Question

Given the impedance diagram of a simple system as shown in Figure 2.31, draw the admittance diagram for the system and develop 4x4 the bus admittance matrix Y_bus by inspection.

Short answer

Therefore, the admittance for the system is

The admittance matrix for the system is,

Step-by-step solution

convert the impedances into admittances.

The impedance inversely proportional to the admittance. The elation between impedance and admittance is given by

Substitute the values and convert the all impedance into admittance.

Calculate admittance Y₁₂.

Calculate admittance Y₁₃.

Calculate admittance Y₂₁.

Calculate admittance Y₂₀.

Calculate admittance Y₂₃.

Calculate admittance Y₃₄.

Convert all the voltage source into current source and substitute the value in the admittance diagram as

Calculated the admittance matrix of given figure,

The matrix 4x4 is given by

Here the diagonal admittance of the matrix can be calculated as

Y_kk= sum 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.