A three phase balanced voltage is applied on a balanced
three phase load makes a current in each of the phases lagging by angle Φ
behind the corresponding phase voltage.
The wattmeter connections must be paid special
attention. The two wattmeters must be connected in such a way that their
current coils are connected in series with the two phases and their pressure
coils must be connected between their respective lines and the remaining third line.
For wattmeter W1
:-
Current through current coil = IR
Potential difference across voltage coil = VRN-
VYN = VRY
Phase difference between IR and VRY is (300+ Φ)
Thus, reading on wattmeter W1 is
W1= VRY IR
cos(300+ Φ)
For wattmeter W2
:-
Current through current coil = IB
Potential difference across voltage coil = VBN-
VYN = VBY
Phase difference between IB and VBY is (300- Φ)
Thus, reading on wattmeter W2 is
W2= VBY IB
cos(300-Φ)
power
measurement by two wattmeter method
Since the load is balanced, | IR |=| IY
|=| IB |= I (Let) and
| VRY |=| VBY |= VL (Let)
∴ W1=
VL I cos(300+ Φ)
while W2= VL
I cos(300-Φ)
Thus, the total power is given by
W= W1+ W2 = VL I cos(300+
Φ) + VL I cos(300- Φ)
= VL I [cos(300+ Φ) + cos(300-
Φ) ]
= √3VL
I cos Φ ∵ { cos(A+B)+cos(A-B)=2cosAcosB }
Thus, with wattmeter
connections as shown above, sum of readings of two wattmeters give the total real power.
power
factor (p.f ) measurement by two wattmeter method
W2- W1 = VL I sin
Φ
Dividing the two equations,
(W2-
W1) /(W1+ W2) = tan Φ/√3
Thus, Φ=
tan-1[√3 (W2- W1) /(W1+ W2)]
and power factor = cos Φ
but, power factor nature i.e lagging or leading can't be known by this method.
and power factor = cos Φ
but, power factor nature i.e lagging or leading can't be known by this method.
Total reactive power power :-
We already have,
W2- W1
= VL I sin Φ
Multiplying by √3,
Reactive power = √3 (W2-
W1) = √3 VL
I sin Φ
For leading loads the angle becomes negative as per our reference, therefore putting in above formula we get
tan Φ=√3 (W1- W2) /(W2+ W1) ...for leading power factor
Two wattmeter method for leading loads
As shown above, the value of tan Φ and
hence power factor cos Φ can be determined from two wattmeter readings.
tan Φ=√3 (W2- W1) /(W1+ W2) ...for
lagging power factor
For leading loads the angle becomes negative as per our reference, therefore putting in above formula we get
tan Φ=√3 (W1- W2) /(W2+ W1) ...for leading power factor
If you analyse by putting all possible
values of Φ i.e from 00 to 900 in W1 and W2 , you will find that W2 is the higher reading wattmeter in lagging
power factor case, and W1 is the higher reading wattmeter in leading
power factor case .
Closely related concepts :-
(1) How to Connect a Wattmeter ?
(2) Power in Star Connection
(3) Relationship between Line and Phase Voltages and Currents in
Star Connection
(1) How to Connect a Wattmeter ?
(2) Power in Star Connection
(3) Relationship between Line and Phase Voltages and Currents in
Star Connection
