OPERATION OF SYNCHRONOUS MOTORS. HUNTING 123 



Consequently, oscillations of speed occur around the normal speed 

 value, the effects being altogether analogous to the oscillations occur- 

 ring in the speed of steam engines which are provided with imperfect 

 jovernors. 



The characteristic feature of the short-period oscillations of the 

 lotor-speed is that this oscillatory movement occurs without loss of 

 synchronism, in other words, each acceleration in one direction or the 

 other is stopped by an opposing torque which limits the amplitude, 

 is the case with the oscillations -of a pendulum. 

 This torque is easily determined by the variation of power 'o'f the 

 two machines (A. Bhndel, " Coupling of Alternators," La Lumiere 

 lletrique, Vol. XLV, p. 352). Let us first suppose these two machines 

 to be similar; let P\ and P% represent,* respectively, the generator - 

 )wer and the motor-power. The variation in the electric power 

 sceived by the motor and transmitted by the generator, per unit of 

 mgle a of angular variation, taking zP to equal the number of poles, 

 according to the formulae on page 38, as follows : 



__ __ 



da da P dO dO 



2pE l E 2 . . 



-i - (sin f cos v). 



In this expression Z equals the total impedance, and f is, as before, 

 the angle of lag between the current and the resultant E.M.F., the 

 relations being such that 



ojL 

 tan r = . 



The correcting torque is obtained by dividing this power by the mean 

 angular velocity 



a> 



P' 

 From this we have 



p 2 \^E\ E? sin f cos 0~\ 



o7 ' ~z ' 



L J 



