a) Figure 11.10 shows the single-phase equivalent circuit.
b) The a-phase line current is
\pmb{I}_{aA}=\frac{120 \angle 0^{\circ}}{(0.2 + 0.8 + 39) + j(0.5 + 1.5 + 28)}
=\frac{120 \angle 0^{\circ}}{40+j30}
= 2.4 \angle -36.87° A.
For a positive phase sequence,
\pmb{I}_{bB}= 2.4\angle -156.87^{\circ} A,
\pmb{I}_{cC}= 2.4\angle 83.13^{\circ} A.
c) The phase voltage at the A terminal of the load is
\pmb{V}_{AN}= \left(39 + j28\right)\left(2.4 \angle -36.87^{\circ}\right)
= 115.22 \angle -1.19 ^{\circ}V .
For a positive phase sequence,
\pmb{V}_{BN}= 115.22 \angle -121.19^{\circ} V,
\pmb{V}_{CN}= 115.22 \angle 118.81^{\circ} V.
d) For a positive phase sequence, the line voltages lead the phase voltages by thus
\pmb{V}_{AB}= \left(\sqrt{3} \angle 30^{\circ}\right)\pmb{V}_{AN}
= 199.58\angle28.81^{\circ} V ,
\pmb{V}_{BC}= 199.58 \angle -91.19^{\circ} V,
\pmb{V}_{CA}= 199.58 \angle 148.81^{\circ} V.
e) The phase voltage at the a terminal of the source is
\pmb{V}_{an}=120-\left(0.2 + j0.5\right)\left(2.4\angle -36.87^{\circ}\right)
= 120-1.29\angle 31.33 ^{\circ} .
= 118.90 – j0.67
= 118.90 \angle-0.32 ^{\circ}V .
For a positive phase sequence,
\pmb{V}_{bn}= 118.90 \angle-120.32 ^{\circ}V,
\pmb{V}_{cn}= 118.90 \angle 119.68 ^{\circ}V.
f) The line voltages at the source terminals are
\pmb{V}_{ab}=\left(\sqrt{3} \angle 30^{\circ}\right)\pmb{V}_{an}
= 205.94\angle 29.68^{\circ} V ,
\pmb{V}_{bc}=205.94\angle -90.32^{\circ} V,
\pmb{V}_{ca}=205.94\angle 149.68^{\circ} V.
g) Changing the phase sequence has no effect on the single-phase equivalent circuit. The three line currents are
\pmb{I}_{aA}= 2.4\angle-36.87^{\circ}A,
\pmb{I}_{bB}= 2.4\angle83.13^{\circ}A,
\pmb{I}_{cC}= 2.4\angle -156.87^{\circ}A.
The phase voltages at the load are
\pmb{V}_{AN}= 115.22 \angle -1.19 ^{\circ}V ,
\pmb{V}_{BN}= 115.22 \angle 118.81^{\circ} V,
\pmb{V}_{CN}= 115.22 \angle -121.19^{\circ} V..
For a negative phase sequence, the line voltages lag the phase voltages by 30° :
\pmb{V}_{AB}= \left(\sqrt{3} \angle -30^{\circ}\right)\pmb{V}_{AN}
= 199.58\angle -31.19^{\circ} V ,
\pmb{V}_{BC}= 199.58 \angle 88.81^{\circ} V,
\pmb{V}_{CA}= 199.58 \angle -151.19^{\circ} V.
The phase voltages at the terminals of the generator are
\pmb{V}_{an}= = 118.90 \angle-0.32 ^{\circ}V ,
\pmb{V}_{bn}= 118.90 \angle 119.68 ^{\circ}V,
\pmb{V}_{cn}= 118.90 \angle-120.32^{\circ}V.
The line voltages at the terminals of the generator are
\pmb{V}_{ab}=\left(\sqrt{3} \angle -30^{\circ}\right)\pmb{V}_{an}
= 205.94\angle -30.32 ^{\circ} V ,
\pmb{V}_{bc}=205.94\angle 89.68^{\circ} V,
\pmb{V}_{ca}=205.94\angle -150.32^{\circ} V.
