Electrical Power Systems

218 Electrical Power Systems
8.6.1 Type-1 Modification
In this case, branch impedance Z b is added from a new bus to the reference bus. That is a new
bus is added to the network and dimension of Z BUS goes up by one.
Notations: i, j – old buses
r – reference bus
K – new bus
igure 8.22 shows a passive linear n-bus power system network. In ig. 8.22, an impedance
Z b is added between new bus K and the reference bus r.
rom ig. 8.22,
V K = Z b I K
\ Z KK = Z b
Therefore,
Z Ki = Z iK = 0; for i = 1, 2, ...., n.
new
Z
BUS
=
L
NM
0
Z
old
BUS
......
0
0
M
M
0
Z
b
O
QP
...(8.22)
old
where ZBUS is bus impedance matrix before adding a new branch.
8.6.2 Type-2 Modification
In this case branch impedance Z b is added from a new bus K to the old bus j as shown in
ig. 8.23.
rom ig. 8.23, we have
ig. 8.23: Type-2 Modification.
V K = V j + Z b I K
ig. 8.22: Type-1 Modification.
\ V K = Z j1 I 1 + Z j2 I 2 + ...... + Z jj (I j + I K) + ...... + Z jn I n + Z b I K
\ V K = Z j1 I 1 + Z j2 I 2 + ...... + Z jj I j + ...... + Z jn I n + (Z jj + Z b ) I K ...(8.23)