SYNCHRONOUS MACHINERY 283 



By adjusting the field rheostats the wattless circulating cur- 

 rents can be eliminated for any load, but if the two machines 

 have different voltage characteristics, as the load varies wattless 

 currents will circulate to correct for the differences of excitation. 



With machines of reasonably high armature reaction the wattless 

 cross currents are small even with large variations of excitation. 



172. Effect of Inequality of Frequency. Two alternators 

 operating in parallel must have the same average frequency, 

 but one may instantaneously drop behind or run ahead of the 

 other. 



Alternators driven by turbines or electric motors will have a 

 constant angular velocity but when the prime movers are steam 

 engines or gas engines the angular 

 velocity will pulsate about its average 

 value during each revolution. 



If two machines in parallel are ex- 

 cited to give the same terminal volt- 

 age and one falls behind the other, 

 a power cross current will circulate 

 through the armatures and transfer 

 energy from the leading to the lagging FlG 2 6i. 



machine. 



Fig. 261 shows the case of two machines when E 2 lags behind 

 EI by angle a. The e.m.f. producing the circulating current is 

 the vector difference between EI and E 2 and it is 



in ..... (270) 



z 



F' 

 The circulating current is /' = - , its absolute value is 



r= , .... (271) 



r 2 ) 2 + ( Xl + xtf 



and it lags behind E f by angle 



, 

 ri -h r 2 



which is very nearly 90 degrees. 



The current is therefore nearly in phase with the terminal 

 voltage EI and in phase opposition to the terminal voltage E 2 ', it 

 thus transfers power from the leading to the lagging machine. 



