Electrical Power Systems

Hence,
new
Z =
BUS
8.6.3 Type-3 Modification
L
Z1j
Z2j
old
ZBUS
M
Znj
Z Z L Z Z + Z
NM
j1 j2 jn jj b
O
QP
Symmetrical ault 219
...(8.24)
In this case, an old bus-j is connected to the reference bus-r and the impedance between these
two bus is Z b as shown in ig. 8.24.
Referring to ig. 8.23, if bus K is connected to
reference bus r, V K = 0.
Thus
L
NM
V
V
V
1
2
.
.
.
.
n
o
O
QP
=
L
NM
Z
old
BUS
Znj
Z Z L Z Z + Z
Z
j1 j2 jn jj b
1j
Z
M
2j
O L
QP
NM
I
I
I
I
1
2
M
n
K
O
QP
...(8.25)
rom equ. (8.25), we get,
O = Zj1 I1 + Zj2 I2 + ... + Zjn In + (Zjj + Zb) IK \ IK =
–1
dZjj + Zbi
(Zj1 I1 + Zj2 I2 + ... + Zjn In) ...(8.26)
Expression of voltage for i-th bus can be written as:
Vi = Zi1 I1 + Zi2 I2 + ..... + Zin In + Zij IK rom equations (8.27) and (8.26), we get
...(8.27)
L
NM
\ Vi = Zi1
Zij Zj1
-
Z + Z
+ . . . . . + Z
jj b
L
NM
in
O
QP
L
NM
Zij Zj2
I + Zi2
-
Z + Z
O
QP
1 2
jj b
Zij Zjn
-
Z + Z
jj b
new
By inspection, Z BUS can easily be written from equation (8.28),
O
QP
I
n
I
ig. 8.24: Type–3 modification.
...(8.28)