Electrical Power Systems

234 Electrical Power Systems
or V s = E s – Z s I s ...(9.51)
where Z s = A –1 Z p A ...(9.52)
\ Z s = 1
3
\ Z s = 1
3
\ Z s = 1
3
\ Z s =
or
L
NM
O
Q
Va1
Va2
V P ao
=
L
NM
L
NM
L
NM
L
NM
Note that E a1 = E a, E a2 = E a0 = 0
\
L
NM
O
Q
Va1
Va2
V P a0
=
2
OL
QP
N
O
QP
L
NM
1 b b Zs + Zn Zn Zn
1 1 1
2 2
1 b b Zn Zs + Zn Zn
b b 1
1 1 1M
Z Z Z + Z
2
n n s n b b 1
Zs
bZs b Zs
1 1 1
2 2
Zs b Zs bZs b b 1
Z 3Z Z 3Z Z 3Z
2
s + n s + n s + n b b 1
0
b
0 O
gQP
bZs O
3ZngQP
3Zs
0 3Zs
0
3 Zs 3Zn
0 0 +
0 0
Zs
0 Zs
0
L
NM
0 0 +
O
Q
L
NM
0 0
Ea1
Zs
Ea2
– Zs
E P 0 0
a0
Zs + 3Zn
L
NM
O
Q
L
N
0 0
2
OL
b gQPNM
O
QP
L
N
Ia1
I a2
I a0
O
Q
OL
QP
NM
O
QP
O
QP
O
QP
...(9.53)
Ea Zs
0 0 I a1
0 – 0 Zs
0 Ia2
...(9.54)
0 P M 0 0 Zs + 3Z
M n I P a0
or V a1 = E a – Z 1 I a1 ...(9.55)
V a2 = –Z 2 I a2
V a0 =–Z 0 I a0
...(9.56)
...(9.57)
where Z 1 = Z s, Z 2 = Z s and Z 0 = Z s + 3Z n
Positive, negative and zero-sequence network of synchronous machine is shown in ig. 9.4.