0195136047.pdf

206 THREE-PHASE CIRCUITS AND RESIDENTIAL WIRING

IAB

IBC

ICA

IC

IA

IAB

IAC

ICA

IBC IL

IB

IC

VBC = 100 ∠ 0 °

45 °

45 °

30 °

30 °

Direction of rotation of phasors

45 °

45 °

(a)

(b) (c)

5 ∠ 45 ° Ω

5 ∠ 45 ° Ω

5 ∠ 45 ° Ω

Z

VAB

ZY

VCA

VBC

|VAB| = |VBC| = |VCA| = VL−L = Vph

|IAB| = |IBC| = |ICA| = Iph

VL−N =∠ 0 °

∠ 45 ° Ω

∆

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

IA =∠− 30 °

VCA = 100 ∠ 240 °

VAB = 100 ∠ 120 °

A

B

C

IB

IA

3 Iph

3 IAB

IB =∠− 3 IBC 30 °

IC =∠− 3 ICA 30 °

3

100

3

5

Z

Z

Figure 4.2.3Balanced delta-connected load.(a)Connection diagram.(b)Phasor diagram.(c)Single-line

equivalent circuit.

The line currents, in magnitude, are

√

3 times the phase currents, and the phase currents lead the

corresponding line currents by 30°.

The preceding example can also be solved by the one-line equivalent method for which the

delta-connected load is replaced by its equivalent wye-connected load. The single-line equivalent

circuit is shown in Figure 4.2.3(c). The details are left as an exercise for the student.

Power in Balanced Three-Phase Circuits

The total power delivered by a three-phase source, or consumed by a three-phase load, is found

simply by adding the power in each of the three phases. In a balanced circuit, however, this is