This document discusses electrical power and energy measurement techniques. It describes the construction, working principles, and sources of error for wattmeters and single-phase energy meters. Wattmeters measure power using an electrodynamic principle where the torque is proportional to the product of supply current and voltage. Single-phase energy meters use electromagnetic induction, with the driving torque proportional to supply voltage, current, and power factor, and the rotation recording consumed energy. Sources of error for both include load power factor, stray fields, temperature variations, and voltage fluctuations.

1. Electrical and Electronic Measurement Techniques
Power and Energy Measurement
Parveen Malik
Assistant Professor
School of Electronics Engineering
KIIT University
parveen.malikfet@kiit.ac.in
September 27, 2019
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2. Outline
1 Measurement of Power
Construction and Formulation
Disadvantages and Errors
2 Energy Meter
Construction
Working
Formulation
Errors in Single Phase induction watthourmeter
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3. Measurement of Power
Watt-meter

4. Wattmeter
Works on the principle of electrodynamometer i.e. mechanical force
exist between two current carrying conductor or coils.
Current coil carries the load current and Potential coil carries
current proportional to supply voltage.
TD ∝ I1I2 cos φ
dM
dθ
Power meter
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5. Watt-meter - Construction and Formulation
Power meter
For D.C.
TD ∝ I1I2 ∝ V I1 ∝ Power (D.C.)
For A.C.
Let v and i be the instantaneous value of voltage and current. Let cos φ be
the lagging power factor between them.
v = Vm sin ωt
i = Im sin (ωt − φ)
Average TD ∝ VrmsIrms cos φ
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6. Wattmeter- Formulation
Power Measurement
For controlling effect , spiral springs are used whose controlling torque is
Tc = kθ
At equilibrium,
TD = Tc
VI = kθ (D.C.)
VrmsIrms cos φ = kθ (A.C.)
Therefore,
θ ∝ Power (Linear Scale)
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7. Disadvantages and Errors
Disadvantages
1 At low power factors, the inductance of the potential coil causes
serious errors.
2 Stray magnetic field may affect the readings.
Errors
1 Error due to connection of potential coil circuit
2 Error due to inductance of potential coil.
3 Error due to capacitance n potential coil circuit.
4 Error due to stray Magnetic field
5 Error due to eddy currents.
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8. Energy Meter

9. Energy Meter
Energy meter works on the principle of electromagnetic induction.
Energy meter
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10. Energy Meter - Construction
Voltage Coil (Pressure Coil) - It is made purely inductive so that there
is 90◦ phase difference between input supply voltage and voltage coil flux
(φv ) is 90◦.
Current Coil - It is made resistive (low resistance) so that current and
voltage phase relation across load is directly determined by power factor of
load.
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11. Energy Meter - Working I
Driving Mechanism
1 The time varying flux produced by the voltage coil i.e φv induces an
emf Eep in the aluminium disc which in turn generates eddy current
(Iep). Similarly, flux produced by the current coil i.e φc induces an emf
Eec in the aluminium disc which in turn generates eddy current (Iec ).
2 The eddy current Iep generated due to voltage (pressure coil) coil
interacts with current coil flux φc while eddy current Iec generated
due to current coil interacts with voltage coil flux φv . This interaction
leads to exertion of two forces (Driving forces) on Al disc in opposite
direction which leads to a driving torque. This Driving torque TD is
directly proportional to product of two fluxes and sine of angle
between them.
TD ∝ φcφv sin θ
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12. Energy Meter - Working II
Braking Mechanism
When Al disc start rotating , it start cutting the stationary flux produced
by Braking magnet. This phenomenon induces an counteracting emf and
eddy current in Al disc which tries to bring its cause i.e . Al disc speed to
zero. and a breaking torque is produced.
TB ∝ N (Speed of Rotation)
Recording Mechanism When spindle rotates, the associated gear system
with it also start rotating the counter, this counter is calibrated directly to
read the no. of energy units (in kWh) consumed.
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13. Energy meter - Formulation
Let V and Ic be the supply voltage and current through load respectively.
Driving Torque
TD ∝ φcφv Sinθ
φc ∝ Ic and φv ∝ V
TD ∝ V IcSinθ
TD ∝ V Icsin (∆ − φ)
TD ∝ V Icsin (90◦
− φ)
TD ∝ VI cos φ
Breaking Torque
TB ∝ N
Where N is speed of disc.
Phaser of energy meter
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14. Energy meter - Formulation
At equilibrium,
TB = TD
N ∝ VI cos φ
N ∝ VI cos φ
Ndt = K VI cos φdt
n = K × Energy
Where n is no. of revolutions and K is meter constant (revolution per unit
KWh)
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15. Errors in 1φ energy meters I
1 Phase Error - It is due to phase difference between supply voltage
and voltage coil(or shunt magnet) flux. When there is no quadrature
phase difference , the power is not exactly proportional to speed of
rotation.
Remedial - Using Cu shading band (Lag or Power factor
adjustment)
2 Speed Error - It is due to high or low speed of Al disc which results
in wrong calculation of energy consumed.
Remedial - Using Breaking magnet (bringing it toward centre would
increase the speed and vice-versa)
3 Frictional Error - It is due to rotor bearing or counting mechanism ’s
mechanical parts and mainly occurs at light load.
Remedial - Two short circuited coils are placed in leakage gap of
shunt magnet to add the driving torque (Light load adjustment)
which nullify the frictional torque.
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16. Errors in 1φ energy meters II
4 Creeping - Slow rotation of Al disc in the absence of load current
and magnetisation of voltage coil by voltage coil current . Mainly
occurs due to overcompensation of frictional errors, vibrations ,
excessive voltage supply and stray magnetic field.
Remedial - Two diametrically opposite holes are drilled inside the Al
disc which results in distortion of field and disc remain stationary
when hole comes under the one of poles of shunt magnet.
5 Voltage Variations - The voltage coil flux increases with supply
voltage which in turn increases the value of driving torque. Since
breaking torque is directly proportional to square of the flux, it effect
is much more pronounced than driving torque. So at high voltages
meter runs slow while at low voltages meter runs faster.
Remedial - Proper design of shunt magnetic circuit.
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17. Errors in 1φ energy meters III
6 Temperature Error - When temp increases, resistance of coil
increases and current decreases so less flux is produced . Thus it
produces less driving torque and counteracts against temperature
variation. Therefore temp errors are small in the energy meter.
7 Frequency Error - When frequency increases or decreases, reactance
of coil changes resulting in error. But this error is generally small as
commercial frequencies are standardized and constrained within limits.
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