AIR-GAP FLUX DISTRIBUTION 289 



maximum armature m.m.f . beyond the center line of the pole, be- 

 cause the angle ty' of Fig. 115 shows merely the lag of the current 

 behind the apparent developed e.m.f.; but, owing to armature dis- 

 tortion, the full-load flux distribution curve (from which the voltage 

 OE'g is derived) will not be symmetrically placed relatively to the 

 center line of the pole; it will be displaced in the direction of 

 motion of the conductors, i.e., to the right in Fig. 108. With the 

 aid of the vector diagram Fig. 115 we can, however, obtain a 

 value for the angle /3 of Fig. 108 which will enable us to place 

 the curve of armature m.m.f. in a position relatively to the field 

 m.m.f. which will be approximately correct for any given power 

 factor of the external load. The construction is shown in Fig. 

 116, and since vectors are used, the assumption of sine-wave 

 functions must still be made. This is where an error is intro- 

 duced, because the distortion of the flux curves, especially with 



FIG. 115. Vector diagram of alternator on lagging power factor. 



salient-pole machines, is not actually in accordance with this 

 simple law; but the final check on the work will be made later 

 when the flux distribution curves are plotted. 



The vectors 07, OE t and OE' g have the same meaning as in 

 Fig. 115, the component PE' g Being the total reactive voltage 

 drop both of end connections (formula 99) and slot leakage 

 (formula 106). Draw the vector OM in phase with OE' to 

 represent the resultant m.m.f. necessary to overcome air gap 

 and tooth reluctance when the air-gap flux is such as would 

 develop OE' g volts per phase in the armature if it were cut by all 

 the conductors. If we neglect the effect of increased tooth 

 saturation, this m.m.f. can be expressed as 



OM = (open circuit SI per pole) X 



OE' 



the open-circuit field excitation being calculated as explained in 

 Arts. 92 and 93. Now draw OM a exactly 90 degrees behind 07, 

 to represent the maximum value of the armature m.m.f. (formula 



19 



