REGULATION OF ALTERNATORS 315 



value of its ordinates calculated. The ratio of this quantity to 

 the volt-amperes is equal to the cosine of the angle ty' in Fig. 133. 

 This vector diagram, can be constructed as follows: 



Draw OE representing the phase of the open-circuit voltage, 

 i. e., the center of the pole, to be used as a reference line 

 from which the phase angles can be plotted. Make the angle 

 E OIc equal to of Fig. 131. This is the estimated lag of 

 current behind the open-circuit electromotive force. Draw 

 OE'g equal in length to the calculated e.m.f. value of the "ap- 

 parent" developed voltage under load conditions, and so that^' = 



(watt^ \ 

 volt-amperes/ ' where the watts referred to are calculated 



by multiplying the corresponding instantaneous values of E' g 

 and I a . From E' g drop a perpendicular on to OI a , and set oS 



IX ( Blots) 

 Eg 

 IX (ends) 



Fia. 133 Vector diagram for determining the inherent regulation of an 

 alternating-current generator. 



E'g E g and EgP to represent the reactance drops per phase in slots 

 and end connections respectively. Draw PE t parallel to 01 a to 

 represent the resistance pressure drop per phase, and join the 

 point with E a and E t respectively. The angle E t OI a and the 

 length of the vector OE t may not correspond with the exact 

 values of external power factor and terminal voltage assumed 

 when the angle was originally estimated; but, by using the 

 vector construction on the assumption of sine-waves throughout, 

 a very close estimate of these quantities can be made. The im- 

 portant point in connection with this method of analysis is that 

 the external power-factor angle e and the terminal voltage E t can 

 be calculated for any value of the armature current I a when the 

 phase displacement of the latter relatively to the open-circuit 

 voltage is assumed. 



