Electrical Power Systems

212 Electrical Power Systems
In ig. 8.19, we excite the passive Thevenin network with – º
V r is in series with Z f .
Now
DV = ZBUS Cf ...(8.5)
Where ZBUS is the bus impedance matrix of the passive Thevenin network and is given by
Z BUS =
L
NM
Z Z ..... Z
Z21 Z22 ..... Z
M M M M
Z Z ..... Z
11 12 1n
nn
n1 n2 nn
O
QP
...(8.6)
and C f is bus current injection vector. The network is injected with current –I f only at the
r-th bus, we have
C f =
L
NM
0
0
M
I
M
0
= -I
rf f
rom equations (8.5) and (8.7), we obtain,
DV r = –Z rr I f
The voltage at the r-th bus under fault is
Also
ig. 8.19: Thevenin network of ig. 8.18 with
–V
º
r
is in series with Zf .
O
QP
...(8.7)
...(8.8)
Vrf = V + D V = V – Z I
...(8.9)
r º
V rf = Z f I f
r r º
rr f
...(8.10)