...Contd from previous slide

We would like to determine the voltage-current relationships of the network shown in Fig. 3.4. It is to be noted that this relation can be written in terms of the node (bus) voltages V₁ to V₄ and injected currents I₁ and I₂ as follows

(3.3)

 or,

(3.4)

It can be easily seen that we get (3.1) from (3.3) and (3.4).

Consider node (bus) 1 that is connected to the nodes 2 and 3. Then applying KCL at this node we get

(3.5)

In a similar way application of KCL at nodes 2, 3 and 4 results in the following equations

	(3.6)
	(3.7)
	(3.8)

Combining (3.5) to (3.8) we get

(3.9)

Comparing (3.9) with (3.3) we can write

(3.10)

In general the format of the Y_bus matrix for an n -bus power system is as follows

(3.11)

where

(3.12)

It is to be noted that Y_bus is a symmetric matrix in which the sum of all the elements of the k th column is Y_kk .

Do an example