Download Power Measurement

EKT112
Principles of Measurement and
Instrumentation
Power Measurement
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Outline
— Power?
— Power in DC and AC Circuits
— Power Measurements
— Power Instrumentation (Wattmeter)
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Concept of Electric POWER
• Power can be defined as the time rate of energy transfer
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or energy dissipation in a load.
Power is the rate of using or supplying energy.
The rate at which work is done to maintain an electric
current in a circuit is termed ELECTRIC POWER.
Electric power is measured in watts (W).
The SI unit of power is the watt (W), where W = 1 J/s.
The kilowatt is a commonly used unit where I kilowatt =
1000 watts.
Electric POWER Formula
— Normally electric power is useful, making a lamp light or
a motor turn.
— ELECTRIC POWER equals the product of the current I
and the potential difference V.
Power = Current x Voltage Difference
P(Watts) = I ( Amperes) x V (volts)
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— If P is positive, the component absorb power.
— If P is negative, the component produces power.
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POWER in DC Circuits
— The POWER in DC circuit is equal to the product of voltage and
current. [Power = Current ×Voltage]
— When the system voltage is constant, ammeter readings are almost
a sufficient indication of the POWER taken.
— The POWER is calculated by using voltmeter and ammeter or
wattmeter.
— P = I × V = I² × R = V² / R
— where:
— P = power in watts (W)
I = current in amps (A)
R = resistance in ohms (W)
V = voltage in volts (V)
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Example
— How much power is used in a circuit which is 110 volts and
has a current of 1.36 amps?
P = IV
= 1 . 36 A x 110 V
= 150 W
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Examples
— Label on TV state 720W/120V. Find the current supply to
this TV.
— A heater has 30W resistor connected to voltage source 120V.
Find the total power which changed to heat .
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POWER in AC Circuits
— In AC circuits the voltage and current are changing their
magnitude and polarities with reference to time.
— The electric power in the circuit at any instant is equal to the
product of the current and the voltage across its terminals at
that instant.[p = vi]
— The instantaneous power,
p = vi
= Vmax sin q x I max sin(q - f )
= Vmax I max sin q sin(q - f )
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— The mean power
2p
1
p=
Vmax I max sin q - sin (q - f )df
ò
2p 0
Vmax I max cos f
=
2
P = VI cos f
— V and I are rms value of voltage and current and to calculate
power, we should know the power factor of the load in AC circuit.
— Power factors are usually stated as "leading" or "lagging" to show
the sign of the phase angle of current with respect to voltage.
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Example
— The real power is 700 W and the phase angle (f) between
voltage and current is 45.6°.
— The power factor = cos(45.6°) = 0.700.
The apparent power = 700 W / cos(45.6°) = 1000 VA
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•The power output rating of motors is usually expressed in a
power unit call the horsepower (hp)
•The relation between horsepower and watts is 1hp = 746W
•Electric motors and other systems have an efficiency (h) of
operation
Pout
h=
x100%
Pin
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Examples
1. Calculate the power for a 12V battery supply 250A to
a starter motor.
2. Find the current drawn from a 115V line by a DC
electric motor that delivers 1hp by assuming 100%
efficiency of operation.
3. What is the operating efficiency of a fully loaded 2hp
DC electric motor that drawn 19A at 100V?
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Quiz
— The d’Arsonval meter movement known as Permanent
Magnet Moving Coil (PMMC) used to be as voltmeter and
ammeter. For both instruments, what we uses to increase
the voltage range and the current range?
— Answer in 5 minutes and submit.
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Why Wattmeter Needed?
— Ammeter measures load current IL and there is voltage drop
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—
—
—
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VA across ammeter.
VL=V –VA
Pdc= VL IL = (V –VA)IL = VIL –VAIL
[Power measured by meters] = [Power consumed by load] +
[Power loss in ammeter]
The product of ammeter and voltmeter does not give correct
power consumed by load
— If voltmeter shifted across the load to measure the load
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—
—
—
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voltage, it measures VL correctly but ammeter measures
current I.
I = IL + IV
Pdc= VL IL = VL (I - IV)= VL I –VL IV
[Power measured by meters] = [Power consumed by load] +
[Power loss in voltmeter]
Power measured is higher than power actually consumed by
load.
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— The power loss in the instrument (ammeter or voltmeter)
near the load cause an error.
— To avoid that errors in power measurement, we need a device
called wattmeter which gives direct reading of power.
— Ammeter and Voltmeter is not sufficient to measure power in
AC power because the measurement of power consumption
in circuit considering the effect of cos f.
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POWER Measurement
— A wide variety of instrumentation and transducers for the
measurement of POWER in AC and DC circuit.
— Important primarily for the testing, monitoring and
maintenance of the energy supply network and electrical
equipment.
— Required in high frequency and low power circuits.
— A wattmeter suitable used for power meter measurement in
DC and AC systems, which will give the same angle of
deflection for a given power.
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Power Factor Meter
— Single Phase and Three Phase
— This instruments indicate the power factor of a circuit
directly instead of obtaining the watts applied to a circuit
dividing by the volt amperes in the circuit
— Class of power factor meter
Dynamometer type power factor meter
2. Moving iron type power factor meter
1.
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Wattmeters
— Three types of wattmeters
Dynamometer
2. Induction
- can be used on AC circuit only when frequency and supply
voltage are constant.
3. Electrostatic
1.
— Class of Dynamometer
— Suspended coil torsion head
— Pivoted coil direct indicating
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Dynamometer Wattmeter
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Dynamometer Construction
— The moving coil is placed between the two fixed coils.
— The fixed coils is used as a current coils which are made of a few turns of thick
copper wire and are connected in series with the load to carry the load current.
— The moving coil is used as pressure coil which is made of a very light wire
several turns of fine copper wire.
— A high non inductive resistance is connected in series with the moving coil to
limit the current.
— The jewel supported spindle carrying the pressure coil, a pointer damping vane
and control springs.
— The flat aluminium thin pointer is fixed to the pressure coil spindle and moves
over a suitably calibrated scale.
— A cast iron cylinder is placed around the coil to protect against stray magnetic
fields.
— Air friction damping is used.
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Dynamometer Operation
— The fixed coils carry load current and create a flux in the air gap
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—
—
—
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between them.
The pressure coil carries another small current proportional to
load voltage and hence produces a flux in the air gap.
The circuit coil produces a flux in phase with the load current.
The flux produced by the pressure coil is very nearly inphase with
the applied voltage.
The magnetic fields of the fixed and moving coils react on one
another causing the moving coil to turn its axis and a torque
produced on the moving system.
— The torque developed on moving system will be proportional
to product of the two fields and in turn the voltage and
current.
— Deflecting Torque,
— Control Torque,
Td µ VI cos q = W (power)
Tc µ q
— Under steady state condition,
Td = Tc
q µ W µ power
— The angular displacement of the pointer is directly
proportional to average power in circuits.
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Dynamometer
— In dynamometer type instrument
— Deflecting torque is produced by magnetic effect of electric
current.
— Control torque is provided by control springs.
— Damping torque is provided by Air Friction damping.
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Advantages
— Can be used to measure power in DC and AC circuits.
— Gives fairly accurate readings.
— The scale is uniform.
— Free from hysteresis and eddy current losses
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Disadvantages
— The torque-weight ratio is small (even when the current and
pressure coils are fully exicited)
— High cost
— Affected by stray magnetic field
— The inductance of pressure coil tend to be large at low power
factors introduces serious error.
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— Wattmeter's are designed for lower power factor rating. This
improves precision & reduces error.
— As two different ranges of voltage and current are available
for wattmeter to calculate actual power, multiplying factor
should be used.
voltage range x current range x rated power factor
Multiplyin g Factor =
Full Scale Deplection
Measured Power = Wattmeter Reading x Multiplyin g Factor
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Examples
— Let FSD of wattmeter be 1250W. If potential coil is
connected across 250V and the current coil connected for a
current range 5A, What is the multiplying factor?
— In a circuit power is measured with a wattmeter with 13A,
240V, 1500Watts F.S.D. The measurement reading was
700Watts. What is the power consumed by load?
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Error in wattmeter
— Connection error can be reduced by
used for low current,
high voltage circuit.
— Wattmeter Reading = (power consumed by load) + (Power consumed by
current coil)
used for high current, low voltage circuit,
by selecting a proper connection the
— Wattmeter Reading = (power consumed by load) + (power consumed by
pressure coil)
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Example
— A circuit takes 10A at 200V and the power absorbed is
1000W. If a current coil has a resistance of 0.15W
resistance and a pressure coil has a resistance of 5000W ,
Inductance of 0.3H. Find
— The error due to resistance for each of two possible
method of connection.
— The error due to the inductance if the frequency of
50Hz.
— The total error in each case.
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Method of Connections
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Compensated Wattmeter
— While measuring power in low power factor circuits, error
due to connection is not negligible. So compensating winding
is used.
— Compensating winding is a winding connected in series with
pressure coil. It has same number of turns as that of current
coil, but has small cross – section.
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Low Power Factor Wattmeter
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Modifications on LPF Wattmeter
— Pressure coil circuit designed to have low resistance to make more
current can flow through for develop more torque. (10xUFP).
— The large current causes higher voltage drop and power loss in
current coil which is introduce an errors. The provision of a
compensating is a must to reduce flux created by current coil.
— Error caused by pressure coil inductance is proportional to sin q
(power factor angle) which is large at low power factor.
Compensation is carried out by putting a capacitor across a part of
the series resistance
— To have small control torque relative to smaller deflection torque
which able to give higher angular displacement and suitable for
circuits with power factors as low as 0.1.
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A dynamometer type three-phase
wattmeter
— consists of two separate wattmeter movements mounted
together in one case with the two moving coils mounted on
the same spindle.
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— There are two current coils and two pressure coils.
— A current coil together with its pressure coil is known as
an element. Therefore, a three phase wattmeter has two
elements.
— The connections of two elements of a 3 phase wattmeter
are the same as that for two wattmeter method using two
single phase wattmeter.
— The torque on each element is proportional to the
power being measured by it.
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— The total torque deflecting the moving system is the sum of the
deflecting torque of’ the two elements.
— Hence the total deflecting torque on the moving system is
proportional to the total Power.
— In order that a 3 phase wattmeter read correctly, there should not
be any mutual interference between the two elements.
— A laminated iron shield may be placed between the two elements
to eliminate the mutual effects.
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End
of
POWER Measurements
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