Develop the E.M.F. equation of synchronous generator.

8. B] Develop the E.M.F. equation of synchronous generator.

Answer:

Let φ = Flux per pole, in Wb
P = Number of poles
N = Synchronous speed in r.p.m.
f = Frequency of induced e.m.f. in Hz
Z = Total number of conductors
Z_ph = Conductors per phase, For three phase Z_ph = Z/3

T_ph – No of Turns per phase, therefore T_ph = T_ph/2

Consider a single conductor which the cuts the flux „φ‟ produced by each pole in one revolution

The total flux, dφ = φ x P

Time taken to complete one revolution is dt = 60/ N_s

For one revolution of a conductor, according to faraday’s law of electromagnetic Induction

Substituting in equation (i) we get

E_avg = φ x 2f = 2φf

Therefore EMF induced per turn = 2 x (EMF per conductor) = 2 x (2 f φ)

E_avg per turn = 4 f φ volts

Let T_ph be the total number of turns per phase connected in series then

E_avg = 4 f φ x Tph

= 4 f φ T_ph

R.M.S. value of EMF = Kf x Average value = 1.11 x 4 f φ Tph

E_ph = 4.44 f φ T_ph Volts

If Kc – Pitch factor – the reduction in EMF due to short pitched winding
Kd – distribution factor – the reduction in EMF due to distributed winding
Kc and Kd are constants

Therefore the EMF induced in a Short pitched and distributed winding is

K_c= 1 for full pitched winding and K_d = 1 for concentrated winding
For star connection winding line voltage EL = √ E_ph = √𝟑 4.44 f φ T_ph K_c K_d
For delta connection winding line voltage EL = E_ph = 4.44 f φ T_ph K_c K_d