The
electrodynamometer type instrument is a transfer instrument. A transfer
instrument is one which is calibrated with a d.c. source and used
without any modifications for a.c. measurements. Such a transfer
instrument has same accuracy for a.c. and d.c. measurements. The
electrodynamometer type instruments are often used in accurate a.c.
voltmeters and ammeters, not only at the power line frequency but also
in the lower audiofrequency range. With some little modifications, it
can be used as a wattmeter for the power measurements.
Why PMMC Instruments can not be used for a.c. measurements ?
The PMMC instrument cannot be sued on a.c. currents or voltages.
If a.c. supply is given to these instruments, an alternating torque will
be developed. Due to moment of inertia of moving system, the pointer
will not follow rapidly changing alternating torque and will fail to
show any reading. In order that the instrument should be able to read
a.c. quantities, the magnetic field in the air gap must change along
with the change in current. This principle is used in the
electrodynamometer type instrument. Instead of a permanent magnet, the
electrodynamometer type instrument uses the current under measurement to
produce the necessary field flux.
The Fig. 1 shows the construction of electrodynamometer type instrument.
Fig. 1 electrodynamometer type instrument |
The various type of the electrodynamometer type instrument are:
Fixed Coils : The necessary field required for the operation of
the instrument is produced by the fixed coils. A uniform field is
obtained near the center of coil due to division of coil in two
sections. These coils are air cored. Fixed coils are wound with fine
wire for using as voltmeter, while for ammeters and wattmeters it is
wound with heavy wire. The coils are usually varnished. They are clamped
in place against the coil supports. This makes the construction rigid.
Ceramic is usually used for mounting supports. If metal parts
would have been used then it would weaken the field of the fixed coil.
Moving Coil : The moving coil is wound either as a
self-sustaining coil or else on a non-metallic former. If metallic
former is used, then it would induce eddy currents in it. The
construction of moving coil is made light as well as rigid. It is air
cored.
Controlling : The controlling torque is provided by springs. These springs act as leads to the moving coil.
Moving System : The moving coil is mounted on an aluminium
spindle. It consists of counter weights and pointer. Sometimes a
suspension may be used, in case a high accuracy is desired.
Damping : The damping torque is provided by air friction, by a
pair of aluminium vanes which are attached to the spindle at the bottom.
They move in sector shaped chambers. As operating field would be
distorted by eddy current damping, it is not employed.
Shielding : The field produced by these instruments is very weak.
Even earth's magnetic field considerably affects the reading. So
shielding is done to protect it from stray magnetic fields. It is done
by enclosing in a casing high permeability alloy.
Cases and Scales : Laboratory standard instruments are usually
contained in polished wooden or metal cases which are rigid. The case is
supported by adjustable levelling screws.
A spirit level may be provided to ensure proper levelling.
For using electrodynamometer instrument as ammeter, fixed and
moving coils are connected in series and carry the same current. A
suitable shunt is connected to these coils to limit current through them
upto desired limit.
The electrodynamometer instruments can be used as a voltmeter by
connecting the fixed and moving coils in series with a high
non-inductive resistance. It is most accurate type of voltmeter.
For using electrodynamometer instrument as a wattmeter to
measure the power, the fixed coils acts as a current coil and must be
connected in series with the load. The moving coils acts as a voltage
coil or pressure oil and must be connected across the supply terminals.
The wattmeter indicates the supply power. When current passes through
the fixed and moving coils, both coils produce the magnetic fields. The
field produced by fixed coil is proportional to the load current while
the field produced by the moving coil is proportional to the voltage. As
the deflecting torque is produced due to the interaction of these two
fields, the deflection is proportional to the power supplied to the
load.
1.2 Torque Equation
Let i1 = Instantaneous value of current in fixed coili2 = Instantaneous value of current in moving coil
L1 = Self inductance of fixed coil
L2 = self inductance of moving coil
M = Mutual inductance between fixed and moving coils
The electrodynamometer instrument can be represented by an equivalent circuit as shown in the Fig.2.
Fig. 2 |
From the principle of conversation of energy,
Energy input = Energy stored + Mechanical energy... Mechanical energy = Energy input - Energy stored
Substraction (2) from equation (1),
The self inductance L1 and L2 are constant and hence dL1 and dL2 are zero.
