Question 16.12: In a balanced three-phase circuit, the line voltages have an......
In a balanced three-phase circuit, the line voltages have an rms value of VL = 480 V(rms). Using ∠VAB as the phase reference, find all of the line and phase voltages for a positive phase sequence.
The specified phase reference means that we arbitrarily assign ∠VAB = 0°. This assignment together with VL = 480 allows us to write VAB = 480 ∠ 0° V(rms). The other two line voltages have the same rms value, VL = 480, and phase angles that lag ∠VAB at 120° intervals. For a positive (ABC) phase sequence, these voltages are VBC = 480∠−120° V(rms) and VCA = 480∠−240° V(rms). The rms value of the phase voltages is V_{P} = 480/\sqrt{3} = 277 V(rms). In Figure 16–14, we see that the line voltage VAB leads the phase voltage VAN by 30°. Since ∠VAB = 0° is the phase reference, we can write VAN = 277 ∠ −30° V(rms). The other two phase voltages have the same rms value and lag ∠VAN = −30° at 120° intervals. For a positive phase sequence, these voltages are VBN = 277∠−150° V(rms) and VCN = 277∠−270° V(rms).
There is nothing absolute about assigning ∠VAB = 0° as the phase reference. A three-phase circuit has an abundance of voltages and currents all with different phase angles. We have to start somewhere by choosing one of the phasors as the phase reference. The choice is arbitrary, but we often use ∠VAN = 0° as a phase reference. Had we done so in this example, the phasor magnitudes VP and VL would be unchanged but all phase angles would increase by 30°.
