SURGING OF SYNCHRONOUS MOTORS

289

started once will continue indefinitely at constant amplitude.
This phenomenon, a surging by what may be called electro-
mechanical resonance, must be taken into consideration in a
complete theory of the synchronous motor.
167. Let:

EQ = eo = impressed e.m.f. assumed as zero vector.
E = e (cos j3 — j sin 0) = e.m.f. consumed by counter e.m.f.
of motor, where:

= phase angle between E0 and E.

Let:

_
and z = VV2 + x2

= impedance of circuit between
Eo and E, and

4. X

tan a = •

r —

0 ~~

The current in the system is:
® 6° "~ ecos " ?

= - {[e0 cos a — e cos (a + /3)]
— j [eo sin a — e sin (a + /?)]} (1)
The power developed by the synchronous motor is:
Fo = [El]1 = 6 {[cos |8 [g0 cos a - e cos (a + 0)]
+ sin P [e0 sin a — e sin (a + #)] ]
(?
= {[e0 cos (a — jg) — e COB a]}. (2)
If, now, a pulsation of the synchronous motor occurs, resulting
in a change of the phase relation, p, between the counter e.m.f.,. e,
and the impressed e.m.f., eo (the latter being of constant fre-
quency, thus constant phase), by an angle, 5, where 5 is a periodic
function of time, of a frequency very low compared with the
impressed frequency, then the phase angle of the counter e.m.f.,
Cj is p + 5; and the counter e.m.f. is:
E = e {cos 08 + 5) - j sin (ft + 5)},