17 Nov 2015

CHAPTER 8 PRINCIPLES OF A.C. MEASUREMENT

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.
These ‘instrument transformers’ are described more fully in the manual ‘Electrical Distribution Equipment’.

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