Environmental Engineering Reference
In-Depth Information
Figure 4.5
A one - and two - pole pair wound stators
phase produce mmfs F a , F b and F c in the directions indicated in Figure 4.4(b). At the instant
ω
t = 0 ° in Figure 4.4 (a), i a is a positive maximum and i b and i c are negative and one-half
maximum. At this instant, the fl ux contributions in space can now be added as shown in
Figure 4.4(c) for
ω
t = 0 ° . The stator fl ux
Φ
s is the space vector sum of the three fl ux contri-
butions. At
t = 30 °, the relative magnitudes of the three currents have changed and the
position of the resulting stator fl ux has shifted anticlockwise by 30 °. At
ω
t = 60 ° , the current
magnitudes have changed again and the resultant stator fl ux vector has shifted another 30 °.
Over a complete cycle of mains frequency the vector
ω
s would have completed one revolu-
tion. It follows that for a 50 Hz supply the fl ux vector will complete one revolution in one-
fi ftieth of a second; i.e. it will complete 50 revolutions per second. It is said that a rotating
magnetic fi eld (RMF) has been created by virtue of the space distribution of the three wind-
ings and of the time distribution of the currents in the three windings. This is a very important
concept on which the operation of three-phase generators (and motors) depends.
To summarize, if a stationary observer were to position him- or herself inside the stator
cylindrical space of Figure 4.3, he or she will observe a north-south pole pair rotating at 50
Φ
×
60 = 3600 revolutions per
minute for a 60 Hz mains. These are known as the synchronous speeds for 50 and 60 Hz
systems for a one- pole pair winding. Stator windings can be arranged so that not just one
pair but several pairs of poles can be created in the interior of the stator cavity. For example,
a two-pole pair arrangement will have two separate windings for each phase, each winding
side occupying 30 rather than the 60 ° shown in Figure 4.3. It can be shown that with such
an arrangement in one-fi ftieth of a second the rotating magnetic fi eld in a 50 Hz system will
advance by 180 rather than 360 °. The magnetic fi eld produced by an alternator wound for
one- and two-pole pairs is shown in Figure 4.5 (a) and (b) respectively.
This property is used by designers of electrical machines to generate rotating magnetic
fi elds that rotate at submultiples of the fi gures shown above. The reason why such machines
are useful will be explained in the following section. The general relationship linking the
synchronous speed in radians per second
60 = 3000 revolutions per minute for a 50 Hz supply and 60
×
ω
s to frequency f and number of pole pairs p is:
2
π
f
ω
=
(4.4)
s
p
 
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