For the ∆-∆ system shown in Fig. 24.20:
a. Find the phase angles $θ_2 and θ_3$ for the specified phase sequence.
b. Find the current in each phase of the load.
c. Find the magnitude of the line currents.

Question

For the ∆-∆ system shown in Fig. 24.20:
a. Find the phase angles [latex]θ_2 and θ_3[/latex] for the specified phase sequence.
b. Find the current in each phase of the load.
c. Find the magnitude of the line currents.

Accepted Answer

a. For an ACB phase sequence,

[latex]\theta_2 = 120° \qquad and \qquad \theta_3 = −120°[/latex]

b. [latex]V_\phi = E_L[/latex]. Therefore,

[latex]V_{ab} = E_{AB}\qquad V_{ca} = E_{CA} \qquad V_{bc} = E_{BC}[/latex]

The phase currents are

[latex]I_{ab}=\frac{V_{ab}}{Z_{ab}}=\frac{120 V ∠0°}{\frac{(5 Ω ∠0°)(5 Ω ∠-90°)}{5 Ω - j 5 Ω} }=\frac{120 V ∠0°}{\frac{25 Ω ∠-90°}{7.071 ∠-45°} }\[0.5cm] =\frac{120 V ∠0°}{3.54 Ω ∠-45°} =33.9 A ∠45° \[0.5cm] I_{bc}=\frac{V_{bc}}{Z_{bc}}=\frac{120 V ∠120°}{3.54 Ω ∠-45°}=33.9 A ∠165°\[0.5cm] I_{ca}=\frac{V_{ca}}{Z_{ca}}=\frac{120 V ∠-120°}{3.54 Ω ∠-45°}=33.9 A ∠−75° [/latex]

c. [latex]I_L=\sqrt{3}I_\phi =(1.73)(34 A) = 58.82 A.\enspace Therefore,\[0.5cm] I_{Aa} = I_{Bb} = I_{Cc} = 58.82 A[/latex]

Question 24.3: For the ∆-∆ system shown in Fig. 24.20: a. Find the phase an...

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