Adding an Impedance between two Existing Buses
Let us assume that we add an impedance Zb between two existing buses k and j as shown in Fig. 3.9. Therefore the current injected into the network from the bus k side will be Ik - Ib instead of Ik. Similarly the current injected into the network from the bus j side will be Ij + Ib instead of Ij. Consequently the voltage of the ith bus will be
 |
(3.36) |
Similarly we have
 |
(3.37) |
and
 |
(3.38) |
Fig. 3.9 An impedance is added between two existing buses.
We shall now have to eliminate Ib from the above equations. To do that we note from Fig. 3.9 that
 |
(3.39) |
Substituting (3.37) and (3.38) in (3.39) we get
 |
(3.40) |
We can then write the voltage current relations as
 |
(3.41) |
where
 |
(3.42) |
We can now eliminate the last row and last column using the Kron's reduction given in (3.21). |
