VECTOR DIAGRAM OF ALTERNATOR 153 



Having determined the (equivalent) resistance and reactance of 

 our apparatus as explained above, we may construct the vector 

 diagram connecting the constant open-circuit p.d. corresponding to 

 any constant excitation (i.e. any constant value of the exciting current 

 in the case of an alternator, and any constant primary p.d. in the 

 case of a transformer) with the terminal p.d. for a given load current 

 of known power factor. Let us provisionally assume the terminal 

 .d. to be known, and to be represented by OA in Fig. 113. Let ^ 



the angle of lag (cos ^ = power factor of load) of the current 



7TB 



I 



FIG. 113. Vector Diagram of Loaded Alternator or Transformer. 



behind the terminal p.d., so that 01 gives the direction of the current 

 vector. We obtain the open-circuit p.d. (e.m.f. in case of alternator) 

 by adding vectorially to the terminal p.d. OA the resistance drop 

 rl = AB (which is parallel to the current vector 01) and the 

 reactance drop plA = BC (this is perpendicular to 01).* We thus 

 get the open-circuit p.d. OC. Instead of considering the resistance 

 and reactance drops separately, we may consider the impedance drop 



L 

 AC, which makes an angle tan" 1 with the current vector. By 



reversing the construction, we can easily obtain the terminal p.d.'s 

 corresponding to various load currents, as follows. With as centre, 

 and radius = constant open-circuit p.d., describe an arc. Draw OA 

 to represent the direction of the terminal p.d. vector, and 01 to 

 represent the direction of the current vector. From draw a line 



making an angle tan" 1 - with 01, and along it lay off OD to 



(synchronously rotating) field were open-circuited and an alternating p.d. applied to the 

 armature from some external source; whereas, in the cose of the truntformer, the 

 reactance here considered is merely its leakage reactance, which is enormously smaller 

 than the total reactance (or the reactance obtained by open-circuiting the primary and 

 applying an alternating p.d. to the secondary). 



* r = equivalent resistance, L = equivalent inductance, I = load current. 



