The alternators work on the
principle of electromagnetic induction. When is a relative motion
between the conductors and the flux, e.m.f. gets induced in the
conductors. The d.c. generators also work on the same principle. The
only difference in practical alternator and a d.c. generator is that in
an alternator the conductors are stationary and field is rotating. But
for understanding purpose we can always consider relative motion of
conductors with respect to the flux produced by the field winding.
Consider a relative motion of a single conductor under the
magnetic field produced by two stationary poles. The magnetic axis of
the two poles produced by field is vertical, shown dotted in the Fig.1.
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| Fig. 1 Two pole alternator |
Let conductor starts rotating from position 1. At this instant,
the entire velocity component is parallel to the flux lines. Hence there
is no cutting of flux lines by the conductor. So dΦ/dt at this instant
is zero and hence induced e.m.f. in the conductor is also zero.
As the conductor moves from position 1 towards position 2, the
part of the velocity component becomes perpendicular to the flux lines
and proportional to that, e.m.f. gets induced in the conductor. The
magnitude of such an induced e.m.f. increases as the conductor moves
from position 1 towards 2.
At position 2, the entire velocity component is perpendicular to
the flux lines. Hence there exists maximum cutting of the flux lines.
And at this instant, the induced e.m.f. in the conductor is at its
maximum.
As the position of conductor changes from 2 towards 3, the
velocity component perpendicular to the flux starts decreasing and hence
induced e.m.f. magnitude also starts decreasing. At position 3, again
the entire velocity component is parallel to the flux lines and hence at
this instant induced e.m.f. in the conductor is zero.
As the conductor moves from 3 towards 4, the velocity component
perpendicular to the flux lines again starts increasing. But the
direction of velocity component now is opposite to the direction of
velocity component existing during the movement of the conductor from
position 1 to 2. Hence an induced e.m.f. in the conductor increases but
in the opposite direction.
At position 4, it achieves maxima in the opposite direction, as
the entire velocity component becomes perpendicular to the flux lines.
Again from position 4 to 1, induced e.m.f. decreased and finally
at position 1, again becomes zero. This cycle continues as conductor
rotates at a certain speed.
So if we plot the magnitudes of the induced e.m.f. against the
time, we get an alternating nature of the induced e.m.f. as shown in the
Fig. 2.
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| Fig. 2 Alternating nature of the induced e.m.f. |
This is the working principle of an alternator.
1.1 Mechanical and Electrical Angle
We have seen that for 2 pole alternator, one mechanical
revolution corresponds to one electrical cycle of an induced e.m.f. Now
consider 4 pole alternator i.e. the field winding is designed to produce
4 poles. Due to 4 poles, the magnetic axis exists diagonally shown
dotted in the Fig. 3.
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| Fig. 3 |
Now in position 1 of the conductor, the velocity component is
parallel to the flux lines while in position 2, there is gathering of
flux lines and entire velocity component is perpendicular to the flux
lines. So at position 1, the induced e.m.f. in the conductors is zero
while at position 2, it is maximum. Similarly as conductor rotates, the
induced e.m.f. will be maximum at position 4, 6 and 8 and will be
minimum at position 3, 5 and 7. So during one complete revolution of the
conductor, induced e.m.f. will experience four times maxima, twice in
either direction and four times zero. This is because of the
distribution of flux lies due to existence of four poles.
So if we plot the nature of the induced e.m.f; for one revolution
of the conductor, we get the two electrical cycles of the induced
e.m.f., as shown in the Fig. 4.
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| Fig. 4 Nature of the induced e.m.f. |
Note : Thus the degrees electrical of the induced e.m.f.
i.e. number of cycles of the induced e.m.f. depends on the number of
poles of an alternator.
So for a four pole alternator we can write,360o mechanical = 720o electrical
From this we can establish the general relation between degrees mechanical and degrees electrical as,
360o mechanical = 360o x (p/2) electrical
Where P = Number of poles
1.2 Frequency of induced E.M.F.
Let P = Number of polesN = Speed of the rotor in r.p.m.
and f = Frequency of the induced e.m.f.
From this discussion above in section 1.1, we can write,
One mechanical revolution of rotor = P/2 cycles of e.m.f. electrically.
Thus there are P/2 cycles per revolution.
As speed is N r.p.m., in one second, rotor will complete (N/60) revolutions.
But cycles/sec = frequency = f
Frequency f = (No.of cycles per revolution) x (No.of revolution per second)
... f = (P/2) x (N/60)
So there exists a fixed relationship between three quantities,
the number of poles P, the speed of the rotor N in r.p.m. and f the
frequency of an induced e.m.f. in Hz (Hertz).
Note : Such a machine bearing a fixed relationship between
P, N and f is called synchronous machine and hence alternators are also
called synchronous generators.
Synchronous speed (Ns)
From the above expression, it is clear that for fixed number of
poles, alternator has to be rotated at a particular speed to keep the
frequency of the generated e.m.f. constant at the required value. Such a
speed is called synchronous speed of the alternator denoted as Ns.
In our nation, the frequency of an alternating e.m.f. is standard
equal to 50 Hz. To get 50 Hz frequency, for different number of poles,
alternator must be driven at different speeds called synchronous speeds.
Following table gives the values of the synchronous speeds for the
alternators having different number of poles.
From the table, it can be seen that minimum number of poles for
an alternator can be two hence maximum value of synchronous speed
possible in our nation i.e. for frequency of 50 Hz is 3000 r.p.m.
