Introduction to Electric Circuits

Figure 5.4

03

a

b' c

C

a'

(a)

5.4 Balanced three-phase systems 109

EatsE c

Eb

(b)

5.4 BALANCED THREE-PHASE SYSTEMS

It is important that the system is not only symmetrical (i.e. the voltage phasors

are mutually displaced by 120 ~ ) but also balanced (i.e. the voltages are equal in

magnitude so that the phasors are of equal length). This can be achieved by

ensuring that the coils are identical and that their mutual 120 ~ separation is

maintained. If this is done then the three generated voltages may be repre-

sented as follows:

9 EA = Emsin ~ot

9 EB = Em sin (~ot- 27r/3)

A by 120~

9 Ec = Em sin (wt- 47r/3)

A by 240 ~

where E m is the maximum value of the generated emf;

since the emf generated in coil B lags that in coil

since the emf generated in coil C lags that in coil

We could also express Ec as E m sin (~ot + 27r/3) because Ec is also 120 ~ ahead

of EA. Phasorially this is represented as shown in Fig. 5.5 and the phasors can be

drawn to represent E m or E (the rms values).

jE sin 60 E!,~

i rk I.,I \

f, \/,oo

• cos o~ i/"

-IE sin 60 ~ ~B

EA =E + j0

Figure 5.5

Note also that with EA as the reference phasor, we can use the complex (j)
notation to write

9 EA=E(I+j0)