Blondel's theorem
If
the common point for the potential coil is one of the conductors,
the
number of wattmeters is reduced by one.
Thus it
is possible to measure the power in a three-phase system using only
two
wattmeters, irrespective of whether the three-phase
system is balanced.
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Measurement of Power by Two Wattmeter Method in Star Connection
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W1 = I1 (VL1-N – VL3-N)
W2
= I2
(VL2-N
–
VL3-N)
W1 + W2 = I1 (VL1-N – VL3-N) + I2
(VL2-N
–
VL3-N)
= I1 VL1-N – I1 VL3-N + I2
VL2-N
–
I2 VL3-N
= I1 VL1-N + I2
VL2-N
– I1 VL3-N – I2
VL3-N
= I1 VL1-N + I2
VL2-N
+ (–I1 –I2) VL3-N
∵ balance 3 phase star system : I1 + I2 + I3 = 0 è I3 = (– I1 – I2)
∴ W1 + W2 = I1 VL1-N + I2
VL2-N + I3 VL3-N
Two meter = Power Power Power
of
+ of + of
phase 1
phase
2 phase 3
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Measurement of Power
by Two Wattmeter Method in Delta Connection
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W1 = (I1 – I3) VL1-L3
W2
= (I2
–
I1)
VL2-L3
W1 + W2 = (I1 – I3) VL1-L3 + (I2
–
I1)
VL2-L3
= I1 VL1-L3 –I3 VL1-L3 + I2
VL2-L3
–I1
VL2-L3
∵ balance 3 phase delta system : VL1-L2 + VL2-L3 + VL3-L1 = 0
∴ è VL2-L3 = (–VL1-L2 –VL3-L1)
= I1 VL1-L3 –I3 VL1-L3 + I2
VL2-L3
–I1 (–VL1-L2 – VL3-L1)
= I1 VL1-L3 –I3 VL1-L3 + I2
VL2-L3 + I1 VL1-L2
+
I1 VL3-L1
∵ VL1-L3 = –VL3-L1
= I1 VL1-L3 –I3 VL1-L3 + I2
VL2-L3 + I1 VL1-L2
+ I1
VL3-L1
= –I3 VL1-L3 + I2
VL2-L3 + I1
VL1-L2
∵ VL1-L3 = –VL3-L1
=
I3 VL3-L1 + I2
VL2-L3 + I1
VL1-L2
∴ W1 + W2 = I1 VL1-L2 + I2 VL2-L3 + I3 VL3-L1
Two meter =
Power Power Power
of
+ of
+ of
phase 1 phase 2 phase 3