Question

For the circuit shown in Figure 2.29, convert the voltage sources to equivalent current sources and write nodal equations in matrix format using bus 0 as the reference bus. Do not solve the equations.

Short answer

Therefore, the voltage source converted into the current source and the result for E_s1& E _s2 are (1.96∠-48.69^o), (1.96∠ 78.69^o)respectively and the nodal equation into the matrix form

$\left[\begin{array}{c}0.8796+\mathrm{j}3.127-0.4950+4.950\\ -0.4950+\mathrm{j}4.9500.8796+3.127\end{array}\right]$$\left[\begin{array}{c}{\mathrm{V}}_1\\ {\mathrm{V}}_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

Use the source transformation of voltage source and determine the value of the current.

Convert the voltage sources into current sources Es₁ by using the source transformation

Solve for the current l₁.

Similarly, convert the voltage sources into current sources E_s2 by using the source transformation.

Find the nodal equation in the form of matrix form.

Convert the impedance into to the admittances.

Similarly, solve admittance for the impedance j0.10.1+j0.5.

Similarly, solve admittance for the impedance -j0.1 .

The admittance diagram is drawn as