CHAP. VIII] REACTION IN SYNCHRONOUS MACHINES 143 



Prob. 5. Let a synchronous machine be loaded in such a way that 

 the armature current reaches its maximum when the conductors a and 6 

 (Fig. 36) are midway between the poles, in other words, when the current 

 is displaced by 90 electrical degrees with respect to the e.m.f. induced 

 at no load. Prove that the average distortion during a complete cycle 

 is zero, but that the flux is weakened if the armature current lags behind 

 the induced e.m.f., and is strengthened by a leading current. Hint: 

 The flux is weakened in both of the symmetrical positions, x and x f t of 

 the conductors, but the distortion is in opposite directions. 



Prob. 6. In a single-phase synchronous machine (ho armature 

 current roaches its maximum when the armature conductors are dis- 

 placed by an angle with respect to the centers of the poles; 1 prove that 

 the field is distorted by the component i cos ^ of the current and is 

 weakened or strengthened by the component i sin 



47. The Performance Diagram of a Synchronous Machine with 

 Non-Salient Poles. Let, in a machine with non-salient poles, the 

 field winding be placed in several slots per pole, so that the field 

 m.m.f. in the active layer of the machine is approximately distrib- 

 uted according to the sine law. Consider the machine to be a 

 polyphase generator supplying a partly inductive load. The ampli- 

 tude of the first harmonic of the armature reaction has the value 

 given by eq. (64) in Art. 43, and revolves synchronously with the 

 field m.m.f., as is explained there. Since the sum of two sine waves 

 is also a sine wave, the resultant m.m.f. is also distributed in the 

 active layer of the machine according to the sine law. 



To deduce the phase displacement, in space, between the two 

 sine waves, consider the coil a 6 (Fig. 36) to be one of the phases of 

 the polyphase armature winding. For reasons <>f symmetry, the 

 maximum m.m.f. produced by a polyphase winding J 8 a t the center 

 of the coil in which at that particular moment the current is at a 

 maximum. Assume first that the current in the phaseaft reaches its 

 maximum when the conductors a and 6 are opposite the centers of 

 the poles. The maximum armature m.m.f. at that instant is dis- 

 placed by 90 electrical degrees with respect to the (enter li- 

 ef the poles. The direction of the armature current is determine. 1 

 by the well-known rule, and it is found to lx> such that the arma- 

 ture m.m.f. lags behind that of the pole, connid< -rim: the direction 

 of rotation of the poles as po itiv. . Since both m.m.fs. revolve 

 synchronously, this angle between the two m.m.f. crests is prr- 



1 The angle # is different from the external phase-angle between the 

 current ami tin- terminal voltage; sec Fir 



