326 ELECTRICAL MACHINERY 



Now suppose that, owing to the fact that a load has 

 been put on the motor, it has been retarded for a fraction 

 of a second until its voltage vector has taken a position 

 not quite opposite to that of the line voltage; this is shown 

 at OE m '. The resultant of OE m ' and OEi is shown at 

 OR'; this voltage OR' causes a current to flow almost 

 90 behind the voltage because of the high inductance 

 -5- resistance ratio of the motor armature. The angle is 



V 



determined by the relation tan = -, where X m = 2x/L m 



Rm 



= the inductance of the motor armature, and R m is the 

 resistance of the motor armature. 



Magnitude of the Phase Shift. The magnitude of this 

 current is determined by the relation IZ m = OR', where 

 Z m is the impedance of the motor armature. As Z m is 

 generally small, it requires only a small voltage to force 

 the full-load current through the armature, and hence 

 only a small phase shift, a, is required. On some machines 

 tested a phase shift of 20 (electrical) was sufficient to 

 make the motor vary its load from zero to full load. 



Phase Shift Proportional to Load. The current is shown 

 at 01' and evidently this represents a motor input of 

 OEiXOI'Xcos ([>. If more mechanical load is put on the 

 motor a further shift in the phase of OE m occurs. Suppose 

 it moves back to OE m ", producing a resultant voltage, 

 OR". The current which this voltage causes is shown 

 by the vector 01", much larger than 01' and in a slightly 

 different phase. The input = OEiXOI"X cos 4/, which will 

 be just sufficient to give a mechanical output equal to the 

 assumed increased load. 



Power-factor Variation with Load. It will be noticed 

 from this diagram that <j> changes from a leading to a lag- 

 ging angle as the load in increased. If it is desired to 

 maintain a power factor of unity for the motor as the load 

 is varied, it is evident that the motor voltage must be slightly 

 increased as the load is increased. This is also shown in 



