Y-bus is a symmetric matrix if no mutual coupling exists.

Off-diagonal elements $Y_{ij}$ (where $i \neq j$) represent the negative of the admittance between buses $i$ and $j$.

Diagonal elements $Y_{ii}$ include all lines connected to bus $i$ and all shunt elements connected to bus $i$.

Adding shunt admittance does not change mutual coupling parameters if they are zero.

Simplifies power flow calculations

Sparse nature of Y-bus improves computational efficiency

Requires recalculation of diagonal elements if network topology changes

Assumes constant admittance values

Power flow studies (Newton-Raphson, Gauss-Seidel)

Short circuit analysis

The modification $Y_{ii} = Y_{ii} + y$ is a fundamental property used in Gauss-Seidel power flow iterations.

Option A ($Y_{ij}$) and C ($Y_{ji}$) represent mutual admittances between buses $i$ and $j$, which remain unchanged by a shunt connection at node $i$.