Question

Determine the 4 x 4 bus admittance matrix Y_bus and write nodal equations in matrix format for the circuit shown in Figure 2.30. Do not solve the equations

Therefore, the nodal equation in the matrix form is,

Short answer

Therefore, the admittance matrix Y_busis

And the nodal equation in the matrix form is

Step-by-step solution

Find the matrix 4x4 from the given circuit. 

The matrix 4x4 is given by

Here the diagonal admittance of the matrix can be calculated as

Y_kksum of the admittance connected to the node K

The non-diagonal admittance can be calculated as

Y_{kn =-}(The sum of the admittance connected between the k and n).

Thus, the admittance matrix of the given figure is shown below.

Write the nodal equation of the given figure.

The standard form of the nodal equation by using the admittance matrix

Substitute the matrix and solve as,

Thus, the nodal equation in the matrix form is,