136 ELEMENTS OF ELECTRICAL ENGINEERING. 



the polar projections of the field magnet, that is, if the armature 

 were completely and uniformly surrounded with iron as shown in 

 Figs. 1 13^, \\Afb and 115^, then the combined effect of two mag- 

 netizing actions A and B would be as follows : Consider the 

 flux <I> across the armature due to A and the flux <3>' due to 

 B. Draw lines in the directions of <E> and <>' and let the lengths 

 of these lines represent the magnetomotive force values (ampere- 

 turns) of A and B respectively. Then the vector sum of these 

 lines will represent the direction and value (in ampere-turns) of 

 the single magnetizing action which is equivalent to the combined 

 action of A and B. This is the fundamental idea of the mag- 

 netomotive force method for calculating voltage regulation, and 

 the method is best explained by considering numerical examples. 

 Let it be required to calculate the voltage regulation (full load to 

 zero- load) of the 2OOO-volt, 2OOO-kilowatt, 3 -phase alternator re- 

 ferred to in connection with Figs. 117 and 118, (a) for receiving 

 circuits of unity power factor and (b) for receiving circuits of 0.85 

 power factor, the resistance of one of the armature windings (one 

 phase) being 0.07 ohms. 



(a) Unity power factor. When the alternator delivers full- 

 load current of 333 amperes from each of its armature windings 

 to noninductive receiving circuits, the two components of the 

 total induced voltage parallel to and at right angles to the cur- 

 rent are 2023.3 volts and 1150 volts as explained above under 

 the electromotive force method. From Fig. 1 1 7 we find that a 

 field current of 84 amperes is required to give 2023 volts total 

 induced electromotive force ; and a field current of 42 amperes 

 is required to give a total induced electromotive force of 1150 

 volts. To give these two quadrature electromotive forces simul- 

 taneously a field current equal to 94 amperes (= 1/84 2 -j- 42 2 ) 

 would be required ; and, according to Fig. T 1 7, this field current 

 of 94 amperes would give a total induced electromotive force of 

 2 200 volts, which is the value to which the terminal voltage of 

 the machine would rise at zero load, Therefore the regulation 

 of the machine is (2200 2000) / 2000 = o.io or 10 per cent. 



