I;

298

ELECTRICAL APPARATUS

caused by the pulsation of the armature reaction, as discussed in
"Theory and Calculation of Alternating-Current Phenomena."

Any appliance increasing the area of the magnetic cycle of
pulsation, as short-circuits around the field poles, therefore,
increases the steadiness of a steady and increases the unsteadi-
ness of an unsteady synchronous motor.

In self-exciting synchronous converters, the pulsation of e is
intensified by the pulsation of direct-current voltage caused
thereby, and hence of excitation.

Introducing now the term, P2 = — /i2s, into the differential
equations of paragraph 169, gives the additional cases:

fe < 6, or negative, that is:

c2 +

< 0,

Hence, denoting:

- c2 - pP0

~

(31)

(32)

gives :
4. If:

6i2 > a,

(33)

That is, without oscillation, the motor drifts out of step, in
unstable equilibrium.

5. If: a > fci2, g = Va^^feT2,

§ = JJ€ + bl'cos (00 + 5). (34)

That is, the motor oscillates, with constantly increasing am-
plitude, until it drops out of step. This is the typical case of
cumulative surging by electro-mechanical resonance.

The problem of surging of synchronous machines, and its
elimination, thus resolves into the investigation of the coefficient:

., c« + 7»P.-W (35)

while the frequency of surging, where such exists, is given by:

, _ fee, sin (a - ft) tc2 + pP» -

/0 ~ V - 4W^ --- 64^M7

Case (4), steady drifting out of step, has only rarely been
observed.
The. avoidance of surging thus requires: