Introduction to Electric Circuits

5.5 Power in balanced three-phase circuits 117

Measurement of power in balanced three-phase circuits

For a four-wire system it is only necessary to use just one wattmeter connected
as shown in Fig. 5.15. A wattmeter is calibrated to read the product VI cos ~b
where V is the voltage across its voltage coil, I is the current through its current
coil and ~b is the angle between them. The wattmeter in Fig. 5.15 has the phase
voltage across its voltage coil and the phase current (which is also the line
current in this case) through its current coil. It will therefore read the power in
one phase and so the total power is obtained by multiplying the reading by
three.

No

Co

Bo,^1

A

Ao

Figure 5.15

For a three-wire system, however, the so-called two-wattmeter method is
used, the two wattmeters being connected as shown in Fig. 5.16. Since a
wattmeter reads the product of the voltage across its voltage coil with the
current through its current coil and the cosine of the angle between them,
then

9 W~ will read VAC/A COS ~1 (~1 is the angle between VAC and IA)

" W2 will read VBclB COS 4~2 (4~2 is the angle between VBc and IB).

The phasor diagram is drawn in Fig. 5.17 assuming a lagging power factor of

Ao_ ' I

z

Co- ......... ~-~

W2

Figure 5.16