166 ALTERNATING CURRENTS 



Assume that the prime mover of generator 1 speeds up tempora- 

 rily. The internal induced voltage of this generator will advance 

 an angle a with respect to EZ. That is, EI will advance to posi- 

 tion E'i. The vector sum of the two alternator emfs. E\ and 

 EZ will no longer be zero, but due to the change in their relative 

 phase positions, the vector sum of E\ and EZ will be E . 



The result is the same as with the two 



l= 2 a J > 



e=iov.rr~ ~~Qe=8v. batteries of Fig. 165. No. 1 has an emf. 



r-o.soli _ . _ lT r =o.5Q O f 10 volts and 2 has an electromotive 



NO. i. ~~ NO. 2. force of 8 volts. If the load current is 



FIG. 165. Batteries in zero, the current circulating between 



these batteries is then found by dividing 



the sum of the two voltages, giving each the proper sign, by 

 the sum of the resistances of the two batteries. That is, 



10 + (-8) 

 /0= 0.5 + 0.5 =2am P- 



In the same way, the current circulating between the two 

 alternators is the resultant voltage divided by the sum of the 

 impedances of the two machines. 



= 2 = . (44) 



?i + ?z V(Ri + # 2 ) 2 + (Xi + XzY 



Where Zi, Z 2 , R\, Rz, and X\, X z , are the respective impedances, 

 resistances and reactances of the two machines. As the resis- 

 tance of an alternator armature is very small compared to its 

 reactance, this circulatory current will lag by an angle |8, nearly 

 90, with respect to the voltage E producing it, as shown in Fig. 

 164. 



It will be observed that J is nearly in phase with the voltage 

 E'i. Therefore, it puts a power load on generator 1, and this 

 tends to slow down this generator. On the other hand I is 

 nearly 180 from E 2 , that is, it is acting in opposition to EZ. There- 

 fore, 7 develops motor action in generator 2, as the induced 

 electromotive force acts in opposition to the current. This motor 

 action tends to speed up machine 2. Therefore, if two alternators 

 in parallel attempt to pull out of step, a current is developed which 

 circulates between the two machines. This current tends to acceler- 

 ate the lagging machine and to retard the leading machine, and so 

 to prevent the alternators from pulling out of synchronism. 



