Determine the symmetrical components of the following line currents: (a) $I_{a}=10 \angle 90^{\circ}$, $I_{b}=10 \angle 340^{\circ}, I_{c}=10 \angle 200^{\circ} \mathrm{A}$; (b) $I_{a}=100, I_{b}=j 100, I_{c}=0 \mathrm{~A}$.

Name: Determine the symmetrical components of the following line currents: (a) $I_{a}=10 \angle 90^{\circ}$, $I_{b}=10 \angle 340^{\circ}, I_{c}=10 \angle 200^{\circ} \mathrm{A}$; (b) $I_{a}=100, I_{b}=j 100, I_{c}=0 \mathrm{~A}$.
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The Answer is (a)

\begin{aligned}{\left[\begin{array}{l}\bar{I}_{0} \\bar{I}_{1} \\bar{I}_{2}\end{array} ight] } & =\frac{1}{3}\left[\begin{array}{ccc}1 & 1 & 1 \1 & a & a^{2} \1 & a^{2} & a\end{array} ight]\left[\begin{array}{c}10 \angle 90^{\circ} \10 \angle 340^{\circ} \10 \angle 200^{\circ}\end{array} ight]=\frac{10}{3}\left[\begin{array}{c}1 \angle 90^{\circ}+1 \angle 340^{\circ}+1 \angle 200^{\circ} \1 \angle 90^{\circ}+1 \angle 100^{\circ}+1 \angle 80^{\circ} \1 \angle 90^{\circ}+1 \angle 220^{\circ}+1 \angle 320^{\circ}\end{array} ight] \& =\frac{10}{3}\left[\begin{array}{c}0+j 0.316 \0+j 2.9696 \0-j 0.2856\end{array} ight]=\left[\begin{array}{c}1.0533 \angle 90^{\circ} \9.8987 \angle 90^{\circ} \0.9520 \angle-90^{\circ}\end{array} ight] \mathrm{A}\end{aligned}

(b)

\left[\begin{array}{l}\bar{I}_{0} \ \bar{I}_{1} \ \bar{I}_{2}\end{array} ight]=\frac{1}{3}\left[\begin{array}{ccc}1 & 1 & 1 \ 1 & a & a^{2} \ 1 & a^{2} & a\end{array} ight]\left[\begin{array}{c}100 \angle 0^{\circ} \ 100 \angle 90^{\circ} \ 0\end{array} ight]=\frac{100}{3}\left[\begin{array}{c}1 \angle 0^{\circ}+1 \angle 90^{\circ} \ 1 \angle 0^{\circ}+1 \angle 210^{\circ} \ 1 \angle 0^{\circ}+1 \angle 330^{\circ}\end{array} ight]

(c)

=\frac{100}{3}\left[\begin{array}{c}\sqrt{2} \angle 45^{\circ} \0.5176 \angle-75^{\circ} \1.9319 \angle-15^{\circ}\end{array} ight]=\left[\begin{array}{c}47.13 \angle 45^{\circ} \17.253 \angle-75^{\circ} \64.4 \angle-15^{\circ}\end{array} ight] \mathrm{A}

Determine the Symmetrical Components of the Following Line Currents: (A) Ia=10∠90∘I_{a}=10 \angle 90^{\circ}Ia​=10∠90∘

Determine the Symmetrical Components of the Following Line Currents: (A) $I_{a}=10 \angle 90^{\circ}$