SYNCHRONOUS INDUCTION GENERATOR 201

The powers generated by the stator and by the rotor, how-
ever, are proportional to their respective frequencies, and so are
inversely proportional to their respective turns.

if ni and n2, and therewith the two frequencies, are very different,
the two powers, P3 and P2, are very different, that is, one of the
elements generates very much less power than the other, and |{
since both elements, stator and rotor, have the same active
surface, and so can generate approximately the same power, the
machine is less economical.
That is, the commutator permits the generation of any de-
sired frequency, /i, but with best economy only if f\ = ~°, or
half-synchronous frequency, and the greater the deviation from !$;,
this frequency, the less is the economy. If one of the fre- yj
quencies is very small, that is, fi is either nearly equal to syn- 'i\
chronism, /0, or very low, the low-frequency structure generates |'
very little power.
By shifting the commutator brushes, a component of the rotor
current can be made to magnetize and the machine becomes a
self-exciting, alternating-current generator.
The use of a commutator on alternating-current machines is
in general undesirable, as it imposes limitations on the design,
for the purpose of eliminating destructive sparking, as discussed
in the chapter on"Alternating-Current Commutating Machines."
The synchronous-induction machines have not yet reached a
sufficient importance to require a detailed investigation, so only
two examples may be considered.
119. 1. Double Synchronous Alternator.
Assume the stator and rotor of an induction machine to be
wound for the same number of effective turns and phases, and
connected in multiple or in series with each other, or, if wound
for different number of turns, connected through transformers
of such ratios as to give the same effective turns when reduced
the same circuit by the transformer ratio of turns.
Let:
. Yi = g — jb = exciting admittance of the stator,
Zi = TI + jxi = self-inductive impedance of the stator,
Z2 = r2 + jx% = self-inductive impedance of the rotor,