# Generation of Three-phase Voltages

• Let us consider an elementary 3-phase 2-pole generator as shown in Fig: 1. On the armature are three coils, ll’, mm’, and nn’ whose axes are displaced 120° in space from each other. • When the field is excited and rotated, voltages will be generated in the three phases in accordance with Faraday’s law. If the field structure is so designed that the flux is distributed sinusoidally over the poles, the flux linking any phase will vary sinusoidally with time and sinusoidal voltages will be induced in three-phases. These three waves will be displaced 120 electrical degrees (Fig. 2) in time as a result of the phases being displaced 120° in space. The corresponding phasor diagram is shown in Fig. 3. The equations of the instantaneous values of the three voltages (given by Fig. 2) are:

e l’ l  = E max .. sin rot

e m ‘m = E max. sin (wt- 120°)

e n ‘n = E max. sin (wt – 240°)

The sum of the above three e.m.fs. is always zero as shown below : Resultant instantaneous e.m.f.

= e l’ l + e m’ m + e n’ n

= E max. sin wt+ E max. sin (wt- 120°) + E max. sin ( wt – 240°)

= E max. [sin rot + (sin wt cos 120° – cos wt sin 120° + sin wt cos 240° – cos wt sin 240°)]

= E max. [sin rot+ (- sin wt cos 60° – cos rot sin 60° – sin wt cos 60° + cos wt sin 60°)]

= E max. (sin rot – 2 sin wt cos 60°)

= E max. (sin rot- sin wt) = 0.  