Three-phase induction motors

With reference to Figure 22.1, the windings are represented by three single-loop conductors, one for each phase, marked R_SR_F, Y_SY_F and B_sB_F, the S and F signifying start and finish. In practice, each phase winding comprises many turns and is distributed around the stator; the single-loop approach is for clarity only.

When the stator windings are connected to a three-phase supply, the current flowing in each winding varies with time and is as shown in Figure 22.1(a). If the value of current in a winding is positive, the assumption is made that it flows from start to finish of the winding, i.e. if it is the red-phase, current flows from R_s to R_F,

i.e. away from the viewer in R_s and towards the viewer in R_F. When the value of current is negative, the assumption is made that it flows from finish to start, i.e. towards the viewer in an ’S’ winding and away from the viewer in an ’F’ winding.

At time, say t₁ shown in Figure 22.1(a), the current flowing in the red phase is a maximum possible value. At the same time, t₁, the currents flowing in the yellow and blue phases are both 0.5 times the maximum value and are negative. The current distribution in the stator windings is therefore as shown in Figure 22.1 (b), in which current flows away from the viewer (shown as X) in R_s since it is positive but towards the viewer (shown as ˙) in Y_S and B_s, since these are negative. The resulting magnetic field is as shown, due to the ’solenoid’ action and application of the corkscrew rule.

A short time later at time t₂, the current flowing in the red phase has fallen to about 0.87 times its maximum value and is positive, the current in the yellow phase is zero and the current in the blue phase is about 0.87 times its maximum value and is negative. Hence the currents and resultant magnetic field are as shown in Figure 22.1(c). At time t₃, the currents in red and yellow phases are 0.5 of their maximum values and the current in the blue phase is a maximum negative value. The currents and resultant magnetic field are as shown in Figure 22.1(d).

Similar diagrams to Figure 22.1(b), (c), (d) can be produced for all time values and these would show that the magnetic field travels through one revolution for each cycle of the supply voltage applied to the stator windings. By considering the flux values rather than the current values, it can be shown that the rotating magnetic field has a constant value of flux.

If six windings displaced from one another by 60° are used, as shown in Figure 22.2(b), by drawing the current and resultant magnetic field diagrams at various time values, it may be shown that one cycle of the supply current to the stator windings causes the magnetic field to move through half a revolution. The current distribution in the stator windings is shown in Figure 22.2(b), for the time t shown in Figure 22.2(a).

It can be seen that for six windings on the stator, the magnetic flux produced is the same as that produced by rotating two permanent magnet north poles and two permanent magnet south poles at synchronous speed. This is called a 4-pole system and an induction motor using six phase windings is called a 4-pole induction motor. By increasing the number of phase windings the number of poles can be increased to any even number. In general, f is the frequency of the currents in the stator windings and the stator is wound to be equivalent to p pairs of poles, the speed of revolution of the rotating magnetic field, i.e. the synchronous speed, n_s is given by:

${\text{n}}_{\text{s}}\text{=}\frac{\text{f}}{\text{p}}\text{rev/s}$

In the type most widely used, known as a squirrel-cage rotor, copper or aluminium bars are placed in slots cut in the laminated iron, the ends of the bars being welded or brazed into a heavy conducting ring, (see Figure 22.3(a)). A cross-sectional view of a three-phase induction motor is shown in Figure 22.3(b).

When a three-phase supply is connected to the stator windings, a rotating magnetic field is produced. As the magnetic flux cuts a bar on the rotor, an e.m.f. is induced in it and since it is joined, via the end conducting rings, to another bar one pole pitch away, a current flows in the bars. The magnetic field associated with this current flowing in the bars interacts with the rotating magnetic field and a force is produced, tending to turn the rotor in the same direction as the rotating magnetic field (see Figure 22.4).

When there is no load on the rotor, the resistive forces due to windage and bearing friction are small and the rotor runs very nearly at synchronous speed. As the rotor is loaded, the speed falls and this causes an increase in the frequency of the induced e.m.f.’s in the rotor bars and hence the rotor current, force and torque increase. The difference between the rotor speed, n_r, and the synchronous speed, n_s, is called the slip speed, i.e.

$slipspeed=n_s-n_{r}rev/s$

The ratio (n_s − n_r)/n_s is called the fractional slip or just the slip, s, and is usually expressed as a percentage. Thus

$slip,s=\frac{n_s-n_r}{n_s}\times 100\%$

Typical values of slip between no load and full load are about 4% to 5% for small motors and $1\frac{1}{2}\%$ to 2% for large motors.

Single-phase induction motor

split-phase start,

capacitor start,

capacitor start and run,

shaded pole,

permanent-split capacitor induction motors, and so on.

These motors may be used on many of the loads driven by induction motors but (i) are normally more expensive, (ii) require both a.c. and d.c. supplies, (iii) require additional equipment to run them up to near to their normal running speed, so that the rotor magnetic field can be locked to the rotating magnetic field, and (iv) have higher maintenance costs than induction motors. However, they can run at higher efficiencies and when used adjacent to several induction motors can lead to a higher efficiency of the whole system (power factor correction). Due to the disadvantages listed above, three-phase synchronous motors are normally used for applications requiring a large power input, where savings due to higher efficiency outweigh the disadvantages. Their uses include driving large water pumps (power stations, water supply), driving rolling lines in steel mills and driving mine ventilating fans.