Page 409 - Power Electronic Control in Electrical Systems

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388 Examples, problems and exercises

(ii) Draw the circuit diagram of a wye-connected supply with a delta-connected
load. Also draw two separate phasor diagrams, one for the voltages and
currents of the supply, and the other for the voltages and currents of the
load. Use the phasor diagrams to show that under balanced conditions
p
V LL ˆ 3V ph and I L ˆ I ph at the supply, and
p
V LL ˆ V ph and I L ˆ 3I ph at the load;
where I L is the line current, I ph is the phase current, V LL is the line±line
voltage, and V ph is the phase voltage.
(iii) A 415-V, three-phase, three-wire supply has phase sequence RYB, with the
following loads:

6.0 kW at unity power-factor between lines R,Y;
4.5 kW at 0.8 power-factor lagging between lines Y,B;
2.7 kW at 0.5 power-factor leading between lines B,R.
Taking V RY as reference phasor, calculate all three-phase currents and all
three-line currents. Hence, calculate the ratio of the average-line current to
the average-phase current.
(i) Advantage of wye: provides earthing point. If three-wire, it suppresses tri-
plen-harmonic currents and permits two-wattmeter method to be used.
Advantage of delta: provides path for triplen currents.

Fig. 9.10