CTAILED STUDY OF OPERATION WITH NORMAL LOAD 87 



AAi' = ZiJ w , makes, it is known, the angle f\ with the voltage 



The second, A\A\=Z\J & will lag behind the first, since J^ is 



2 



ring behind J w . The resultant A\A corresponds to the real 

 2 



(33) 



and the line OA\ represents the internal E.M.F. which the generator 

 must produce in order that the distributing voltage shall equal U. 

 The diagram gives the following formula, which is analogous to 

 ula (26): 



nn)- (34) 



In this case f\ being always very large, A\A is almost parallel to U. 

 In general, we can write, approximately, 



( 35 ) 



It is seen that the reactive current requires a much greater increase 

 of E.M.F. than the active current. If we had ^ o, tne alternator 

 would develop the same power with a lower current, AA\ ', and a 

 lower E.M.F., ol?. 



Let us suppose the current / to be the maximum which the alterna- 

 tors can produce; and let us describe, around A as a center, a circle 

 of radius AA\ ^\J- The manufacturer must have allowed a suf- 

 ficient margin in the excitation to attain the E.M.F. EQ, which enables 

 this current to be produced through a dead resistance while keeping 

 the distribution-voltage at the value U; but if he confined himself to 

 doing that, as was his right, it would be necessary, when the lag 

 increases, to reduce the output in such manner that the point A\ will 

 remain on the circle A C, described from O as a center, with EQ as 

 radius. 



In such cases the effect of the reactive current becomes absolutely 

 objectionable, and it is then very necessary to reduce it by employing 

 means such as those just considered. 



Fig. 43 can serve as a numerical example in the case of a 2000- 

 volt distribution where the receiving apparatus has a mean power- 

 factor of 0.70 and the generator has an impedance of 15 ohms (the 



