CHAP. VIII] REACTION IN SYNCHRONOUS MACHINES 151 



pole, distorts the flux; while a current in quadrature with the 

 former exerts a direct reaction only. It is natural, therefore, to 

 resolve the actual current in each phase into two components, in 

 time quadrature with each other, and in such a way that each 

 component reaches its maximum in one of the above-mentioned 

 principal positions of the conductor with respect to the field-poles. 

 Let the current in each phase be i, and let it reach its maximum at 

 an angle after the induced no-load voltage is a maximum (Fig. 

 40) . Then, the two components of the current are 



and 



it = i cos <fr. 



The component i d produces a direct armature reaction only, 

 and the component i t a transverse reaction only. 1 



For practical calculations, and in order to get a concrete picture 

 of the armature reaction, it is convenient to represent the armature 

 reaction as shown in Fig. 39. Namely, the direct reaction, due to 

 the components i d of the armature currents, is replaced by an equiv- 

 alent number of concentrated ampere-turns M d on the pole. The 

 value of M d is selected so that its action hi reducing or strength- 

 ening the flux is equal to the true action of the armature currents. 

 The transverse reaction, due to the component i t of the armature 

 currents, is replaced by a certain number of ampere-turns, M .. on 

 the fictitious poles, (S), (N), shown by dotted lines between tl 

 poles. For simplicity, and for other reasons given in Art. 51, the 

 fictitious poles are assumed to be of a shape 4 identical with that of 

 the real poles. The number of exciting ampere-turns M t is so 

 chosen, that the effect of the fictitious poles is approximately the 

 same as that of the distorting ampere-turns on the armature. 



The flux of the fictitious poles strengthens the flux of the 

 poles on one side and weakens it by the same amount on the other 

 side, so that the fictitious poles actually distort the main flux 

 wit IK. ut altering its value. Strictly speaking, the complete action 

 of the distorting ampere-turns on the armature < -annot be imitated 



The resolution of the armature reaction in a synchronous machine 

 into a direct and a transverse reaction was first <i<>n<> l>y A. Hlondcl. See 

 r Industrie EUctriquc, 1800, p. 481; also his book MoUun Synchrony (1000), 

 :nI two papers of his i,, d,, Trans. Intern. Elcctr. Conyrew, St. Louis, 1004, 

 Vol. 1, pp. 620 and 635. 



