0195136047.pdf

4.2 BALANCED THREE-PHASE LOADS 205

30 °

IB

IC

IA

IC

IA

IB

IL

IC

Z

10 ∠ + 20 ° Ω

VCN = 120 ∠− 150 °

20 °

20 ° 20 °

70 °

60 °

(a)

(b)

(c)

10 ∠ + 20 ° Ω

10 ∠ + 20 ° Ω

Z

VAB

VBC

3

Z

VCA

VCN

VBN

VAN

−VCN = VNC

|VAN| = |VBN| = |VCN| = VL−N = Vph

|VAB| = |VBC| = |VCA| = VL−L =

VL−N∠ 0 °

|IA| = |IB| = |IC| = IL = Iph

IN = 0

VAN =∠−VAB 30 °

−VBN = VNB

−VAN = VNA

VBN = 120 ∠− 30 °

VAN = 120 ∠ 90 °

A

N

B

C

Z

IB

IN

IA

VBN =∠− 3 30 °

VBC

VCN =∠− 3 30 °

VCA

3 Vph

Direction of rotation of phasors

Reference

Figure 4.2.2Balanced wye-connected load.(a)Connection diagram.(b)Phasor diagram.(c)Single-line
equivalent circuit.

I ̄C=I ̄CA+I ̄CB= 20  195°− 20  −45°= 34. 64  165° (4.2.11)

The phasor diagram showing the line-to-line voltages, phase currents, and line currents is drawn
in Figure 4.2.3(b). The load power factor is lagging, and is given by cos 45°.
For abalanceddelta-connected load, the phase voltages and the line-to-line voltages are
equal in magnitude, and the line voltages are in phase with the corresponding phase voltages.