Introduction to Electric Circuits

110 Three-phase a.c. circuits

9 EB = -E cos 60 ~ - jE sin 60 ~ = E(-0.5 - j0.866)

9 Ec = -E cos 60 ~ + jE sin 60 ~ = E(-0.5 + j0.866).

A balanced system is one in which the load impedance on each phase is the

same in quality and quantity so that if the load impedances are ZA(=RA + jXA) ,

ZB(=RB +jXB) and Zc(=Rc+jXc) then RA = RB = Rc (=R say) and

XA=XB=Xc (=X say). The phase angles &A (=tan-I(XA/RA)),

4~(=tan -1 (XB/RB)) and &c ( =tan-1 (Xc/Rc)) are also equal (to & say).

Six-wire system

If a load is connected to each of the phases separately, six wires would be

needed as shown in Fig. 5.6.

Figure 5.6

a

a' ~

ZA

Four-wire system

By connecting together the three return wires (a', b' and c') of the six-wire

system they could be replaced by just one wire making a total of four wires. The

common return wire is called the neutral wire and the junction of the three coils

is called the neutral point. This connection, shown in Fig. 5.7, is called a four-

wire star connection.

Figure 5.7

EA

', b', c', n

f

1

c

ZA

ZB