Jkffco IT — Electrical Design of A. 0. High Tension Transmission Lines. 77 



Put X = I, and we find 



V^ = Vi cosh ml - nCi sinh ml, 



V 

 Co = C, cosh ml - ^ sinh ml. 

 n 



These equations give 



Vx = Vi cosh ml + n Co sinh ml, 



Fo 

 C, = Co cosh ml + — =sinh nd, 



n 



which may also be obtained similarly to the foregoing eqnations by putting « = I 

 in tlie general equations which determine A and B. 



The power put in per phase is P, = V,C\ cos ((/>, - (^/)> where </)i and (^Z are 

 the phase angles of Vi and C, respectively referred to the phase of Co as 

 standard ; 



.-. Pj = V^ cos (/>! X C\ cos 0i' + J\ sin ^^ x C^ sin f^'. 



If the receiving end is open, 



Cj = 0, Tj' = 7V cosh ml, and C/ = -^ sinh mZ, 



which is the charging current. 



If the receiving end is short-circuited, F, = 0. Then 



r/' = 71 Ca" sinh ml and C/' = CV' cosh 771/. 



We thus find for the voltage regulation at the receiving end that the ratio of the 

 voltage at the receiving end, on throwing off the load, to the full load voltage is 



p, = ^' = T. \ p sii^ce Fi = V,', 

 ^ V,2 Fo cosh ml 



the transmitting voltage remaining constant. 



The efficiency is the ratio of the power taken from the line at the receiving 



Po 



end to that put in at the sending end, or 77 = -vp-. 



10. We now turn attention to corona loss, or the loss of power from the Ihie 

 occasioned by the discharge from the conductor due to ionization of the surrounding 

 atmosphere. Above a certain disruptive critical voltage this loss can take place. 

 The magnitude of the loss depends on the amount by which the line voltage 

 exceeds "the disruptive critical voltage, and, to some extent, on the temperature 

 and pressure of the atmosphere. For single-phase and symmetrical three-phase 

 hues it has been shown by Peek (Trans. Am. Inst. El. Eng., vol. xxx, 1911) to be 

 expressible in the form 



Q = 5-53 X I X M X ( F - VcY X 10"« watts, 

 where the disruptive critical voltage Vc is given by 



F, = 123,400 ySalogio^ 



effective volts to neutral. 



