OPERATION OF SYNCHRONOUS MOTORS. HUNTING 117 



is in series with it. To bring the phases of the two currents 



ito proper relation, the brushes are moved an angle equal to 



2 



luring the operation of starting. When synchronism is attained, the 

 crushes are brought back to their place, and the excitation-circuit 

 connected in shunt to one coil alone of the armature, so as to reduce 

 ic voltage. 



Theory of Initial Synchronizing. Two cases must be considered, 

 lepending on whether the field, when separately excited, maintains 

 its normal value independently of the speed, or whether the field is 

 produced by means of commutated currents. 



Separate Excitation. Let us again suppose the motor to be con- 

 iccted to a constant potential source E\ and let us retain the same 

 as before. Let us designate by T 2 the duration of the period 

 the motor, which will differ from T\ the period of the supply-current, 

 long as synchronism is not attained. For simplicity, let us write 



27T 

 7fT 

 2 



The equation of the current proceeding from the source of supply 

 jward the motor is 



^-=Ei sincu/ -- -7?2sin (tool 6), 

 at o)\ 



where 2 equals the E.M.F. induced at the speed of synchronism, 

 and 6 represents, as before, the lag in phase of the motor. From this, 

 neglecting the exponentials which occur in the integral, but which 

 always neutralize each other quickly, and taking 



we have 



, i . 2 



tan o>= , tan <b= , 

 r r 



. E\ sin (ajti <f>) 102 2 sin (ct2/ </>) 





Vr 2 +aji 2 l 2 "i 

 The power supplied to the motor at each instant is 



2- . 



e 2 i=E 2 sin 



^ raisi 



0) -- 

 V 



0-0)] 



- - . 

 2 2 l* J 



