18 TRANSMISSION LINE FORMULAS 



TABLE I. FORMULAS FOR SHORT LINES. 

 CONDITIONS GIVEN AT RECEIVER END. 



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

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

 Conditions given: 

 K.V.A. = K.V.A. at receiver end. 



E = Full load voltage at receiver end. 

 cos = Power factor at receiver end. 

 K.W. = K.V.A. cos 0. 



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

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

 / = Length of line in miles. 



1000 K.V.A. cos T , 

 Then P= g = In-phase current at receiver end (m 



total amps.). 



_ 1000 K.V.A. sin 



Q = = Reactive current at receiver end (m 



ML, 



total amps.) when current is lagging 



1000 K.V.A. sin . 

 = ^ when current is leading. 



Find the following quantities: 



Three phase or two phase. Single phase. 



A = E + Prl + Qxl. A = E + 2 Prl + 2 Qxl. 



B = Pxl - QrL B = 2 Pxl - 2 Qrl. 



Formulas (capacity neglected) : 



(1) Voltage at supply end = A -\ -. 



2 A. 



(2) Regulation of line = A -\ j E. (Same as line drop.) 



2 A. 



IOO ( A + 7J- E } 



(3) Per cent regulation of line = - 7: per cent. 



(Same as per cent line drop.) 



(4) K.V.A. at supply end = -^- x K.V.A. 



(5) K.W. at supply end = (AP - BQ). 



IOOO 



(6) Power factor at supply end - - 1 - 



30 ' ' ' ~ l X K.V.A. 



('+5) 



(hi decimals). 



