## Friday, September 10, 2021

### WORKING OF A.C GENERATOR AND MOTOR

A.C GENERATORS AND MOTORS

The outline of a d.c machine shown earlier in the previous article will serve also as a small alternating-current generator or alternator. Alternators, of course, have no commutator, and the direct current for energizing the field magnet must be obtained from a separate source. A small d.c generator termed an exciter is sometimes mounted on the same shaft for this purpose.

As in the d.c generator, the field-magnet poles, if there are more than two, are alternately n south, and since a complete cycle of current is generated every time a conductor passes north and south pole in succession, the frequency of the current is given by the equation;

FREQUENCY = Revolution per second ×Number of pairs of poles.

The armature carries several groups of conductors, the groups being spaced around the periphery so as to occupy similar positions in relation to the field-magnet poles. The current is collected from the armature by means of slip-rings.

Since all that is necessary for the generation of current is relative motion between conductors and field, a generator could be made to work by holding the armature and rotating the field magnet around it. This would be very inconvenient, but a similar effect can be obtained by placing the field-magnet system on the central rotating part, and the conductors in which the current is generated on the surrounding stationary part. As the field-magnet windings then rotate, they must be connected to the d.c source by a pair of slip-rings.

Part of an alternator in which the conductors move and the field magnets are stationary is shown in the diagram below, while the corresponding arrangement, in which the field-magnets move and the conductors are stationary. In both cases the slots in which the conductors are housed are indicated, but the conductors themselves are omitted for the sake of clearness.

In order to avoid confusion, the terms stator and rotor are used instead of armature and field-magnet. The stator is the stationary part and the rotor is the rotating part, no matter which of them carries the armature conductors and with the field-magnet system.

The advantage of the arrangement shown below is that the slip-rings and moving windings have to deal only with the comparatively low voltage and small current necessary to produce the field.

As the conductors in which the alternating current is generated are stationary, their insulation is simplified, while the fact that the connection can be made to them without slip-rings and brushes removes another difficulty in the generation of high voltages. Alternators of this type are therefore normal and can be made for much larger outputs than are practicable in d.c generators.

Note that the right-hand rule for finding out in which direction induced current flows assumes that the conductor is moving across the field, and not vice versa. When the conductor is stationary and the field is moving, the rule must be applied as though the direction of motion were reversed.

POLYPHASE CURRENTS

From the generating point of view, it is better to produce a steady current than one that is continually varying. In the d.c generator we were able to do this by spacing a number of conductors around the armature, so that while some were generating their maximum e.m.f., others were generating their minimum. Something of the same kind can be done in the case of an alternator, by causing it to generate at the same time two or more currents differing in phase. The different currents must be taken from the machine over different circuits, and we are thus led to a polyphase system comprising several more or less independent supplies of the same frequency, as distinct from a single-phase system having only one supply.

Polyphase systems also enable the winding space on the generator to be utilized more efficiently. Moreover, they simplify the design of alternating-current motors and lead to economies in the amount of copper required for transmission lines.

Suppose that we provide an alternator with two sets of conductors, the grouping in relation to the spacing of the rotating field-magnets being such that one set is producing its maximum. We then have two independent sources of current, the phase relationship of the voltages being represented by curves a and b. This is a two-phase system, and the difference in phase is one-quarter of a cycle or ninety electrical degrees.

In a similar manner, we can provide a generator with three independent groups of conductors, thus obtaining three separate sources of current, the phase relationship of the three voltages being as a, b and c  in the diagram below. This is a three-phase system and the difference in phase is one-third of a cycle or 120 electrical degrees.

Instead of fitting a three-phase generator with six output terminals, we can connect one end of each winding to a common point, thus using only four.

The arrangement will then be shown on the diagram below in which the coils represent the three generator windings, and the center point the fourth terminal. Conductors a,b and c are connected to the terminals at the free ends of the windings. The common return path to the center point. Conductors a, b and c are known as the three lines, and the common center point (which is usually earthed) as the neutral point.

