Ybus with nominal π model, line lengths

With the nominal π model, each line's total series reactance is $x \times \text{length}$ and its total shunt susceptance $B = b \times \text{length}$ is split as $B/2$ at each end. Resistance is not given, so it is taken as zero.

Given: $x = 0.001$ pu/km, $b = 0.0016$ pu/km.

Step 1: Line parameters

Step 2: Diagonal elements

$Y_{ii}$ = sum of series admittances at bus $i$ + sum of half-line-charging susceptances at bus $i$:

$$\begin{aligned} Y_{11} &= (-j10 - j5) + j(0.08 + 0.16) = -j14.76 \\ Y_{22} &= (-j10 - j2.5) + j(0.08 + 0.32) = -j12.10 \\ Y_{33} &= (-j5 - j2.5) + j(0.16 + 0.32) = -j7.02 \end{aligned}$$

Step 3: Off-diagonal elements

$$\begin{aligned} Y_{12} &= Y_{21} = -y_{12} = j10 \\ Y_{13} &= Y_{31} = -y_{13} = j5 \\ Y_{23} &= Y_{32} = -y_{23} = j2.5 \end{aligned}$$

Result

$$Y_{bus} = \begin{bmatrix} -j14.76 & j10 & j5 \\ j10 & -j12.10 & j2.5 \\ j5 & j2.5 & -j7.02 \end{bmatrix}\ \text{pu}$$

Answer: $Y_{11} = -j14.76$, $Y_{22} = -j12.10$, $Y_{33} = -j7.02$, $Y_{12} = j10$, $Y_{13} = j5$, $Y_{23} = j2.5$ pu. The shunt charging only reduces the magnitude of the diagonal terms; off-diagonal terms are unaffected.