Find the phase voltages $V_{a n}, V_{b n}$, and $V_{c n}$ whose sequence components are: $V_{0}=20 \angle 80^{\circ}, V_{1}=100 \angle 0^{\circ}, V_{2}=30 \angle 180^{\circ} \mathrm{V}$.

Name: Find the phase voltages $V_{a n}, V_{b n}$, and $V_{c n}$ whose sequence components are: $V_{0}=20 \angle 80^{\circ}, V_{1}=100 \angle 0^{\circ}, V_{2}=30 \angle 180^{\circ} \mathrm{V}$.
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\begin{aligned}{\left[\begin{array}{l}\bar{V}_{a n} \\bar{V}_{b n} \\bar{V}_{c n}\end{array} ight] } & =\left[\begin{array}{ccc}1 & 1 & 1 \1 & a^{2} & a \1 & a & a^{2}\end{array} ight]\left[\begin{array}{c}20 \angle 80^{\circ} \100 \angle 0^{\circ} \30 \angle 180^{\circ}\end{array} ight]=\left[\begin{array}{c}20 \angle 80^{\circ}+100 \angle 0^{\circ}+30 \angle 180^{\circ} \20 \angle 80^{\circ}+100 \angle 290^{\circ}+30 \angle 300^{\circ} \20 \angle 80^{\circ}+100 \angle 120^{\circ}+30 \angle 60^{\circ}\end{array} ight] \& =\left[\begin{array}{c}73.47+j 19.70 \-31.53-j 92.89 \-31.53+j 132.3\end{array} ight]=\left[\begin{array}{c}76.07 \angle 15.01^{\circ} \98.09 \angle 251.3^{\circ} \135.98 \angle 103.4^{\circ}\end{array} ight] \mathrm{V}\end{aligned}

Find the Phase Voltages Van,VbnV_{a n}, V_{b n}Van​,Vbn​ , And VcnV_{c n}Vcn​

Find the Phase Voltages $V_{a n}, V_{b n}$ , And $V_{c n}$