Suppose that three exactly similar loads are connected, one between each of lines a, b, and c. The three currents will then be equal, and their phase relationship will be the same as that of the voltages. They can therefore be represented by the curves from which it will be seen that when anyone current is at a maximum, the other two are halfway towards a maximum in the opposite direction and that when anyone is zero, the other two are equal and opposite. Similar conditions apply at all points on the curves, so that the sum of the three currents at any moment, taking their directions into account, is zero.

It follows that so long as loads remain the same, there is no current flowing in either direction in the conductor, which under these conditions could be omitted. Each of the three lines is then acting in turn as a return path for the other two. Even if the loads are not the same, the conductor has to carry only the difference between the current flowing outwards and that flowing inwards over the three lines at any instant. It can therefore be smaller in size than the others.

Instead of connecting each load between one of the lines a, b, c, and the conductor, we can connect one load between a and b, one between b and c,  and one between c, and a. the voltage applied to each load is then derived from two of the generator windings, but as the two voltages do not reach their maximum at the same time, the joint value is not twice that of one winding, but some smaller figure. The actual value is √3 or 1.732, times the voltage of one winding. The current in each line is obviously equal to the current in one winding.

Generator windings arranged as shown below are said to be star connected.

The voltage between any two of the lines a, b, and c  is called the line voltage, and that between any one of them and the neutral point the phase voltage.

Line voltage = phase voltage × 1.732 = 400.

Phase voltage = 400/1.732 = 230.

An alternating arrangement of the generator windings is shown  below, and in this case they are said to be delta connected or mesh connected.

The term “delta” is taken from the Greek capital letter Δ. There is no tendency for current to circulate around the closed path because the sum of the voltages at any instant is zero. The line voltage is that produced by one winding and is therefore equal to the phase voltage. The current in each line, however, is √3 or 1.732, times the current in one winding.

Note that the two methods of connection (star and delta) apply not only to the generator windings but also to the loads. Thus, in the first case we considered, if the loads are connected between each of lines Ia, b, c, and the conductor, they are star-connected, but if between a and b, b and c, and c and a, they are delta connected. This can readily be seen by drawing an example.

A.C MOTORS

A.C generators, like d.cgenerators can be made to run as motors, but only when the frequency of the supply is in step with the frequency at which the armature conductors pass the frequency at which the armature conductors pass the pairs of poles. The  motor must therefore be rotated by some other means until it is running fast enough to continue in synchronism with the supply frequency.

Machines designed to operate in this manner are called synchronous motors. Motors that do not operate in synchronism with the supply frequency are the most important class of asynchronous motors that depend upon a special property of polyphase currents which we shall now examine.

ROTATING FIELDS

Consider the two pairs of coils shown below. If coils are energized, there will be a magnetic field in line with their axis; let us call this direction north and south. If coils b are energized, there will be a magnetic field in line with their axis; let us call this direction east and west.

Suppose now that the coils are connected to a two-phase supply. We can use a phase diagram to represents the two currents, each curve corresponding to the similarly lettered coils. Starting on the left-hand side, current a is at a maximum in one direction; let us assume that this produces a flux in coils a towards the north. At this moment, current b is at zero, so there is no flux in coils b. the flux at the center may therefore be represented by the arrow in the sketch below:

Halfway between these positions, curve a is still some distance from zero, and curve b is some distance from its maximum. This is the point at which the curves cross, and the two currents are therefore equal. The two small arrows in sketch 2 represent these conditions, and their combined effect is to produce a field towards the north-west as shown by the heavy arrow.

This combination of two fields should be noted. It follows from the fact that the lines of force can not have more than one direction at the same place and time. An analogy may be helpful. Suppose that we set up two electric fans at right angles so that one produces a wind towards the north and the other a wind towards the west. If only the first fan is blowing, a particle caught in the wind will move north. If only the second fan is blowing, it will move west. If both fans are blowing, its tendency will be to move north-west.

As the field from coils a dies away and that from coils b  grows, the combined field, starting from sketch 1, passes through all the intermediate positions to sketch 2, and then through all the intermediate positions to sketch 3. We have, therefore, a rotating field produced by fixed coils. Moreover, it can be shown mathematically that the strength of the field does not vary, being always equal to that produced by one of the coils when the current in the other is at zero.

