8.1 USE OF D.C. INSTRUMENTS FOR A.C.
In the manual ‘Fundamentals of Electricity 1’, Chapter
11, are described a number of different types of instrument used for d.c.
measurements. They are the hot-wire,
moving-iron, moving-coil and dynamometer types and are there described and
illustrated in detail.
Some of them may also be used for
a.c. measurements, and each is considered below in that application.
8.2 HOT-WIRE INSTRUMENTS
This instrument depends for its action on the heating
and stretching of a wire due to the passing of current through it. The heating with a d.c. current is at the
rate I 2 R, where R is the resistance of the internal hot
wire. But with a.c. the heating is also
at the rate I2 R provided
that I is the rms current - indeed, it has been
shown that rms current is defined as that a.c. current which produces the same
heating as a d.c. current of the same numerical value.
Consequently a hot-wire instrument
to which a.c. is applied will correctly indicate the rms value of the applied
quantity.
FIGURE 8.1
MOVING-IRON INSTRUMENT MEASURING A.C.
8.3 MOVING-IRON INSTRUMENTS
A moving-iron instrument will also correctly indicate
the rms value of an applied a.c. quantity.
Figure 8.1 shows a basic moving-iron instrument. As explained in the manual ‘Fundamentals of
Electricity 1’ the fixed coil induces in the moving-iron poles of opposite
polarity to the flux which induces them.
Thus, in Figure 8.1(a), which is assumed to be the state during a
positive half-cycle of current in the coil, the coil’s field is from right to
left. A N-pole will be induced on the
right tip of the moving iron, and a S-pole on its left. Each pole will be attracted towards the axis
of the coil, so giving a clockwise torque.
On the next half-cycle the coil field will be reversed,
as shown in Figure 8.1(b). The field
will now be from left to right, and a N-pole will be induced on the left tip of
the moving iron and a S-pole on the right.
Each will be attracted to the axis of the coil, and the torque is again
clockwise. There is thus no reversal of
torque as between positive and negative half-cycles, and the pull will be
always in the same direction.
The magnitude of the magnetic pull between a coil and
its induced magnetic pole is proportional to the product of the coil’s flux
(and so the current in it) and of the strength of the induced pole. But that strength is itself proportional to
the flux causing it, so the total pull - and hence the torque on the moving
iron - is proportional to the square of the coil current.
Therefore, like the hot-wire type, the moving-iron
instrument responds not simply to the current but to the square of the
current. Its scale will be uneven and
crowded towards the lower end, and it will indicate the rms value of the
current being measured. Moving-iron
instruments are relatively cheap and are widely used ashore and in platforms on
a.c. switchboards. They can be instantly
recognised by their scales.
8.4 MOVING-COIL INSTRUMENTS
Moving-coil instruments cannot be used with a.c. for the
following reason.
Figure 8.2 is a reproduction of the
corresponding moving-coil figure in the manual ‘Fundamentals of Electricity 1’.
As explained there, a permanent magnet provides a constant field in which a
moving coil rotates.
FIGURE 8.2
MOVING-COIL
INSTRUMENT ATTEMPTING TO MEASURE A.C.
In the figure the N-pole is assumed to be on the right,
and the field in the gap is therefore from right to left.
The current to be measured flows through the moving coil
and gives rise to its own flux. This flux reacts with the permanent field and
causes a torque on the moving coil. The
coil turns against a control spring so as to try to align its own axis with
that of the permanent magnet. This is
shown in Figure 8.2(a), which is assumed to be the state during a positive
half-cycle of current in the moving coil.
The coil’s ‘S’ side is attracted towards the magnet’s N-pole, and its
‘N’ side to the magnet’s S-pole, so producing a clockwise torque.
Half a cycle later the coil current is reversed, as
shown in Figure 8.2(b), but the direction of the permanent magnet field is
unchanged. The coil’s ‘N’ side is now on
top and is repelled by the magnet’s N-pole, just as its ‘S’ side is repelled by
the magnet’s S-pole. The two combine to
produce an anti-clockwise torque.
The direction of torque thus reverses with every
half-cycle, and, because of the inertia of the movement, no motion whatever
takes place (though there might be a buzz).
