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Electrodynamometer wattmeter
1
Electrodynamometer wattmeter conti……
Fixed coil is a current carrying coil.
Moving is a pressure coil.
Spring control is used.
Air friction damping is used.
2
Electrodynamometer wattmeter conti……
3
Electrodynamometer wattmeter conti……
4
Errors in Electrodynamometer wattmeter
(i) Pressure Coil Inductance
(ii) Pressure coil capacitance
(iii) Error due to Mutual Inductance Effects
(iv) Errors caused because of Connections
(v) Eddy current Errors
(vi) Stray magnetic field errors
(vii) Errors caused by Vibration of Moving system
(viii) Temperature Errors
5
Errors in Electrodynamometer wattmeter…….
(i) Pressure Coil Inductance
error
For lagging load (wattmeter will read higher than
actual)
Error Cosφ/ cos β.cos (φ – β)
For leading load (wattmeter will read lower than
actual)
tanφ.tanβ x VI Cosφ,
Compensation
6
Errors in Electrodynamometer wattmeter…..
7
(a) Power indicated by wattmeter=
power consumed by load + power loss in current
coil (small current)
(b) Power indicated by wattmeter=power
consumed by load + power loss in pressure coil
(large current)
Low power factor wattmeter
(electrodynamometer type)
Measurement of power by ordinary electrodynamometer is
difficult in case of circuit having low power factor
Because
(i) The deflecting torque on the moving system is
small (owing to low power factor) even when
the current and pressure coils are fully excited.
(ii) Errors introduced because of inductance of
pressure coil tend to be large at low power
factors
Low power factor wattmeter…….
9
Low power factor wattmeter…….
Features incorporated in an electrodynameter to
make it a low power factor type wattmeter.
(a) Pressure coil current.
The pressure coil circuit is designed to have a low
value of resistance, so that the current, flowing
through it, is increased to give and increased
operating torque.
The pressure coil current in a low power factor
wattmeter may be as much as 10 times the value
employed for high power factor wattmeter.
10
Low power factor wattmeter…….
(b) Compensation for pressure coil current
The power being measured in a low power
factor circuit is small and current is high on
account of low power factor, connection of fig
(a) cannot be used because owing to large load
current there would be a large power loss in
the current coil and ,therefore ,the wattmeter
will give a large error. 11
Low power factor wattmeter…….
(c) If we use connection of fig (b) ,the power loss in
the pressure coil circuit is included in the reading
given by the wattmeter.
Thus with this connection also the wattmeter
will give a serious error as the power loss in the
pressure coil may be a large percentage of the
power being measured.
There fore ,it is absolutely necessary to
compensate for the pressure coil current in a low
power factor wattmeter.
12
Low power factor wattmeter…….
(c) Compensation for Inductance of Pressure coil
The error caused by pressure coil inductance is
VI.sinφ.tanβ
Now, with low power factor, the value of φ is large
and, the error is correspondingly large.
Hence in a low power factor wattmeter we must
Compensate for the error caused by inductance of the
pressure coil.
