
Modern Power System Analysis with MATLAB Applications
288
They are represented by,
I
bus
()1
=
1
2
0
0
0
0
0
1
p
N
I
fa
−
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
()
and pre-fault voltage =
1
1
1
1
1
1
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
f
(6.57)
The positive sequence bus voltages in the faulted system namely,
bus
()1
=
1
2
1
1
2
1
1
1
p
N
V
V
V
V
a
a
pa
Na
()
()
()
()
⎡
⎣
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
(6.58)
can be obtained using ‘Superposition Theorem’. Due to two sources, the positive sequence bus
voltages in the faulted system are,
bus
()1
=
1
2
1
1
2
1
1
1
p
N
V
V
V
V
a
a
pa
Na
()
()
()
()
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
=
ZZ ZZ
ZZ ZZ
Z
p
11
1
12
1
1
1
1
1
21
1
22
1
2
1
2
1
() () () ()
() () () ()
11
1
2
1
1
1
1
1
2
111
() ()
()
()
() () () ()
ZZZ
ZZ ZZ
p
pp
pN
NN
Np NN