SPEED AND FREQUENCY OF SYNCHRONOUS GENERATOR

The frequency of the generated voltage depends upon the number of field poles and on the speed at which the field poles are rotated. one complete cycle of voltage is generated in an armature coil when a pair of field poles passes over the coil.

P = total number of field poles.

p = pair of field poles 

N = speed of the field in r.p.m.

n = speed of field poles in r.p.s.

f = frequency of the generated voltage in Hz.

N/60 = n

P/2 = p

In one revolution of the rotor , an armature coil is cut by P/2  north poles and P/2 south poles. Since one cycle is generated in an armature coil when the pair of field poles passes over the coil, the number of cycles generated in one revolution of the rotor will be equal to the number of pars of the poles . that is,

Number of cycles per revolution = p
Also number of revolution per second = n

Equation give the relationship between the number of poles, speed and frequency.

Synchronous speed :

Equation shows that the rotor speed N bear constant relationship with the field poles and the frequency of the generated voltage in the armature winding. the speed given by equation is called synchronous speed Ns . A machine which runs at synchronous speed is called synchronous machine. a synchronous machine is an a.c. machine in which the rotor moves at a speed which bears constant relationship to the frequency of the generated voltage in the armature winding and number of poles of the machine.
 standard form of frequency in india is 50 Hz.

Calculate the speed of the alternator which has poles 4 and frequency is 50 Hz
speed given by the relation 

the speed of the alternator  4 pole is 1500 r.p.m. and maximum speed of the alternator 2 pole is 3000 r.p.m. at 50 Hz frequency.