The three-phase Δ-connected generator represented in Figure 21–17 is driving a balanced load such that each phase current is 10 A in magnitude. When $I_{θa} = 10∠30^{\circ} A$ , determine the following:

(a) The polar expressions for the other phase currents

(b) The polar expressions for each of the line currents

(c) The complete current phasor diagram

Question

The three-phase Δ-connected generator represented in Figure 21–17 is driving a balanced load such that each phase current is 10 A in magnitude. When [latex]I_{θa} = 10∠30^{\circ} A[/latex], determine the following:

(a) The polar expressions for the other phase currents

(b) The polar expressions for each of the line currents

(c) The complete current phasor diagram

Accepted Answer

(a) The phase currents are separated by 120°; therefore,

[latex]I _{ heta b}=10 \angle\left(30^{\circ}+120^{\circ} ight)= 1 0 \angle 150^{\circ} A[/latex]

[latex]I _{ heta c}=10 \angle\left(30^{\circ}-120^{\circ} ight)= 1 0 \angle- 90^{\circ} A[/latex]

(b) The line currents are separated from the nearest phase current by 30°; therefore

[latex]I _{L 1}=\sqrt{3} I_{ heta a} \angle\left(30^{\circ}-30^{\circ} ight)= 1 7 . 3 \angle 0 ^{\circ} A [/latex]

[latex]I _{L 2}=\sqrt{3} I_{ heta b} \angle\left(150^{\circ}-30^{\circ} ight)= 1 7 . 3 \angle 1 2 0 { }^{\circ} A[/latex]

[latex]I _{L 3}=\sqrt{3} I_{ heta c} \angle\left(-90^{\circ}-30^{\circ} ight)=17.3 \angle-120^{\circ} A[/latex]

(c) The phasor diagram is shown in Figure 21–18.

Question 21.3: The three-phase Δ-connected generator represented in Figure ...

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