This is done by connecting a capacitor across a part
of series resistance in the pressure coil circuit
(d) Small control torque
Low power factor wattmeter are designed with to
have a small control torque so that they give full scale
deflection for power factor as low as 0.1
13
14
A wattmeter has a current coil of 0.1Ω resistance and a pressure coil of 6500 Ω
resistance. Calculate the percentage error due to resistance only (a) when the
pressure coil is connected on supply side (b) when pressure coil is connected on
load side. a)when the input 12A at 250V with unity power factor b) when the input
12A at 250V with 0.4 power factor
a) power = Vicosφ = 250x12x1=3000w
when the pressure coil is connected on supply side
Power loss in current coil = I2R = 122x0.1=14.4 w
Error =(14.4/3000)x100=0.48%
when pressure coil is connected on load side
power loss in pressure coil V2/Rp= (250)2/6500=9.6w
Error =(9.6/3000)x100=0.32%
b) power = Vicosφ = 250x12x0.4=1200w
when the pressure coil is connected on supply side
Power loss in current coil = I2R = 122x0.1=14.4 w
Error =(14.4/1200)x100=1.2%
when pressure coil is connected on load side
power loss in pressure coil V2/Rp= (250)2/6500=9.6w
Error =(9.6/1200)x100=0.8%
Three wattmeter method
15
at common pt V=0
V1=v1’, v2=v2’, v3=v3’
Sum of the instantaneous reading of the wattmeter
P=v1i1+v2i2+v3i3
Two wattmeter method (star connection)
16
Instantaneous power of P1 wattmeter P1=i1(v1-v3)
Instantaneous power of P2 wattmeter P2=i2(v2-v3)
Sum of instantaneous power P=P1+P2=v1i1+v2i2-v3(i1+i2)
kirchhoff ‘s law i1+i2+i3=0
i1+i2= -i3
Hence P=v1i1+v2i2+v3i3
Two wattmeter method (delta connection)
17
Instantaneous power of P1 wattmeter P1= - v3(i1-i3)
Instantaneous power of P2 wattmeter P2= v2(i2-i1)
Sum of instantaneous power P=P1+P2=v2(i2-i1) - v3(i1-i3)
kirchhoff ‘s law v1+v2+v3=0
v2+v3= -v1
Hence P=v1i1+v2i2+v3i3
Two element wattmeter
18
In a dynamometer wattmeter the moving coil has 500 turns of
mean diameter 30mm. Estimate the torque if the axes of the field
and the moving coils are at (a) 60° (b) 90° when the flux density
produced by field coils is 15x10-3 wb/m2, the current in moving coil
is 0.05A and the power factor is 0.866.
19
flux linking with moving coil= area x component of flux
perpendicular to area
=(Π/4)D2xBxcosθ
flux linkages with moving coil = N x(Π/4)D2xBxcosθ=Mmaxcosθ
Td=(VI/Rp) x (dM/dθ) cosθ =
= N x(Π/4)D2xBxIpx sinθ cosφ
a) θ=60, sin60=0.866
Td=500 x (Π/4) x (30x 10-3)2 x 15x10-3 x0.05x0.866x 0.866
=198.8 x 10-6 Nm
b) θ=90, sin90=1
Td=500x(Π/4)x(30x10-3)2 x15x10-3x0.05x0.866 =229.5x 10-6 Nm
A 220V, 5A dc energy meter is tested at its marked rating. The
resistance of Pressure coil is 8,800 Ω and that of current coil is 0.1
Ω. Calculate the power Consumed when testing the meter with:
(a) direct load arrangement. (b) Phantom loading with current
circuit excited by 6V battery.
20
Direct loading:
Power consumed in pressure circuit=2202/8800=5.5 w
Power consumed in current circuit=220 x5=1100 w
Total power consumed =1100+5.5 =1105.5 watts
phantom loading:
Power consumed in pressure circuit=2202/8800=5.5 w
Power consumed in current circuit=6 x5=30 w
Total power consumed =30+5.5 =35.5 watts
04-03-09 Nkp/eee skcet
Energy meters
04-03-09 Nkp/eee skcet
Single Phase Energy Meter
04-03-09 Nkp/eee skcet
Poly Phase Energy Meter
Phantom loading
When the current rating of a meter under test is high, a
test with actual loading arrangements would involve a
considerable waste of power. In order to avoid phantom
loading or Fictitious Loading is used.
24
A 230V, single phase watt-hour meter has a constant load of 4A
passing through it for 6 hours at unity power factor. If the meter
disc makes 2,208 revolutions during this period, what is the meter
constant in revolutions per KWH? Calculate the power factor of
the load if the numbers of revolutions made by the meter are
1,472 when operating at 230V, 5A for 4 hours. .
