142 THE MAGNETIC CIRCUIT [AKT. 46 



a given power-factor; a leading power-factor is usually prescribed, 

 in order to raise the lagging power-factor of the whole plant. The 

 problem is solved in like manner to that of the generator, by 

 taking into account the proper signs when calculating the reactance 

 drop and the armature reaction. The results, plotted in the form 

 of curves, are called the phase characteristics, or V-curves of a 

 synchronous motor. 1 



It will be seen from Fig. 36 that the crowding of the flux to one 

 pole-tip, by the armature currents, is primarily due to the fact that 

 the poles shown there are projecting or salient, so that the reluc- 

 tance along the air-gap is variable. With non-salient poles the 

 flux is simply shifted side wise without being distorted. Therefore, 

 before going into the details of the calculation of armature reaction 

 in machines with salient poles we shall first consider (in the next 

 article) the case of a machine with non-salient poles. 



Prob. 1. Draw the distribution of the flux, similar to that shown 

 in Fig. 36, when the armature conductors are opposite the centers of the 

 poles, and when they are somewhere between the adjacent pole-tips. 



Prob. 2. Explain the details of the flux distribution in Fig. 36, by 

 means of a hydraulic analogy, assuming A and B to represent two main 

 centrifugal pumps, and a and 6 to be two smaller pumps placed in the 

 stream. 



Prob. 3. Let each field coil in Fig. 36 have N turns, and let the 

 exciting current be /; let the number of conductors at a be C 8 , and the 

 instantaneous value of the armature current i. What is the total flux 

 per pole, if the average permeance of the machine per pole is (P perms 

 per electrical radian, and the angles 6 and x are in electrical radians? 



Ans. (2NIO-C 9 ix)G*. in maxwells. 



Prob. 4. Let a synchronous machine be loaded in such a way that 

 the armature current reaches its maximum when the conductors a and b 

 (Fig. 36) are opposite the centers of the poles, in other words, the current 

 is in phase with the e.m.f. which would be induced at no load. Prove 

 that (neglecting saturation) the average flux per pole during a complete 

 cycle is the same as without the armature reaction, but is crowded to 

 the leading tip of the pole, i.e., in the direction of rotation in the case of 

 a motor, and to the trailing tip, or against the direction of rotation when 

 the machine is working as a generator. Hint: The flux is weakened as 

 much in the position x of the conductors as it is strengthened in the 

 symmetrical position z'; the distortion is in the same direction in both 

 positions. 



1 See the author's " Experimental Electrical Engineering'' Vol. 2, p. 121; 

 also his " Essays on Synchronous Machinery," General Electric Review, 

 1911, p. 214. 



