Question

For the circuit shown in Figure 2.29, (a) determine the 2 X 2 bus admittance matrix (b) convert the voltage sources to current sources and determine the vector of source currents into buses 1 and 2.

Short answer

(a) Therefore, 2 X 2 admittance matrix is

$\left[\begin{array}{c}\begin{array}{c}0.8796+\mathrm{j}3.127-0.4950+4.950\\ -0.4950+\mathrm{j}4.9500.8796+3.127\end{array}\end{array}\right]$

(b) The vector of the current source

$\left[\begin{array}{c}\mathrm{l}\mathrm{st}\\ {\mathrm{l}}_{\mathrm{s}2}\end{array}\right]$=$\left[\begin{array}{c}1.96\angle -48.69°\\ 1.96\angle -78.69°\end{array}\right]$

Step-by-step solution

Step 1: Determine the 2 X 2 bus admittance matrix.

(a)

Consider the circuit for the further calculation

The admittance is inversely proportional to the impedance. Convert the impedance into admittance as,

Similarly, solve for -j0.1

Similarly, solve for 0.02+j0.2

On bases of the above calculation the circuit can be drawn as

Step 2: Convert the voltage sources to current sources and determine the vector of source currents into buses 1 and 2.

(b)

Convert the voltage sources E_s1

Similarly, convert the voltage sources E_s2

Hence, the vector of the current source