It is important to note that the rotating field is not a matter of approximation, or of a sudden jump from north to west, or even from north to north-west. The rotation of the field is quite smooth and regular, owing to the gradual dying away of flux in one direction and its equally gradual building up at right angles.

Continuing the sequence, the current in coil b dies away again after reaching its maximum, and the field towards the west gradually weakens. At the same time, coil a is energized by a growing current in the direction opposite to that which produced a field towards the north. This produces a field towards the south, which, in conjunction with the weakening field towards the west, produces a field passing through the south-west as shown in the sketch above. when the current in coils a has reached a maximum in this direction and that in coils b is at zero, the field is towards the south. We have now traced the changes for a complete half-cycle, it will be found that the rotation continues through south-east, east, and north-east until the field is again towards the north. The number of revolutions per second made by the field is therefore equal to the frequency of the current.

We have examined the production of a rotating field by two-phase current because this is the easiest case to follow without a detailed mathematical statement. A similar effect can, however, be produced by three-phase currents. In this case, three sets of coils are needed, and the field rotates through 120 degrees between the maximum in one set of coils and the maximum in the next. As this time represents one-third of a cycle, the field again rotates at the supply frequency.

INDUCTION MOTORS

The fact that a rotating field can be produced by stationary coils has led to the development of the induction motor. In this machine, coils carried by the stator produce the rotating field and the rotor is provided with heavy copper conductors accommodated in the usual slots.  In many cases, these conductors have no external connections but are simply joined together at each end of the rotor by heavy copper rings. The term squirrel-cage is often applied to rotors of this type.

As the magnetic field rotates, it cuts the rotor conductors and induces currents in the circuits completed by the copper end rings. These currents produce a field that reacts with the rotating field. in accordance with Lenz’s law, the effect is to produce motion that will tend to prevent the change of flux linkage, i.e., to make the conductors follow the field.

The rotor therefore turns. It does not, however, actually reach the speed of the rotating field; if it did there would no longer be any induced currents, and there would be no power even to overcome the friction of the motor bearings. The difference between the speed of the rotor and that of the field is known as the slip, and at full load may amount in practice to, say, 4% of the speed.

The squirrel-cage rotor without slip-rings is very simple and robust but is not suitable for starting under heavy loads. Some induction motors are therefore fitted with wound rotors. The winding is in three sections and is brought out to three slip-rings. The object of the slip-rings is to enable starting resistances to be gradually cut out as the motor speeds up until conditions are then similar to those of the squirrel-cage machine.

MISCELLANEOUS A.C MACHINES

In addition to the machines we have described, the following types may be mentioned.

SINGLE-PHASE INDUCTION MOTORS – Although a single-phase supply cannot produce a rotating magnetic field in the way described for polyphase currents, it is nevertheless possible to design a single-phase motor operating on the induction principle. Machines of this kind are not very efficient, but in small sizes they have come into increasing use in recent years. They are not naturally self-starting but can be made so at the cost of some complication.

MAGNETO GENERATORS – These are miniature generators in which the field is produced by permanent magnets. The armature (rotor) is usually of the simple two-slot form also known as H-armature shown below.

One cycle of alternating current is generated during each revolution. Magneto generators have been used for the generation of ringing current in some telephone systems, and for ignition current in internal combustion engines. In the latter case, provision is made for interrupting the armature current periodically. The result is to induce a very high voltage in a second winding, also carried by the armature. The high-voltage current so made available is led to the sparking-plugs, where it produces the spark which ignites the explosive mixture in the cylinders.

COMMUTATOR MOTORS – Since in a d.c motor, reversal of both field and armature connections at the same time does not alter the direction of rotation, it is possible to run such motors on alternating current. Owing to the greater tendency to eddy-current losses, however, all the iron, including the field magnet, should be laminated. Small machines of this kind suitable for either d.c or a.c supplies are made and are called universal motors.

MINIATURE SYNCHRONOUS MOTORS – For driving electric clocks, miniature synchronous motors are used. They must be operated from mains on which the frequency is “controlled” i.e., kept at or near its stated value over long periods. The motor then runs at a known speed, so that by means of reduction gearing it can be made to operate the hands of a clock. Some but not all of these motors are self-starting. Miniature synchronous motors of slightly larger sizes are commonly used for rotating gramophone turntables.