Diagonal elements $Y_{ii}$ and $Y_{jj}$ include the sum of all admittances connected to the respective bus.

Off-diagonal elements $Y_{ij}$ represent the negative of the admittance connected between buses $i$ and $j$.

Adding an element between two distinct buses always affects four entries in the $Y_{bus}$ matrix due to the symmetry of the network.

This calculation is fundamental for building the $Y_{bus}$ matrix using the inspection method.

Simple mathematical update to the $Y_{bus}$ matrix

Efficient for iterative power flow analysis

Requires sparse matrix storage to avoid memory issues for large grids

Manual calculation is prone to sign errors

Load flow studies

Short circuit analysis

Stability studies

For self-admittance (shunt at node $i$), only $Y_{ii}$ is modified.

Option B is incorrect because it ignores the change to the off-diagonal mutual coupling terms $Y_{ij}$ and $Y_{ji}$.