For this reason moving-coil instruments cannot be used directly on a.c.,
although they can be used with transducers (see para. 8.6).
8.5 DYNAMOMETER INSTRUMENTS
A dynamometer instrument consists of fixed coils and a
moving coil.
When used as an ammeter or voltmeter (rarely done), the fixed and moving coils are in series or parallel respectively, and therefore both fixed and moving fluxes reverse together with each half-cycle. Therefore there is no change in the direction of torque, and the pull is always one way, as shown in Figure 8.3.
FIGURE 8.3
DYNAMOMETER INSTRUMENT USED AS AN A.C. WATTMETER
Moreover, since the torque depends on the product of the
currents in both the fixed and moving coils, and since these are either equal
(in an ammeter, where they are in series) or proportional (in a voltmeter,
where they are in parallel), the torque is proportional to the square of the
coil current. The instrument will
therefore have an uneven scale and will indicate rms current or voltage.
Dynamometer instruments can consequently be used as
ammeters or voltmeters on an a.c. system, where they will indicate rms values,
although, as already said, this is not often done because of cost.
The dynamometer instrument is however principally used
as a wattmeter, where the fixed coils carry the line current and the moving
coil the line voltage. Here again when
going from a positive to negative half-cycle, both change sign together, so
that there is no reversal of torque.
The magnitude of the torque depends on the product of
the voltage (moving) field strength, of the current (fixed) field strength and
of the cosine of the phase angle between them.
The torque therefore is proportional to VI cos j.
But cos j is the power factor, so the torque is proportional to the active
power in watts. The dynamometer
instrument can consequently be used as an a.c. wattmeter.
This instrument can also be adapted for 3-phase working,
where, by suitable connections between the phases, it can be made to indicate
the total watts in a balanced or an
unbalanced 3-phase system. By suitable
reconnections between the phases the same instrument can be made to indicate VI sin j - that is, reactive power, and so is used as a varmeter.
8.6 TRANSDUCER-OPERATED INSTRUMENTS
There are in big installations many disadvantages in
carrying the signals (especially currents) from the sensing devices over long
distances to a control centre. Also
wattmeters and similar instruments of the dynamometer type are expensive. Much cost can be saved and the
instrumentation simplified if all a.c. measurements could be converted to
simple equivalent d.c. voltages proportional to the quantities sensed, and the
d.c. signals so derived distributed to all control points in parallel and
displayed on simple d.c. moving-coil voltmeters. The scale would of course not be in d.c.
volts, but it would be calibrated in whatever unit the original sensing device
was measuring. This may be volts,
amperes, watts, hertz (frequency), power factor or any other quantity.
The sensing device, most usually a current transformer
or voltage transformer (see para. 8.8), feeds its signal into a solid-state electronic
circuit where the signals are processed, converted to d.c. exactly proportional
to the quantity sensed and passed out as a variable-voltage d.c. signal to be
displayed on voltmeters wherever desired.
Such an electronic device is called a ‘transducer’; it is relatively
cheap and may be incorporated inside the instrument, or it may be in a separate
box near to the sensing point when remote instruments need to be connected to
the d.c. side.
8.7 INDUCTION (EDDY-CURRENT) INSTRUMENTS
There is another class of instrument which works on a
totally different principle and which operates only with alternating
current. They are ‘induction’
instruments, also called ‘eddy-current’ type, as shown in Figure 8.4.
The movement consists of a thin copper or aluminium disc
which is caused to rotate between the poles of a special electromagnet. As it rotates it winds up a spiral control
spring which opposes the rotation increasingly as the disc moves.
FIGURE 8.4
INDUCTION MOVEMENT
The electromagnet is of a special shape, as shown in
Figure 8.4. It is wound with an exciting
coil: the coil is connected in series with the line current to be measured if
the instrument is to be an ammeter, or in parallel with the line voltage if it
is to be a voltmeter.
