SURGING OF SYNCHRONOUS MOTORS

295

have a similar relation as resistance and reactance in alternating-
current circuits, or in the discharge of condensers. - a is the
same term as in paragraph 167.

Differential equation (19) is integrated by:

6 = Aece, (21)

which, substituted in (19), gives:

aA€c° + 2 bCAecd + CzAec& = 0,
a + 2 bC + C2 = 0,
which equation has the two roots:

c\ = -

(22)

1. If a < 0, or negative, that is ft > a, C\ is positive and C2
negative, and the term with Ci is continuously increasing, that
is, the synchronous motor is unstable, and, without oscillation,
drifts out of step.

2. If 0 < a < 62, or a positive, and fc2 larger than a (that is,
the energy-consuming term very large), C\ and C2 are both
negative, and, by substituting, + \/b2 — a = g, it is:

hence:

That is, the motor steadies down to its mean position logarith-
mically, or without any oscillation.

fe2 > a,
hence:

(24)

is the condition under which no oscillation can occur.

As seen, the left side of (24) contains only mechanical, the
right side only electrical terms.

3. a > 62.

In this case, -\/b2 — a is imaginary, and, substituting:

it is:

g = 2,
Ci = -&+jfff,
C2 = -b-jg,