106 TRANSMISSION LINE FORMULAS 



TABLE II. FORMULAS FOR SHORT LINES. 



CONDITIONS GIVEN AT SUPPLY END. 



These formulas are exact when the line is short. When the line is 20 

 miles long, they are correct within approximately -fa of i% of line voltage. 



Conditions given: 



K.V.A. = K.V.A. at supply end. 



E a = Full load voltage at supply end. 

 cos 6 = Power factor at supply end. 

 K.W. = K.V.A. cos e. 



r = Resistance of conductor per mile. (From Tables VII-VIII.) 

 x = Reactance of conductor per mile. (From Tables IX-XII.) 

 I = Length of line in miles. 



1000 K.V.A. cos 6 

 Then P 8 = - g = In-phase current at supply end 



(in total amps.). 



1000 K.V.A. sin 

 Q 9 = = = Reactive current at supply end 



(in total amperes) when current is 

 lagging. 



1000 K.V.A. sin e 

 = - when current is leading. 



-C-8 



Find the following quantities: 



Three Phase or Two Phase. Single Phase. 



F = E 8 - P 8 rl - Q 8 xl F = E 8 -2 P 8 rl - 2 Q,xl 



G = Q 8 rl - P 8 xl G = 2 Q 8 rl - 2 P 8 xl. 



Formulas (capacity neglected): 



(1) Voltage at receiver end = F -\ = 



(2) Regulation of line = E 8 F p. (Same as line drop.) 



2 IE.-F-?-} 



(3) Per cent regulation of line = -^J __ L per cent. 



(Same as per cent line drop.) 



(4) K.V.A. at receiver end = g - X K.V.A. 



