CHAP. VIII] REACTION IN SYNCHRONOUS MACHINES 149 



therefore solved by trials, assuming a certain reasonable value of 

 E, and calculating the expression Eicos<f>', until a value of E 

 is found, for which this expression, corrected for the core loss, fric- 

 tion, and windage, becomes a maximum. The problem of finding 

 i and <' for an assumed E is a definite one, because the four equa- 

 tions (71), (72), (76a) and (77) contain only four unknown quanti- 

 ties, i, <f>, <t> t , and <f>'. Instead of solving the problem by trials, an 

 analytical relation can be assumed between E and Af n , on the use- 

 ful part of the no-load saturation curve, for instance a straight line 

 (not passing through the origin), a parabola, etc. The problem is 

 then solved by equating the first derivative of the product 

 Ei cos <j>' to zero, having previously expressed E, t, and cos $' 

 through some one independent variable. Both methods have 

 been worked out for a synchronous motor with salient poles. 1 The 

 relations are simplified for a machine with non-salient poles. 



The foregoing theory of the armature reaction does not apply 

 directly to single-phase machines. The pulsating armature reac- 

 tion in such a machine can be resolved into two revolving reactions, 

 as in Art. 42. The reaction which revolves in the same direction 

 with the main field is taken into account as in a polyphase machine. 

 The inverse reaction is partly wiped out by the eddy currents pro- 

 duced in the metal parts of the revolving structure; it is therefore 

 difficult to express the effect of this reaction theoretically. The 

 treatment in this book is limited to polyphase machines, which are 

 used in practice almost exclusively. 2 



Prob. 7. In the 100 kva., 440-volt, 6-pole, two-phase alternator, 

 pivon in Problem 6, Art. 43, the amplitude of the first harmonic of the 

 armature reaction was 4800C, ampere-turns. What is the per rent 

 voltage regulation of the machine at a power-factor of 80 per 

 lagging, if C, 1, that is if the armature has one conductor per slot? 

 The armature reactance is 0.038 ohm, and the armature resistance is 

 0.008 ohm, both per phase. The no-load saturation curve of the 

 machine is as follows: 



e- 400 440 490 525 550 volts. 

 M n -6.7 8.0 10.0 12.0 14.0 kiloamp.-turns. 



Ans. 22 per < 



1 See the author's " Essays on Synchronous Machinery," General Electric 

 Review, 1011, July and September. 



1 In regard to the armature reaction in (tingle-phase machines, see E. 

 Arnold, Die Weduektromtechnik, Vol. 4 (1904), pp. iohelmayer, 



Dynamobau (1908), pp. 251-259; Max Wengner, Theoretbehe und Expert 

 mcnicUc Untfriturhungtn an der Synehronen Einphaxn-Matchinc (Olden bourg, 

 1911.) 



