GENERAL PRINCIPLES OF SYNCHRONOUS MOTORS 13 



On the other hand, to obtain a difference of phase ahead, between 

 O and C, it is necessary to apply to the shaft an effort in the direction 

 of rotation, i.e., it is necessary to apply to the shaft a certain amount 

 of propelling power which must, evidently, be transformed into elec- 

 trical energy. 



The armature current has been supposed constant. In practice, 

 it is the voltage of the supply-circuit which is constant, at its terminals; 

 and the question is thus complicated by the spontateous variation of 

 the current with the variation in phase-difference. This variation, 

 itself, depends on the ratio of the induced E.M.F. of the motor to the 

 voltage applied at its terminals. 



In fact, as they displace themselves before the armature at the 

 synchronous speed, the poles of the inducing field induce in the wind- 

 ings counter E.M.F.'s. which are of the same order and magnitude as 

 the voltage at the terminals. If, mentally, we locate the E.M.F.'s. in the 

 wires which are placed in the slots, we perceive readily that the E.M.F. 

 in each slot varies periodically and passes through a maximum at the 

 moment when the middle of a revolving pole comes in line with the 

 slot. The axes of maximum values of the induced E.M.F.'s therefore 

 coincide with the axes of the inducing poles, and revolve with them. 

 If the currents were in phase with the E.M.F.'s, they would give rise to 

 revolving fields whose axes would be retarded in phase by an amount 

 equal to half the width of a pole, since each conductor forms a coil 

 with a conductor similarly placed, but in the contrary direction, under 

 the next pole. 



But we must take into account the voltage at the terminals, with 

 which the induced E.M.F. combines, and also the self-induction of 

 the machine, which throws the current out of phase by a quarter of a 

 period, i.e., half an interpolar space. Therefore the question can only 

 be treated with precision by calculation, as will be seen later. From 

 the qualitative point of view, the result differs but slightly from the 

 preceding result. The form of the curve of torque remains analogous 

 to that of Fig. 9, but it is no longer so symmetrical, and the lags OC 

 and OB, which determine the limits of stability, take a value, f, which 



is a little lower than , and which is defined by the relation 



2 



ojL 

 tan r = ; 



(uL and R being, respectively, the reactance and the resistance of the 

 armature circuit. 



