Given the Line-To-Ground Voltages $V_{a g}=280 \angle 0^{\circ}, V_{b g}=290 \angle-130^{\circ}$

Essay

Given the line-to-ground voltages $V_{a g}=280 \angle 0^{\circ}, V_{b g}=290 \angle-130^{\circ}$ , and $V_{c g}=260 \angle 110^{\circ}$ volts, calculate (a) the sequence components of the line-to-ground voltages, denoted $V_{\mathrm{L} g 0}, V_{\mathrm{L} g 1}$ , and $V_{\mathrm{L} g 2}$ ; (b) line-to-line voltages $V_{a b}, V_{b c}$ , and $V_{c a}$ ; and (c) sequence components of the line-to-line voltages $V_{\mathrm{LL} 0}, V_{\mathrm{LL} 1}$ , and $V_{\mathrm{LL} 2}$ . Also, verify the following general relation: $V_{\mathrm{LL} 0}=0, V_{\mathrm{LL} 1}=\sqrt{3} V_{\mathrm{L} g 1} \angle+30^{\circ}$ , and $V_{\mathrm{LL} 2}=\sqrt{3} V_{\mathrm{L} g 2} \angle-30^{\circ}$ volts.