Question 21.5: Determine the load voltages and load currents in Figure 21–2...
Determine the load voltages and load currents in Figure 21–23, and show their relationship in a phasor diagram.
Using V_{L}=\sqrt{3} V_{\theta} (Equation 21–2) and the fact that there is 30° between each line voltage and the nearest phase voltage, the load voltages are
V _{Z a}= V _{L 1}=2.0 \sqrt{3} \angle 150^{\circ} kV = 3 . 4 6 \angle 1 5 0 ^ { \circ } kV
V _{Z b}= V _{L 2}=2.0 \sqrt{3} \angle 30^{\circ} kV =3.46 \angle 30^{\circ} kV
V_{Z c}=V_{L 3}=2.0 \sqrt{3} \angle-90^{\circ} kV =3.46 \angle-90^{\circ} kV
The load currents are
I _{Z a}=\frac{ V _{Z a}}{ Z _{a}}=\frac{3.46 \angle 150^{\circ} kV }{100 \angle 30^{\circ} \Omega}=34.6 \angle 120^{\circ} A
I _{Z b}=\frac{ V _{Z b}}{ Z _{b}}=\frac{3.46 \angle 30^{\circ} kV }{100 \angle 30^{\circ} \Omega}= 3 4 . 6 \angle 0 ^{\circ} A
I _{Z c}=\frac{ V _{Z c}}{ Z _{c}}=\frac{3.46 \angle-90^{\circ} kV }{100 \angle 30^{\circ} \Omega}=34.6 \angle-120^{\circ} A
The phasor diagram is shown in Figure 21–24.