Mechanical energy = i1 i2 dM
If Ti is the instantaneous deflecting torque and dθ is the change in the deflection then
Mechanical energy = Mechanical workdone
= Ti dθ
i1 i2 d M = Ti dθ
This is the expression for the instantaneous deflection torque. Let us see its operation on a.c. and d.c.
D.C. operation : For d.c current of I1 and I2,
Thus the deflection is proportional to the product of the two currents and the rate of change of mutual inductance.
A.c. operation : In a.c. operation, the total deflecting torque over a cycle must be obtained by integrating Ti over one period.
Average deflecting torque over one cycle is,where i1, i2 are the r.m.s. values of the two currents as,
Thus the deflection is decided by the product of r.m.s. values of
two currents, cosine of the phase angle (power factor) and rate of
change of mutual inductance.
For d.c. use, the deflection is proportional to square of current
and the scale is nonuniform and crowded at the ends. For a.c. use the
instantaneous torque is proportional to the square of the instantaneous
current. The i2 is positive and as current varies, the deflecting torque also varies.
But moving system, due to inertia cannot follow rapid variations and thus finally meter shows the average torque.
Thus the deflection is the function of the mean of the squared
current. The scale is thus calibrated in terms of the square root of the
average current squared i.e. r.m.s value of the a.c. quantity to be
measured.
If an electrodynamometer instrument is calibrated with a d.v.
current if 1 A and pointer indicates 1 A d.c. on scale then on a.c., the
pointer will deflect upto the same mark but 1A in this case will
indicate r.m.s value.
Thus as it is a transfer instrument, there is direct connection
between a.c. and d.c. Hence the instrument is often used as a
calibration instrument.
The instrument can be used as an ammeter to measure currents upto
20 A while using as a voltmeter it can have low sensitivity of about 10
to 30 Ω/v
The Fig. 3(a), (b) and (c) shows the connections of the
electrodynamometer instrument as ammeter, voltmeter and the wattmeter.
1) As the coils are air cored, these instruments are free from hysteresis and eddy current losses.
2) They have a precision grade security.
3) These instruments can be used on both a.c. and d.c. They are also used as a transfer instruments.
4) Electrodynamometer voltmeter are very useful where accurate r.m.s values of voltage, irrespective of waveforms, are required.
5) Free from hysteresis errors.6) Low power Consumption.
7) Light in weight.
1.4 Disadvantages of Electrodynamic Instruments
1) These instruments have a low sensitivity due to a low torque to
weight ratio. Also it introduces increased frictional losses. To get
accurate results, these errors must be minimized.
2) They are more expensive than other type of instruments.
3) These instruments are sensitive to overload and mechanical impacts. Therefore can must be taken while handling them.
4) They have a nonuniform scale.
5) The operation current of these instruments is large due to the fact that they have weak magnetic field.
1.5 Errors in Electrodynamometer Instruments
The various errors in electrodynamometer instruments are,
1. Torque to weight ratio : To have reasonable deflecting torque,
mmf of the moving coil must be large enough. Thus m.m.f. = NI hence
current through moving coil should be high or number of turns should be
large. The current cannot be made very high because it may cause
excessive heating of springs. Large number of turns hence is the only
option but it increases weight of the coil. This makes the system heavy
reducing torque to weight ratio. This can cause frictional errors in the
reading.
2. Frequency errors : The changes in the frequency causes to
change self inductances of moving coil and fixed coil. This causes the
error in the reading. The frequency error can be reduced by having equal
time constants for both fixed and moving coil circuits.
3. Eddy current errors : In metal parts of the instrument the
eddy current gets produced. The eddy current interacts with the
instrument current, to cause change in the deflecting torque, to cause
error. Hnec metal parts should be kept as minimum as possible. Also the
resistivity of the metal parts used must be high, to reduce the eddy
currents.
4. Stray magnetic field error : Similar to moving iron
instruments the operating field in electrodynamometer instrument is very
weak. Hence external magnetic field can interact with the operation
field to cause change in the deflection, causing the error. To reduce
the effect of stray magnetic field, the shields must be used for the
instruments.
5. Temperature error : The temperature errors are caused due to
the self heating of the coil, which causes change in the resistance of
the coil. Thus temperature compensating resistors can be used in the
precise instrument to eliminate the temperature errors.
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