Copyright 20 13 Dorling Kindersley (India) Pvt. Ltd

I
R
I
R
V
RY
V
YB
V
YB
V
RY
I
Y
I
Y
I
B
I
B
Fig. 8.7-1 
Two-wattmeterconnection
(i) Let the reference phasor be the R-phase phase voltage in the equivalent Y-connected system 
and let the current 
I
R
be I
L
 
∠-
q
. Then, show that, under balanced operation, (i) the wattmeter 
in R-line reads W
1 
=
√
3 V
L
I
L
cos(30
° + 
q
) W, (ii) the wattmeter in B-line reads W
2 
=
√
3 V
L
I
L
cos(30
° - 
q
) W and (iii) the total active power in the three-phase system is 
=
W
1
+ 
W
2
W. 
Draw the required phasor diagrams.
(ii) What is the range of load power factor for which the first wattmeter in two-wattmeter method 
of power measurement in Fig. 8.7-1 will try to read negative value? What is the corrective 
action needed to take readings? How is the correction incorporated in the expression for total 
three-phase power?
(iii) Wattmeters used in two-wattmeter method are often constructed with reversing switch 
that will reverse the voltage applied to pressure coil. What is the need for this reversing
switch?
10. A 400 V rms 
D
-connected source shown in Fig. 8.7-2 has 
I
1
=
10
∠-
30
°
A rms, 
I
2
=
10
∠-
120
°
and 
I
3
=
10
√
2
∠
105
°
A rms. (i) Find the line currents delivered, (ii) Find the three-phase active 
power and reactive power delivered (iii) Find a delta-connected load that will result in this
loading.

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Problems

8.39
Y
B
R