If

198

ELECTRICAL APPARATUS

I

p*

If

' I

I i'i

a circuit of frequency, /2, the stator generates a frequency
/i - /o - /*•
116. The power generated in the stator, PI, and the power
generated in the rotor, P2, are proportional to their respective
frequencies:
Pi :P2 :Po =/i :/2:/o,
where Po is the mechanical input (approximately, that is, neg-
lecting losses).
As seen here the difference between the two circuits, stator
and rotor, disappears—that is, either can be primary or sec-
ondary, that is, the reactive lagging current required for excita-
tion can be supplied to the stator circuit at frequency, fi, or to
the rotor circuit at frequency,/2, or a part to the stator and a part
to the rotor circuit. Since this exciting current is reactive or
wattless, it can be derived from a synchronous motor or con-
verter, as well as from a synchronous generator, or an alter-
nating commutating machine.'
As the voltage required by the exciting current is proportional
to the frequency, it also follows that the reactive power input or
the volt-amperes excitation, is proportional to the frequency
of the exciting circuit. Hence, using the low-frequency circuit
for excitation, the exciting volt-amperes are small.
Such a synchronous-induction generator therefore is a two-
frequency generator, producing electric power simultaneously
at two frequencies, and in amounts proportional to these fre-
quencies. For instance, driven at 85 cycles, it can connect with
the stator to a 25-cycle system, and with the rotor to a 60-cyclo
system, and feed into both systems power in the proportion of
25 -T- 60, as is obvious from the equations of the general alter-
nating-current transformer in the preceding chapter
117. Since the amounts of electric power at the two fre-
quencies are always proportional to each other, such a machine
is hardly of much value for feeding into two different systems,
but of importance are only the cases where the two frequencies
generated by the machine can be reduced to one.
This is the case:
1. If the two frequencies are the samer/i = fa = -£• In thin
A
case, stator and rotor can be connected together, in parallel
or in series, and the induction machine then generates electric
power at half the frequency of its speed, that is, runs at double