The Two-Wattmeter Method
In a three
phase, wye or delta three wire
system, under balanced or unbalanced
conditions,
with any power factor, the two-wattmeter method is a practical and
commonly
used method of measuring total three phase power.
A
simplified circuit diagram of the two-wattmeter connections is shown in Fig.1.
Figure1
is
simplified in the sense that the ammeters, current transformers, selection
switch, and
polarity
switch have been omitted. The polarities of the voltage and current connections
to the
wattmeters are significant. Note that the line in which the current is not
measured,
line “c”,
is connected to the negative voltage terminal on both wattmeters.
Figure 1:
Connections for the two-wattmeter method. Notice that this is a three-wire
system.
The total
power delivered to the load is given by Eq.1.
Ptotal = P1 + P2
(1)
As
indicated in Fig.1, each wattmeter measures a line current and a line to line
voltage.
The
wattmeter reading indicates the product of line current, the line to line
voltage, and
the cosine
of the angle between them. At unity power factor (θ = 0, cos θ = 1), the
angle
between
phase current and line to line voltage is 30o.
Referring to Fig.1 and with the aid
of a
phasor diagram, Fig. 2, it can be shown that the wattmeter readings at any
power
factor
are:
P1
=
Vac Ia
P2 = Vbc Ib cos(θ + 30o) (3)
Figure 2:
Phasor diagram for a lagging power factor.
Note that
depending on the phase angle, θ, the signs on P1
and
P2 can be positive or
negative.
Table 1 shows the sign of P1 and P2
for
values of θ
ranging
from –90o to 90o. At
| θ | = 60o, one of the
wattmeters will read zero. If | θ | > 60o, one of
the readings will be
negative and the other will be positive.
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