Energy Systems II
Spring 2006
Two Wattmeter Method
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
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Energy Systems II
Spring 2006
Two Wattmeter Method
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 cos(θ - 30o)
(2)
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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Energy Systems II
Spring 2006
θ
(Degrees)
-90
-80
-60
-30
0
30
60
80
90
Two Wattmeter Method
Sign of P1
P1 = Vac Ia cos(θ -30o)
0
+
+
+
+
+
+
Sign of P2
P2 = Vac Ia cos(θ +30o)
+
+
+
+
+
+
0
-
Table 1: Polarities of wattmeter readings at different phase angles. This table assumes
that the wattmeters are connected as shown in Fig.1. This particular data is for a balanced
load. Otherwise θ would not necessarily be the same in each phase.
Procedure
In the lab, only one wattmeter will be used per test table. The ammeter patch plug,
voltage selection switch, and the polarity switch are used to select the desired voltages
and currents that are connected to the wattmeter. An ammeter is always and a current
transformer is normally used with the wattmeter in this laboratory. The use of the
ammeter and the current transformer along with the wattmeter makes it impractical and
very inconvenient to actually use two wattmeters. Figure 3 shows the wattmeter
connected in both positions at once to the three lines running through the test table.
Polarities are important in the two-wattmeter method. The voltage is measured from line
“a” to line “c” (Vac) with the wattmeter in position 1 as shown in Fig. 3.The voltage is
measured from line “b” to line “c” (Vbc) with the wattmeter in position 2 as shown in
Fig.3. When switching from one position to the other, the voltage selection switch must
be changed to insure that measurements are made between the correct two lines and the
polarity switch must be set such that wattmeter reads upscale.
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Energy Systems II
Spring 2006
Two Wattmeter Method
a
+
Ammeter
Plug and CT
+
A
M
+ Ia
+
Vac or Vca
Selector Switch
Polarity Switch
P1
Three - Phase
Wye or
Delta
Three wire Load
b
+
Ammeter
Plug and CT
+
A
M
Selector Switch
Polarity Switch
+ I
b
+
Vac or Vca
P2
c
Figure 3: A laboratory test table set up for the two-wattmeter method. Notice that only
one wattmeter, ammeter, and CT are used. They are shown in two different positions as
facilitated by the combination of switches on the table.
A few examples might help explain the situation.
1. If the voltage line selection and polarity switch positions are as shown in Fig. 3 and
both readings are positive, simply add the two readings directly to obtain Ptotal.
2. If voltage line selection and polarity switch positions are as shown in Fig. 3 and one
reading is positive and the other negative, the magnitude of the phase angle, θ, is
greater than 60o (assuming a balanced load, for this case). Positive meter deflection
can be obtained for the negative reading by reversing the polarity switch. Record this
reading as negative. It is important that the original polarity switch positions be tried
when making any additional measurements. In this case, the opposite polarity switch
position is only being used as a convenience while obtaining positive meter deflection
for recording negative values.
3. If voltage line selection and polarity switch positions are as shown in Fig. 3, but both
readings turn out to be negative, a positive meter deflection can be obtained by
exchanging the two current leads or by reversing the polarity switch. In this case, both
readings are negative. The total power can be negative if the load is replaced by an
AC generator. Again, it is wise to trace through the lines on the test table to be sure
that you understand what you are doing.
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Energy Systems II
Spring 2006
Two Wattmeter Method
In the lab, it is always a good idea to set up a purely resistive load to start with. With
resistive loads, the wattmeter should read upscale in both positions. This quick test
provides an easy check on your polarities.
Reactive Power and Power Factor
The magnitude of the reactive power can be obtained using Eq. 4.
Qtotal =
3 ( P1 - P2 )
(4)
The phase angle, θ, and the power factor, cos θ, and be determined from the wattmeter
readings alone, if the system is balanced.
 | Qtotal | 

| θ | = tan –1 
 | Ptotal | 
For example:
1. P1 = -80 Watts
P2 = 127 Watts
| Ptotal | = 47.0 Watts
| Qtotal | = 358.5 VARS
 | 358.5 | 
 = 82.53o
| θ | = tan –1 
 | 47 | 
2. P1 = 127 Watts
P2 = -80 Watts
| Ptotal | = 47.0 Watts
| Qtotal | = 207.0 VARS
 | 207 | 
 = 77.21o
| θ | = tan –1 
 | 47 | 
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