25
Energy supplied= VICosφ x t x 10-3
= 230 x 4 x 6 x 10-3 = 5.52 kwh
Meter constant = revolutions / Kwh
= 2208/5.52 = 400 rev/Kwh
Energy consumed when meter makes 1472 rev=1472/400 = 3.68Kwh
Now energy consumed = VICosφ x t x 10-3
230 x 5 x Cosφ x 4 x 10-3 = 3.68
Cosφ = 0.8

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Unit 2

  • 2. Electrodynamometer wattmeter conti…… Fixed coil is a current carrying coil. Moving is a pressure coil. Spring control is used. Air friction damping is used. 2
  • 5. Errors in Electrodynamometer wattmeter (i) Pressure Coil Inductance (ii) Pressure coil capacitance (iii) Error due to Mutual Inductance Effects (iv) Errors caused because of Connections (v) Eddy current Errors (vi) Stray magnetic field errors (vii) Errors caused by Vibration of Moving system (viii) Temperature Errors 5
  • 6. Errors in Electrodynamometer wattmeter……. (i) Pressure Coil Inductance error For lagging load (wattmeter will read higher than actual) Error Cosφ/ cos β.cos (φ – β) For leading load (wattmeter will read lower than actual) tanφ.tanβ x VI Cosφ, Compensation 6
  • 7. Errors in Electrodynamometer wattmeter….. 7 (a) Power indicated by wattmeter= power consumed by load + power loss in current coil (small current) (b) Power indicated by wattmeter=power consumed by load + power loss in pressure coil (large current)
  • 8. Low power factor wattmeter (electrodynamometer type) Measurement of power by ordinary electrodynamometer is difficult in case of circuit having low power factor Because (i) The deflecting torque on the moving system is small (owing to low power factor) even when the current and pressure coils are fully excited. (ii) Errors introduced because of inductance of pressure coil tend to be large at low power factors
  • 9. Low power factor wattmeter……. 9
  • 10. Low power factor wattmeter……. Features incorporated in an electrodynameter to make it a low power factor type wattmeter. (a) Pressure coil current. The pressure coil circuit is designed to have a low value of resistance, so that the current, flowing through it, is increased to give and increased operating torque. The pressure coil current in a low power factor wattmeter may be as much as 10 times the value employed for high power factor wattmeter. 10
  • 11. Low power factor wattmeter……. (b) Compensation for pressure coil current The power being measured in a low power factor circuit is small and current is high on account of low power factor, connection of fig (a) cannot be used because owing to large load current there would be a large power loss in the current coil and ,therefore ,the wattmeter will give a large error. 11
  • 12. Low power factor wattmeter……. (c) If we use connection of fig (b) ,the power loss in the pressure coil circuit is included in the reading given by the wattmeter. Thus with this connection also the wattmeter will give a serious error as the power loss in the pressure coil may be a large percentage of the power being measured. There fore ,it is absolutely necessary to compensate for the pressure coil current in a low power factor wattmeter. 12
  • 13. Low power factor wattmeter……. (c) Compensation for Inductance of Pressure coil The error caused by pressure coil inductance is VI.sinφ.tanβ Now, with low power factor, the value of φ is large and, the error is correspondingly large. Hence in a low power factor wattmeter we must Compensate for the error caused by inductance of the pressure coil. This is done by connecting a capacitor across a part of series resistance in the pressure coil circuit (d) Small control torque Low power factor wattmeter are designed with to have a small control torque so that they give full scale deflection for power factor as low as 0.1 13
