57G ELECTRICAL MEASUREMENTS 



Referring to Fig. 355, 

 Let: 



Ni and NI = number of primary and secondary turns, respectively. 

 R and X = equivalent resistance and reactance of the transformer. 

 .Riand X\ resistance and reactance of the primary windings. 

 /o = exciting current. 

 V\ and Vi = primary and secondary terminal voltages. 



6 = power factor angle of the secondary load. 

 S = angle between 7 and V 2 reversed. 



7 = phase angle of the transformer, or the angle between V \ and V* 



FIG. 355. Diagram for potential transformer. 



The component of the primary current which is in opposition 

 to the secondary current is 7 2 TT = /. To determine the ratio, 



projecting V\ on F 2 and adding up the components of the projec- 

 tion, gives 



V l cos 7 = F 2 j-r + IR cos 6 + IX sin + / #i cos 8 + I X l sin 5. 



i 



2 F 2 



In potential transformers 7 is usually considerably less than 

 1, so cos 7 = 1 very closely, and 



Fi _ Ni IR cos 6 + IX sin 6 + /ofli cos 5 + IoX l sin d 



F 2 N 2 "* F 2 



To determine the phase angle, projecting on a line perpendicu- 

 lar to F 2 , gives 



Fi sin y = IR sin IX cos + / #i sin 6 /o^i cos 5 

 but for small angles sin 7 = 7 approximately, so 



7 = ^IR sin 6 - IX cos 6 + I Ri sin d - I X l cos 



In the potential transformer the small change of exciting cur- 

 rent, /o, between no-load and full-load produces a negligible 

 effect on the results. 



