Three Phase Generator

The three phase generator in has three induction coils placed 120 degree apart on the station , as shown symbolically. Since the three coils have an equal number of turns, and each coil rotates with the same angular velocity the voltage induced across each coil has the same peak a value shape and frequency.
As the shift of the generator is turned by some external means the induced voltage Ean, Ebn are generator simultaneously as shown in note the 120 degree phase shift between waveforms and the similarities in appearance of the three sinusoidal functions.



At any instant of time , the algebraic sum of the three phase voltage of a three-phase generator is zero.


This is shown at wt=0 in where it is also evident that when one induct voltage is zero, the other two are 86.6% of their positive or negative maximums. In addition when any two are equal in magnitude and sign (at 0.5Em) the remaining induced voltage has the opposite polarity and a peak value.
The sinusoidal expression for each of the induced voltage



                      Ean=Em(an)sin wt
                      Ebn=Em(bn)sin (wt-120degree)
                      Ecn=Em(cn)sin (wt-240degree)= Em(cn)sin(wt+120degree)



The phasor diagram of the induced of the induced voltages is shown in where the effective value of each is determined by


                     Ean=0.707Em(an)
                     Ebn=0.707Em(bn)
                     Ecn=0.707Em(cn)

and
                     Ean=Ean lessthan0degree
                     Ebn=Ebn lessthan0degree
                     Ecn=Ecn lessthan0degree


   By rearranging the phasors as shown in and applying a law of vectors which states that the vector sum of any number of vectors drawn such that the head of one is connected to the tail of the next and that the head of the last vector is connected to the tail of the first is zero, we can conclude that phasor sum of the phase voltages in a three-phase system is zero. That is,

                     Ean=Ebn+Ecn=0