The pole on one side of the disc is split into two
parts, ‘A’ and ‘B’, and one of the parts is surrounded by a bare copper ring,
called a ‘shading ring’. The alternating
flux due to the exciting coil passes freely through the disc from pole ‘A’, but
the parallel flux in pole ‘B’ sets up an alternating emf, and so a current, in
the closed shading ring which produces its own flux. The combined effect of these two fluxes in
pole ‘B’ is to produce a net flux which lags nearly 90o on that in
pole ‘A’.
There is thus a situation where the fluxes in poles ‘A’
and ‘B’ are separated in both space and time - the classic requirement for a
travelling magnetic field - see manual ‘Fundamentals of Electricity 2’. On the left of Figure 8.4 is shown the
situation at the instant when the current in the coil is at a positive peak
(time t1). The flux in
pole ‘A’ is maximum (downwards, say), and the flux in pole ‘B’ is zero.
One-quarter of a cycle later (time t2,
right-hand side of Figure 8.4) the flux in pole ‘A’ is zero and the flux in
pole ‘B’, which lags 90° on that in pole ‘A’, is now maximum
positive. So the peak flux has moved
from ‘A’ to ‘B’ in one-quarter of a cycle - it has, in fact, travelled
from ‘A’ to ‘B’.
As a flux wave travels, it induces in the metal disc a
mass of so-called ‘eddy currents’ - local whirls of current within the disc
which react with the travelling field and, as explained in the manual
‘Fundamentals of Electricity 1’ for the interaction of currents in a magnetic
field, produce a mechanical force on the outside of the disc, causing it to try
to follow the travelling field. The disc
therefore undergoes a torque which is proportional to the travelling flux and
so to the square of the current in the coil.
Under this torque the disc starts to rotate, and as it
does so it begins to wind up the spiral spring.
This continues until the torque exerted by the spring exactly balances
the driving torque due to the travelling field of the magnet; the disc then
comes to rest.
The rest position is thus an indication of the current
in the coil, and the disc actuates a pointer which moves over a scale, which is
calibrated in amperes or volts. Since
the torque is proportional to the square of the current, this type of
instrument, like the moving-iron type, has a non-linear scale and is calibrated
to read rms values.
One distinguishing feature of the
induction-type instrument is that the disc has a far greater range of movement
than is possible in the moving-iron type, and the scale is therefore very long,
or open, covering almost the whole of the face of the instrument.
Induction instruments are now not much used as ammeters
or voltmeters, as the moving-iron type is much cheaper, but the method is used
with integrating meters such as the kWh meter found in domestic and other
installations. In that application there
are two coils, one voltage and one current, on either side of the disc. There is no spiral spring but instead a brake
magnet which controls the disc speed.
The torque is then proportional to the product of the voltage flux, of
the current flux and of the cosine of the phase angle between them, namely:
This instrument’s disc therefore moves, controlled by
the brake magnet, at a speed proportional to the active power, watts. Having no control spring it does not stop but
continues to rotate, operating a counter as it does so; this indicates the
watt-hours (or kWh) which have been consumed by the circuit over any period of
time. It is thus an integrating
meter, in that it continuously adds up the energy consumed.
The induction, or eddy-current, movement is also widely
used in overcurrent relays (see manual ‘Electrical Control Devices’), where the
method is the same as for the watt-hour meter as described, but the disc, after
rotating through a preset angle, strikes an adjustable contact. The time which elapses before this happens
depends on the speed of the disc, and so on the line current causing it. A variable time delay can therefore be set on
this relay, depending on the current being measured and by varying the distance
to be travelled by the disc before striking the contact.
8.8 INSTRUMENT TRANSFORMERS
The current, or voltage, in the operating coil of any
type of a.c. instrument could be the actual line current or voltage of the
system. However, in most a.c. systems
the operating voltages are very high and the currents are large. Severe practical difficulties would arise if
such voltages were applied to these small instruments or switchboards, or if
they had to be designed to carry such heavy currents.
It is therefore universal practice to apply the
operating voltage through a step-down ‘voltage transformer’ or to apply the
operating current through a step-down ‘current transformer’. In either case a much lower voltage or
current, which is an exact proportion of the line voltage or current, is
applied to the instrument. The scale
however is calibrated to read the actual line values, not the ones actually
applied.
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