Vf

! 1 ji 262 ELECTRICAL APPARATUS

5ljl therefore the armature reactance does not .vary with the posi-

•U1 tion of the armature in the field, as shown in Fig. 125, such self-

^ ' excitation by reactive armature currents does not occur, and

direct-current field excitation is always necessary (except in the
so-called "hysteresis motor").

Vectorially this is shown in Figs. 124 and 125 by the relative
position of the magnetic flux, <i>, the voltage, E, in quadrature to
$>, and the m.m.f. of the current, 7. In Fig. 125, where I and
<i> coincide, I and E are in quadrature, that is, the power zero.
Due to the polar structure in Fig. 124, / and $ do not coincide,

FIG. 124.—Diagram of machine with FIG. 125.—Diagram of machine with
polar structure. uniform reluctance.
thus I is not in quadrature to E, but contains a positive or a
negative energy component, making the machine motor or
generator.
As the voltage, E, is produced by the current, /, it is an e.m.f.
of self-induction, and self-excitation of the synchronous machine
by armature reaction can be explained by the fact that the
counter e.m.f. of self-induction is not wattless or in quadrature
with the current, but contains an energy component; that is,
that the reactance is of the form X = h + jxy where x is the watt-
less component of reactance and h the energy component of
reactance, and h is positive if the reactance consumes power—
in which case the counter e.m.f. of self-induction lags more than
90° behind the current—while h is negative if the reactance
produces power—in which case the counter e.m.f. of self-induction
lags less than 90° behind the current.
. 149. A case of this nature occurs in the effect of hysteresis,
from a different point of view. In' 'Theory and Calcuation of Al-
ternating Current37 it was shown, that magnetic hysteresis distorts
the current wave in such a way that the equivalent sine wave,