0195136047.pdf

202 THREE-PHASE CIRCUITS AND RESIDENTIAL WIRING

(a)

(c)

A

C

B

ebn

ean

VBN

VAN V

AB

VCA

VCN

C VBC

Bus

or

(b)

B

A

N

N

b c

a

n

ecn

Vph

−

+

−

−

+

+ VBC^ = VL^ ∠^0 ° (Ref.) VAN^ =∠^90 °

VL

3

VAB = VL ∠ 120 ° VBN =∠− 30 °

VL

3

VCA = VL ∠ 240 °

VL−N

IL

VCN =∠− 150 °

VL

3

Figure 4.1.4(a)Balanced wye-connected, three-phase source.(b)Phasor diagram for three-phase source

(sequenceABC). Note that such relations asV ̄AB=V ̄AN+V ̄NBare satisfied; alsoV ̄AN+V ̄BN+V ̄CN=0;

V ̄AB+V ̄BC+V ̄CA=0.(c)Single-line equivalent circuit.

sequence can be seen to beA–B–C. Unless otherwise mentioned, the positive phase sequence is

to be assumed.

4.2 Balanced Three-Phase Loads

Three-phase loads can be connected in either wye (also known as star or Y) or delta (otherwise

known as mesh or ). If the load impedances in each of the three phases are the same in both

magnitude and phase angle, the load is said to be balanced.

For the analysis of network problems, transformations for converting a delta-connected

network to an equivalent wye-connected network and vice versa will be found to be useful.

The relationships for interconversion of wye and delta networks are given in Figure 4.2.1. These

are similar to those given in Section 2.4 for resistive network reduction. They can be obtained

by imposing the condition of equivalence that the impedance between any two terminals for

one network be equal to the corresponding impedance between the same terminals for the other

network. The details are left as a desirable exercise for the student. For the balanced case, each

wye impedance is one-third of each delta impedance; conversely, each delta impedance is three

times each wye impedance.