- When a three-phase voltage is applied to the three-phase stator winding of the induction motor is rotating magnetic field is produced, which by transformer action induces a ‘working’ e.m.f. in the rotor winding. The rotor-induced e.m.f. is called a working e.m.f. because it causes a current to flow through the armature winding conductors. This combines with the revolving flux-density wave to produce torque. Thus revolving field is a key to the operation of the induction motor.
It will now be shown that when three-phase windings displaced in space by 1200, are fed by three-phase current displaced in time by 1200, they produce a resultant magnetic flux which rotates in space as if actual magnetic poles were being rotated mechanically.
- Fig. 7 shows three-phase currents which are assumed to be flowing in phases ‘l’, ‘m’ and ‘n’ respectively. These currents are time-displaced by the 120 electrical degrees.
- Fig. 8 shows the stator structure and the three-phase winding. Each phase (normally distributed over 60 electrical degrees) for convenience is represented by a single coil. Thus coil ‘l-l’ represents the entire phase ‘l’ winding having its flux axis directed along the vertical. This means that whenever phase ‘l’ carries current it produces a flux field directed along the vertical-up or down. The right-hand flux rule readily verifies this statement. Similarly, the flux axis of phase ‘m’ is 120 electrical degrees displaced from phase ‘l’; and that of phase ‘n’ is 120 electrical degrees displaced from phase ‘m’. the unprimed letters refer to the beginning terminals of each phase.
- Magnitude and direction of the resultant flux corresponding to time instant t1. (Fig. 7). At this instant the current into phase ‘l’ is at its positive maximum value while currents in phases ‘m’ and ‘n’ are at one-half their maximum values. In Fig. 8 it is arbitrarily assumed that when current in a given phase is positive, it flows into the paper with respect to the unprimed conductors. Thus since, at time t1, i1 is positive, a cross is used for conductor ‘l’ [Fig. 8(‘i’]. Of course a dot is used for ‘l’ because it refers to the return connection. Then by the right-hand rule it follows that phase ‘l’ produces a flux contribution directed downward along the vertical. Moreover, the magnitude of this contribution is the maximum value because the current is at maximum. Hence Φl = Φmax, where Φmax is the maximum flux per pole of phase ‘l’. It is important to understand that phase ‘l’ really produces a sinusoidal flux field with the amplitude located along the axis of phase ‘l’ as shown in Fig. 9. However, in Fig. 8 (i) this sinusoidal distribution is conveniently represented by the vector Φl.
For determining the magnitude and direction of the field contribution of phase ‘m’ at time t1, we first find that the current in phase ‘m’ is negative with respect to that in phase ‘m’. Hence the conductor that stands for the beginning of phase ‘m’ must be assigned a dot whole ‘m’ is assigned a cross. Hence the instantaneous flux contribution of phase ‘m’ is directed downward along its flux axis and the magnitude of phase ‘m’ flux is one-half the maximum because the current is at one-half its maximum value. Similar reasoning leads to the result shown in Fig. 8 (i) for phase ‘n’.
A glance at space picture corresponding to the t1, as illustrated in Fig. 8 (i), should make it apparent that the resultant flux per pole is directed downward and has a magnitude of ½ times the maximum flux per pole of any one phase. Fig. 9 depicts the same results as Fig. 8 (i) but does so in terms of sinusoidal flux waves rather than flux vectors.
A glance at space picture corresponding to time t1, as illustrated in Fig. 8(i), should make it apparent that the resultant flux per pole is directed downward and has a magnitude of ½ times the maximum flux per pole of any one phase. Fig. 9 depicts the same results as Fig. 8 (i) but does so in terms of sinusoidal flux waves rather than flux vectors.
- Magnitude and direction of the resultant flux corresponding to time instant t3 [Fig. 8(ii)]. Here phase ‘l’ current is zero, yields no flux contribution. The current in phase ‘m’ is positive and equal to its maximum value. Phase ‘n’ has the same current magnitude but is negative. Together phases ‘m’ and ‘n’ combine to produce a resultant flux having the same magnitude as at time t1. See Fig. 8 (ii). It is important to note, too, that an elapse of 90 electrical degrees in time results in rotation of the magnetic flux field of 90 electrical degrees.
- At time instant t5. A further elapse of time equivalent to an additional 90 electrical degrees leads to the situation depicted in Fig. 8 (iii).
From the above discussion it is apparent that the application of three-phase currents through a balanced three-phase winding gives rise to a rotating magnetic field that exhibits the following two characteristics.
- It is of constant amplitude.
- It is of constant speed. It follows from the fact that the resultant flux transverses through 2π electrical radians in space for every 2π electrical radians of variation in time for the phases currents. Hence for a 2-pole machines where electrical and mechanical degrees are identical, each cycle of variation of current produces one complete revolution of the flux field. Hence this is a fixed relationship which is dependent upon the frequency of the currents and number of poles for which the three-phase winding is designated. In the case where the winding is designed for four poles it requires the cycles of variation of the current to produce one revolution of the flux field. Therefore it follows that for a p-pole machine the relationship is:
Ns (r.p.m.) is called the synchronous speed and all synchronous machines run at their respective synchronous speeds.
It may be noted that the speed of rotation of the field as described by eq. (1) is always given relative to the phase windings carrying the time-varying currents. Accordingly, it a situation arises where the winding is itself revolving, then the speed of rotation of the field relative to inertial force is different from it with respect to the winding.