For Problem 8.14, calculate the real and reactive power delivered to the three-phase load.

Problem 8.14

Given the line-to-ground voltages \(V_{a g}=280 \angle 0^{\circ}, V_{b g}=250 \angle-110^{\circ}\), and \(V_{c g}=290 \angle 130^{\circ}\) volts, calculate

(a) the sequence components of the lineto-ground voltages, denoted \(V_{\mathrm{Lg} 0}, V_{\mathrm{Lg} 1}\) and \(V_{\mathrm{Lg} 2}\);

(b) line-to-line voltages \(V_{\mathrm{LL} 0}, V_{\mathrm{LL} 1}\), and \(V_{\mathrm{LL} 2}\); and

(c) sequence components of the line-to-line voltages \(V_{\mathrm{LL} 0}=0, V_{\mathrm{LL} 1}\), and \(V_{\mathrm{LL} 2}\). Also, verify the following general relation: \(V_{\mathrm{LL} 0}=0, V_{\mathrm{LL} 1}=\sqrt{3} V_{\mathrm{Lg} 1} \angle+30^{\circ}\), and \(V_{\mathrm{LL} 2}=\sqrt{3} V_{\mathrm{Lg} 2} \angle-30^{\circ}\) volts.