Relation between speed and frequency
One complete revolution will produce one complete positive and negative pulse each cycle when the number of pole is two. The frequency in cycles per second (Hz) will depend directly on the speed or number of revolutions per second (rpm/60) of the rotating field.
If the ac synchronous generator has multiple poles (having, say, two, four, six, or eight poles...), then for a speed of one revolution per second (1 rpm/60), the frequency per revolution will be one, two, three, or four ..., cycles per revolution, respectively. The frequency per revolution, is therefore, equal to the number of pairs of poles. Since the frequency depends directly on the speed (rpm/60) and also on the number of pairs of poles (P/2), then these two may be combined together into a single equation in which
P is the number of poles
N is the speed in rpm (rev/min)
f is. the frequency in hertz
ωm is the speed in radians per second (rad/s)
ωe is the speed electrical radians per second.
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