CHAPTER 3 PRINCIPLES OF ALTERNATING AND ROTATING MAGNETIC FIELDS

3.1       ALTERNATING MAGNETIC FIELDS

It is shown in the manual ‘Fundamentals of Electricity 1’ how Oersted’s discovery that a magnetic field surrounds every current-carrying conductor led to the construction of coils, with or without an iron core, which concentrated the magnetic field surrounding each single piece of wire in each turn of the coil to give a strong magnetic field mainly along the axis of the coil.

FIGURE 3.1

MAGNETIC FIELD AROUND A COILED CONDUCTOR

The word ‘mainly’ is used advisedly, because there is also some return field outside the coil, and not all the inside field is wholly concentrated in the centre.  When iron is present the concentration is greater, but some of the field ‘gets away’, even with iron.  This is known as ‘leakage field’, as distinct from the useful axial field which it is the coil’s purpose to produce.

Taking Oersted’s Law literally, any current in a wire gives rise to a field around it, and the strength of that field is proportional to the strength of the current producing it.  This applies to the direction of the current also.  A current flowing in one direction will produce a certain field; the same magnitude of current flowing in the opposite direction will produce a field of the same strength but in the opposite direction.

Thus in Figure 3.1, with an alternating current flowing, if the current direction in one half-cycle is as shown, the field direction at the same time is also as shown.  Half a cycle later the current will be flowing in the opposite direction; so too the field will be in the opposite direction.

Therefore an alternating current will produce a corresponding alternating field, whose strength at any instant is proportional to the magnitude of the current at that instant and which varies ‘in phase’ with the current - that is, it rises, falls and reverses in exact synchronism with it.

3.2       ROTATING MAGNETIC FIELD

A rotating magnetic field is an essential part of all electrical machines. In an a.c. generator it is provided by the rotor carrying d.c.-excited magnetic poles, whose effect is just as if a large permanent magnet were rotating inside the machine.

A rotating field is also necessary for the operation of an induction motor (see manual ‘Electric Motors’), where it must be produced by the stator which, of course, is not moving.  The problem then is: how to produce a moving, rotating magnetic field from stationary windings.

Fortunately this is possible if the supply is 3-phase.  Three separate windings are provided in the stator slots, and their axes are arranged to be displaced in space by 120° as explained in Chapter 1.  Also the three alternating line voltages of a 3-phase system are displaced 120° in time.  It is this combination which makes possible a rotating magnetic field.  This can be proved mathematically, but the following description explains it using first principles.

FIGURE 3.2

ROTATING MAGNETIC FIELD

In the centre of Figure 3.2 are shown the three stator windings of an induction motor, each drawn as a simple coil.  The winding which is connected to each phase is distinguished by its colour - red, yellow or blue.  The three windings are distributed 120° apart in space around the stator.

At the top is shown one cycle of currents of the 3-phase supply, each current wave being coloured.  The 120° displacement in time is clearly seen.

The current in each of the three windings gives rise to a magnetic field along its axis; these are shown by coloured arrows for each field near the centre of the figure.  As the current alternates, so also does the direction of the field along its axis.  The convention has been adopted that, when the current is positive (above the line in the upper part of the figure), the arrow points towards the centre, and when it is negative, it points away from the centre.

Looking at the left-hand centre figure, taken at the instant where t = 0 (left-hand edge of the current waves), R phase current is at its maximum positive, and Y and B phases are negative and both equal in magnitude to half the maximum.  Therefore the R phase flux is shown as ‘1’ with its arrow pointing towards the centre, and Y and B phase fluxes are both shown as ‘½’ with their arrows pointing away from the centre.

These arrows can be regarded as flux vectors, and in the bottom figure they are resolved.  The R phase flux is at 12 o’clock and pointing downwards, and the Y and B phase fluxes are respectively at 4 and 8 o’clock, half the length of R and pointing outwards in those directions.  The latter two, by normal vector addition, combine to give a single flux of length ½ at 6 o’clock in a downward direction.

The R phase (length 1) and the combined Y and B phases (length ½) are both in the same direction and add together to give a single resultant flux of length 1½ in a 6 o’clock direction.

If exactly the same procedure is adopted for a time one-third of cycle (120°) later, Y phase is now at a maximum positive and B and R phases at half that value negative.  B and R now combine to add to Y, giving a resultant flux of magnitude 1½ in the 10 o’clock direction.

Similarly at a time one-third of a cycle still later (240°), B phase is at a maximum positive and R and Y phases at half that value negative.  R and Y now combine to add to B, giving a resultant flux of magnitude 1½ in the 2 o’clock direction.

One-third of a cycle still later (360°) the conditions are the same as at 0° (t = 0), and the process repeats with each cycle.

As time advances and the current cycle changes from 0°, through 120° and 240°, back to 0° and then repeats, the resultant flux constantly changes direction (but not magnitude, which remains constant at 1½) and swings from 6 o’clock, through 10 and 2 o’clock, back to 6 o’clock and then starts again.  Although only three different points in the cycle have been described, the same treatment at intermediate points would show the resultant flux in intermediate positions.  For example, if the currents were taken at 60° and the fluxes combined as before, the resultant flux would come out at 8 o’clock.

This is therefore a continuous process, and the resultant flux direction moves continuously round the stator, remaining constant in magnitude and completing one revolution per cycle of supply.  A rotating magnetic field has been produced from a set of stationary stator windings.

Note: the statement that the flux completes one revolution per cycle of supply is only true when there is one winding per phase as shown in Figure 3.2; this is a so-called ‘2-pole’ machine (by analogy with d.c.), and with a 60Hz supply the field rotates at 60 rev/s or 3 600 rev/mm (with 50Hz at 50 rev/s or 3 000 rev/mm).  If there were two windings per phase (‘4-pole’ machine), a similar treatment would show that the field rotates only half a revolution per cycle, so that it makes one revolution per two cycles; at 60Hz this is 30 rev/s or 1 800 rev/mm (at 50Hz, 25 rev/s or 1 500 rev/mm).  Similarly a ‘6-pole’ machine (three windings per phase) would at 60Hz have 1 200 rev/mm (50Hz, 1 000 rev/mm), and so on.

3.3       ROTATING FIELD FROM SINGLE PHASE

What has been described (para. 3.2) is the production of a rotating field from a 3-phase supply.  It can however be done from a single-phase supply, although it is seldom found except in the smallest motors which have only a single-phase supply to run on.

FIGURE 3.3

ROTATING FIELD FROM SINGLE-PHASE SUPPLY

(APPLIED TO A CAPACITOR MOTOR)

It is achieved by giving the motor two separate windings displaced in space by 90°  One, the ‘running’ winding, is fed direct from the single-phase supply, and the other, the ‘starting winding’, is fed from the same supply but through a series capacitor.  This causes the current in that winding to lead nearly 90° on the current in the other, so there is the situation where the two windings are displaced 90° in space and are fed from supplies 90° displaced in time.  By an exactly similar treatment to that used for the 3-phase case, it will be found that this too will produce a rotating field, enabling the motor to start and run.  Such a motor is referred to as a ‘Capacitor Motor’ or ‘Split Field Motor’.  It is further described in the manual ‘Electric Motors’.

On most such motors a centrifugal switch cuts out the capacitor-fed starting winding when the motor is up to speed; it will then continue to run with only its single-phase ‘running’ winding connected.  Very small motors often dispense with the centrifugal switch and leave the capacitor in circuit all the time.