SYNCHRONOUS MACHINERY 



257 



Thus, the resultant m.m.f. of the armature of a three-phase alter- 

 nator is 



M a = -| nI , '(246) 



where n is the number of turns in series per phase and 7 is the 

 maximum value of the armature current. 



The armature m.m.f. is fixed in direction relative to the fields 

 and revolves synchronously relative to the armature. (Fig. 235.) 



154. Single-phase Armature Reaction. If n is the number 

 of turns per pair of poles on the armature of a single-phase alter- 

 nator and i = IQ sin (0 <j>) is the in- 

 stantaneous value of the armature cur- 

 rent at time t and angle after the 

 position of zero e.m.f., the m.m.f. of 

 the armature is m a = n! Q sin (0 <f>). 

 (Fig. 236.) It does not revolve rela- 

 tive to the armature and remain fixed 

 relative to the field as in the polyphase 

 machine but revolves with the arma- 

 ture and pulsates between zero and 

 a maximum value nI Q , producing a 

 double-frequency pulsation of the field 

 and a third harmonic ofe.m.f. in the armature. 



The armature m.m.f. may be resolved into two components, one 

 at right angles to the field m.m.f. and the other in line with it. 



The first component is m a sin = nI sin (0 0) sin and is 

 cross magnetizing only. It does not act directly on the niagnetic 

 circuit and only decreases the useful flux due to increased satura- 

 tion. Its effect will be neglected in the following discussion: 



The second component m a cos = n! sin (0 0) cos is di- 

 rectly in line with the field m.m.f. and produces a double-frequency 

 pulsation of the flux linking the magnetic circuit. 



The total m.m.f. acting on the magnetic circuit at time t and 

 angle is 



m = M f + m a cos 



= M f + nI sin (8 <f>) cos 8 



= M f + 7 ^- Ssin (2 8 - 0) - sin J 



>" fk _1_ * (O ft ^\ /O/17\ 



