SYNCHRONOUS GENERATORS 301 



single-phase service. For machines designed for purely single- 

 phase duty, the ratings can, however, be somewhat higher. This 

 is due to the fact that the armature winding can be more efficiently 

 spaced and proportioned, in which case the limit in output as a 

 rule is determined by the temperature rise in the field. 



Wave Shape. The e.m.f. in a conductor is proportional to the 

 rate of cutting the lines of force, and has, therefore, a wave form 

 of the same shape as the curve of flux distribution. Due to the 

 non-uniform flux distribution in definite pole machines, caused 

 by the slots, the shapes of the pole-pieces, the armature reaction, 

 etc., the wave will never have a perfect sine shape. It may, how- 

 ever, be considered as the resultant of a number of sine waves 

 consisting of a fundamental and harmonics. The third and fifth 

 harmonics are generally predominating in three-phase machines, 

 while even harmonics are seldom 

 found in the e.m.f. wave of an 

 alternator. This is due to the 

 fact that the resultant of a funda- 

 mental and an even harmonic 

 gives an unsymmetrical curve, as 



shown in Fig. 178, where the re- , 



f FIG. 178. Unsymmetncal Distorted 

 sultant curve is made up of a E M F Wave. 



fundamental and a second har- 

 monic. If, therefore, the e.m.f. wave is symmetrical, it may be 

 assumed that no even harmonics are present. 



With fractional pitch-windings certain harmonics are elim- 

 inated, depending on the pitch. For example, if the pitch of the 



coil can be shortened by - of the pole pitch, then the nth harmonic 



and its multiples will be eliminated. 



The analyzation of a wave involves a considerable amount of 

 work, but, in general, it is possible to tell at a glance which har- 

 monics are predominating. With a positive third harmonic, that 

 is, if counting from the zero point of the complex wave the har- 

 monic wave rises, the complex wave will be flat-topped. If, how- 

 ever, the harmonic is negative, that is, if after crossing the base 

 line, it rises in opposition to the complex wave, its effect will be to 

 produce a distorted wave of the peaked type. A fifth harmonic, 

 however, if positive will give rise to a peaked saw-toothed wave, 

 and if negative to a flat-topped wave. 



