186 GENERAL DIAGRAMS FOR SYNCHRONOUS MOTORS 



radius E without altering materially the inclination of the segment 

 BF'. Hence, if the reactance is increased beyond a certain point 

 the reactive current IQ, corresponding to zero-load, will increase with it. 

 This reactive current must therefore have a minimum; and to 

 every value higher than this minimum there will correspond two 



reactance values, and two inclina- 

 tions of the line BG, one greater, 

 the other smaller. 



We can learn more about this 

 minimum by calculations based on 

 the fact that the same value of 

 the supply-voltage E enables both 

 the " no-lag ' point G and the 

 " no-load " point F to be obtained. 



To make the case more general, let us suppose a condition wherein 

 jo does not vanish and wherein the voltage with load, e', is different 

 from the voltage e without load. We will have the two following 

 relations: 



FIG. 10. 



At the point G, E 2 =e' 2 +Z 2 I w 2 



At the point F, E? 

 From these, eliminating E, we have 



(a) 

 (6) 



This is the condition required. Solving for 

 we obtain the two following formulas: 



0. ... (4) 



and then for X, 



Y 





In (5) the expression under the radical sign is taken with the + sign 

 only, because, for each value of X, i$ can have only one value, which, 

 necessarily, is positive. On the other hand it has been seen that X 

 has two values for each value of *o; hence it is necessary to retain 

 both signs ( -j- ) before the expression under the radical sign, in Eq. (6). 



