Adding a New Bus to an Existing Bus through an Impedance

This is the case when a bus, which has not been a part of the original network, is added to an existing bus through a transmission line with an impedance of Z_b . Let us assume that p ( p > n ) is the new bus that is connected to bus k ( k < n ) through Z_b. Then the schematic diagram of the circuit is as shown in Fig. 3.8. Note from this figure that the current I_p flowing from bus p will alter the voltage of the bus k . We shall then have

(3.32)

In a similar way the current I_p will also alter the voltages of all the other buses as

(3.33)

Furthermore the voltage of the bus p is given by

(3.34)

Therefore the new voltage current relations are

(3.35)

It can be noticed that the new Z_bus matrix is also symmetric.

Fig. 3.8 A new bus is added to an existing bus through an impedance.

Adding an Impedance to the Reference Bus from an Existing Bus

To accomplish this we first assume that an impedance Z_b is added from a new bus p to an existing bus k . This can be accomplished using the method discussed in Section 3.3.2. Then to add this bus k to the reference bus through Z_b, we set the voltage V_p of the new bus to zero. However now we have an ( n + 1) X ( n + 1) Z bus matrix instead of an n X n matrix. We can then remove the last row and last column of the new Z_bus matrix using the Kron's reduction given in (3.21).