
c u r r e n t l y
p u r s u i n g t h e P h . D .
d e g r e e
a t
N a t i o n a l T a i w a n
U n i v e r s i t y ,
T a i p e i ,
T a i w a n .
B e t w e e n
1 9 9 7
t o
2 0 0 2 h e
w o r k e d
a s a n
e l e c t r i c a l
enginee r i n
t h e
D e p a r t m e n t o f
r e l a y ,
T a i w a n P o w e r
C o m p a n y .
258
V .
~ 0 0
0
1
\
. 1
/
.
..
.
a
1
1 . .
\
to
8 0
E 6 0
8
4 0
:
. 1 2 0
0
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