104 SYNCHRONOUS MOTORS 



thus been able, in a practical case, to reduce these harmonic terms 

 to one-eighth of their value. 



The case is different when the E.M.F.'s of the two machines are 

 equally distorted, because the harmonics which produce the parasite 

 current are then resultants of harmonics of the same order in the two 

 machines. Since these harmonics are all of odd order, the two sets 

 will oppose each other, if the principal sinusoidals are themselves 

 opposed, as is approximately the case under normal operation when 

 there is no lag. 



Consequently, if like machines are used as generators and as motors, 

 a considerably distorted E.M.F. curve would produce parasite effects 

 which are much less important than in the first case, and almost 

 negligible if care is taken to have the operation correspond to the 

 lower part of the bend of the V-curve. 



Simplified Diagrams. The diagrams shown in Figs. 44, 46, 49 

 correspond to the most general case where it is desired to take into 

 account both the direct and the transverse armature-reactions. 



Inasmuch as the direct armature-reaction alone affects the total 

 excitation ampere-turns, it may seem, to some, an unnecessary com- 

 plication to introduce the transverse reaction in the diagrams. For 

 the benefit of those who prefer Kapp's simplified theory, other 

 diagrams have been prepared (Figs. 440, 46a, 490) in which the trans- 

 verse reaction is neglected, i.e., where it is assumed that 7 u .= o. 



In constructing these simplified diagrams it is important, as before, 

 to determine the values of the resultant E.M.F. e 2 by reference to 

 the law of magnetic saturation as represented by the E.M.F. charac- 

 teristic curve shown in Fig. 45a. In this diagram the abscissae represent 

 excitation ampere-turns, and the ordinates represent E.M.F.'s. If the 

 point M' represents the E.M.F. E 2 with open circuit, and if Om' 

 represents the corresponding excitation ampere-turns, then, on sub- 

 tracting from Om the ampere-turns corresponding to the reactive 



current Id or making mm'= ^= ' the ordinate Mm corresponding 



V2 



to the abcissa Om will be the E.M.F. e 2 - 



The impedance involved (2) is that which corresponds to the 

 magnetic leakage of the armature. Fig. 440 shows how the cor- 

 responding potential difference z/-can be resolved into two components 

 obtained by projecting A V A 2 on YY' and on the line DAi perpendicular 

 thereto. 



The component DA V gives the value of I d when 2 is known. 



