140 ELECTRICAL APPARATUS
by hand regulation of the generator or the potential regulator
in the circuit supplying the motor, or by any other method which
is slower than the rate at which the motor speed can adjust itself
to a change of load, then, even if the supply voltage at the
motor terminals is kept constant, for a momentary fluctuation
of motor speed and current, the supply voltage momentarily ^
varies, and with regard to its stability the motor corresponds
not to the condition of constant supply voltage but to a supply
voltage which varies with the current, hence the limit of stability
is reached at a lower value of motor torque.
At constant slip, s, the motor torque, D, is proportional to the
square of the impressed e.m.f., e*. If by a variation of slip
caused by a fluctuation of load the motor current, i, varies by di,
if the terminal voltage, e} remains constant the motor torque, D,
varies by the fraction k8 = yr ~p> or the stability coefficient of
the motor. If, however, by the variation of current, di, the
impressed e.m.f., e, of the motor varies, the motor torque, D,
being proportional to a2, still further changes, proportional to
the change e2, that is, by the fraction kr = -5 -p- = - -T-.J and the
total change of motor torque resultant from a change, di, of the
current, i} thus is fc0 — k8 + kr.
Hence, if a momentary fluctuation of current causes a momen-
tary fluctuation of voltage, the stability coefficient of the motor
is changed from ka to fco = ks + kr, and as kr is negative, the
voltage, e} decreases with increase of current, i, the stability
coefficient of the system is reduced by the effect of voltage regu-
lation of the supply, krj and kr thus can be called the regulation
coefficient of the system.
kr = - -j-. thus represents the change of torque produced by
the momentary voltage change resulting from a current change
di in the system; hence, is essentially a characteristic of the
supply system and its regulation, but depends upon the motor
de
only in so far as ~T. depends upon the power-factor of the load.
dif
In Fig. 54 is shown the regulation coefficient, fcr, of the supply
system of the motor, at 110 volts maintained constant at the
motor terminals, and an impedance, Z = 0.16 + 0.8 j, between
motor terminals and supply e.m.f. As seen, the regulation
coefficient of the system drops from a maximum of about 0.03,