  • 14. 14 A wattmeter has a current coil of 0.1Ω resistance and a pressure coil of 6500 Ω resistance. Calculate the percentage error due to resistance only (a) when the pressure coil is connected on supply side (b) when pressure coil is connected on load side. a)when the input 12A at 250V with unity power factor b) when the input 12A at 250V with 0.4 power factor a) power = Vicosφ = 250x12x1=3000w when the pressure coil is connected on supply side Power loss in current coil = I2R = 122x0.1=14.4 w Error =(14.4/3000)x100=0.48% when pressure coil is connected on load side power loss in pressure coil V2/Rp= (250)2/6500=9.6w Error =(9.6/3000)x100=0.32% b) power = Vicosφ = 250x12x0.4=1200w when the pressure coil is connected on supply side Power loss in current coil = I2R = 122x0.1=14.4 w Error =(14.4/1200)x100=1.2% when pressure coil is connected on load side power loss in pressure coil V2/Rp= (250)2/6500=9.6w Error =(9.6/1200)x100=0.8%
  • 15. Three wattmeter method 15 at common pt V=0 V1=v1’, v2=v2’, v3=v3’ Sum of the instantaneous reading of the wattmeter P=v1i1+v2i2+v3i3
  • 16. Two wattmeter method (star connection) 16 Instantaneous power of P1 wattmeter P1=i1(v1-v3) Instantaneous power of P2 wattmeter P2=i2(v2-v3) Sum of instantaneous power P=P1+P2=v1i1+v2i2-v3(i1+i2) kirchhoff ‘s law i1+i2+i3=0 i1+i2= -i3 Hence P=v1i1+v2i2+v3i3
  • 17. Two wattmeter method (delta connection) 17 Instantaneous power of P1 wattmeter P1= - v3(i1-i3) Instantaneous power of P2 wattmeter P2= v2(i2-i1) Sum of instantaneous power P=P1+P2=v2(i2-i1) - v3(i1-i3) kirchhoff ‘s law v1+v2+v3=0 v2+v3= -v1 Hence P=v1i1+v2i2+v3i3
  • 19. In a dynamometer wattmeter the moving coil has 500 turns of mean diameter 30mm. Estimate the torque if the axes of the field and the moving coils are at (a) 60° (b) 90° when the flux density produced by field coils is 15x10-3 wb/m2, the current in moving coil is 0.05A and the power factor is 0.866. 19 flux linking with moving coil= area x component of flux perpendicular to area =(Π/4)D2xBxcosθ flux linkages with moving coil = N x(Π/4)D2xBxcosθ=Mmaxcosθ Td=(VI/Rp) x (dM/dθ) cosθ = = N x(Π/4)D2xBxIpx sinθ cosφ a) θ=60, sin60=0.866 Td=500 x (Π/4) x (30x 10-3)2 x 15x10-3 x0.05x0.866x 0.866 =198.8 x 10-6 Nm b) θ=90, sin90=1 Td=500x(Π/4)x(30x10-3)2 x15x10-3x0.05x0.866 =229.5x 10-6 Nm
  • 20. A 220V, 5A dc energy meter is tested at its marked rating. The resistance of Pressure coil is 8,800 Ω and that of current coil is 0.1 Ω. Calculate the power Consumed when testing the meter with: (a) direct load arrangement. (b) Phantom loading with current circuit excited by 6V battery. 20 Direct loading: Power consumed in pressure circuit=2202/8800=5.5 w Power consumed in current circuit=220 x5=1100 w Total power consumed =1100+5.5 =1105.5 watts phantom loading: Power consumed in pressure circuit=2202/8800=5.5 w Power consumed in current circuit=6 x5=30 w Total power consumed =30+5.5 =35.5 watts
  • 22. 04-03-09 Nkp/eee skcet Single Phase Energy Meter
  • 23. 04-03-09 Nkp/eee skcet Poly Phase Energy Meter
  • 24. Phantom loading When the current rating of a meter under test is high, a test with actual loading arrangements would involve a considerable waste of power. In order to avoid phantom loading or Fictitious Loading is used. 24
  • 25. A 230V, single phase watt-hour meter has a constant load of 4A passing through it for 6 hours at unity power factor. If the meter disc makes 2,208 revolutions during this period, what is the meter constant in revolutions per KWH? Calculate the power factor of the load if the numbers of revolutions made by the meter are 1,472 when operating at 230V, 5A for 4 hours. . 25 Energy supplied= VICosφ x t x 10-3 = 230 x 4 x 6 x 10-3 = 5.52 kwh Meter constant = revolutions / Kwh = 2208/5.52 = 400 rev/Kwh Energy consumed when meter makes 1472 rev=1472/400 = 3.68Kwh Now energy consumed = VICosφ x t x 10-3 230 x 5 x Cosφ x 4 x 10-3 = 3.68 Cosφ = 0.8