EMF Equation of Synchronous Generator

the poles of the rotor moves under the armature conductor on the stator , field flux cuts the armature conductors. therefor voltage is generated in these conductors.  the voltage is of alternating nature, since poles of alternate polarity successively pass by a given stator conductor.  A 3-phase alternator has a stator with three set of windings. arranged so that is a matual phase displacement of 120 . these winding are connected in star to a 3-phase output.the voltage generated in each winding is given as equation is called emf equation.

Let, 

     Φ  =  useful flux per pole in webers

      P  =  total number of poles

     Z_{p =  total number of conductors}

     Tp  =  total number of coils or tuns per phase

      n = speed of rotation of rotor in revolution per second (r.p.s.)

      f  = frequency of generated voltage ( Hz )

Since the flux per pole is Φ , each stator conductor cuts flux PΦ.

The average value of generated voltage per conductor 

              =            flux cut per revolution in Wb        

                   time taken for one revolution in seconds

Since n revolution are made in one second, one revolution will be made in 1/n second. therefore the time for one revolution of the armature is 1/n second.

Eav/ conductor = PΦ   = nPΦ     .....................................(1).

                           1/n

We know that 

  

                        f = PN/120 =  Pn/2

                      Pn = 2f

these value put in equation 1 we get ,

 Eav/ conductor = 2fΦ           ........................................(2).

sinc there are  Z_p  conductor in series per phase , the average voltage generated per phase is given by

       Eav/ phase = 2fΦ Z_p

since one turn or coil has two sides Zp = 2Tp  , the expression for the average generated voltage per phase can be written as

       
        Eav/ phase = 4fΦTp 

for voltage wave , the form factor is given by 

                     Kf = r.m.s.  value/ average value

For a sinusoidal voltage , Kf =1.11 . therefore . the r.m.s. value of generated voltage per phase can be written as 

    Er.m.s. / phase = Kf x Eav / phase = 1.11 x 4fΦTp = 4.44fΦTp

the r.m.s. value of generated voltage per phase is given by 

Ep =  4.44fΦTp

                                                  

Equation has been derived with the following assumptions:

• Coil have got full pitch.
• all conductor are concentrated in one stator slot.