304 PRINCIPLES OF ELECTRICAL DESIGN 



armature teeth where the air-gap density is greatest. The effect 

 is, however, less marked in alternating-current than in con- 

 tinuous-current generators, because in the former the tooth 

 density is rarely so high as to approach saturation. On low 

 power factor, with lagging current, the armature magnetomotive 

 force tends to oppose the field magnetomotive force, and on zero 

 power factor its effect is wholly demagnetizing, thus greatly re- 

 ducing the resultant air-gap flux. With a leading current the 

 well-known effect of an increased flux and a higher voltage is 

 obtained. The effect known as armature reaction, as distin- 

 guished from armature reactance, is therefore dependent not 

 only on the amount of the armature current but also largely 

 upon the power factor. 



The effect of the individual conductors in producing slot 

 leakage was discussed in Art. 95 of Chap. XIII, and illustrated 

 by Figs. 110 and 111, wherein it is clearly shown that, as current 

 is taken out of the armature, the total flux cut by the active 

 conductors is less than at no load (with the same field excitation) 

 by the amount of the slot flux or equivalent slot flux which 

 passes from tooth to tooth in the neutral zone. 



Turning now to the flux cut by the end connections, i.e., by 

 those portions of the armature winding which project beyond 

 the ends of the slots, this flux is set up almost entirely by the 

 magnetomotive force of the armature windings, and is negligible 

 on open circuit. For a given output and power factor, the end 

 flux in a polyphase generator is fixed in position relatively to the 

 field poles, being stationary in space if the armature revolves. 

 The maximum value of the armature magnetomotive force occurs 

 at the point where the current in the conductors is zero, and on 

 the assumption of a sinusoidal flux distribution, the electromotive 

 force generated by the cutting of these end fluxes may be repre- 

 sented correctly as a vector drawn 90 degrees behind the current 

 vector. It is therefore permissible to consider this e.m.f. com- 

 ponent as a reactive voltage such as would be obtained by con- 

 necting a choking coil in series with the " active" portion of the 

 armature windings; and if the inductance, L e , of the end windings 

 is known, and a sinusoidal flux distribution assumed, the electro- 

 motive force developed by the cutting of the end fluxes under 

 load conditions is given by the well-known expression 2irfL e I c1 

 where I c is the virtual value of the current in the armature wind- 

 ings, and / is the frequency. 



