Question

The bus impedance matrix of a 4-bus power system is given.

A branch having an impedance of \( j0.2 \Omega \) is connected between bus 2 and the reference. Then the values of \( Z_{22,new} \) and \( Z_{23,new} \) of the bus impedance matrix of the modified network are respectively _______.

 

• A. \( j0.5408 \, \Omega \) and \( j0.4586 \, \Omega \)
• B. \( j0.1260 \, \Omega \) and \( j0.0956 \, \Omega \)
• C. \( j0.5408 \, \Omega \) and \( j0.0956 \, \Omega \)
• D. \( j0.1260 \, \Omega \) and \( j0.1630 \, \Omega \)

Hint:

When connecting a branch to ground (reference), only update diagonal and respective off-diagonal elements using matrix algebra.

Answer 1

The Correct Option is B

Step 1: Use matrix reduction method
A new element (impedance) between bus 2 and reference changes only the 2nd row and column of the matrix.
Step 2: Apply updating formula
The updated impedance \( Z_{ii,new} = Z_{ii,old} - \frac{Z_{ik}Z_{ki}}{Z_{kk}+Z_{new}} \)
Here we substitute based on the matrix given and \( Z_{new} = j0.2 \)
Step 3: Final values from matrix
Updated values from computation match: \( Z_{22} = j0.1260 \), \( Z_{23} = j0.0956 \)