Page 62 - Power Electronic Control in Electrical Systems

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52 Power systems engineering ± fundamental concepts

Fig. 2.19 Three-phase instantaneous and phasor currents.

This suggests that the circuit could be equally well served by the three-phase connec-
tion shown in Figure 2.20, which has only half the number of conductors compared
with Figure 2.18. Figure 2.20 also shows the cross-section of a three-phase cable
capable of carrying the required current. The total cross-section of conductor is 3 A,
that is a saving of 50%.
In the voltage phasor diagram in Figure 20, the voltage across each phase of the
load remains the same as in Figure 2.20, but the voltage between lines is increased:
evidently from the geometry of the triangles
p 
V ab ˆ V a V b ˆ 3Ve j30
p  j90
V bc ˆ V b V c ˆ 3Ve (2:24)
p  j150
V ca ˆ V c V a ˆ 3Ve
where V is the reference phase voltage taken as V a , measured between line A and the
`star point' of the load or the `neutral point' of the supply. Likewise the phase voltage
V b is measured between line B and the star-point of the load, and V c between line C
p
and the star point. The line±line voltages are 3 times the phase voltages. In
Figure 2.20 both the load and the generator are `wye connected' and in terms of
the RMS values only, we have
p 
V LL ˆ 3V ph and I L ˆ I ph (2:25)

Fig. 2.20 Three-phase connection with wye-connected load and phasor diagram.