jEt'FCoTT — Electrical Design of A. C. Iliijh Tension Transmission Lines. 73 



mile ; the leakage conductance be K mhos, per mile ; and the permittance or 

 capacity be S fai'ads per mile. 



Let V volts be the effective value of the voltage betv^een one conductor and 

 neutral ; let C amperes be the effective value of the current per line ; and let P 

 watts be the power transmitted per line. Let suffixes 1 and 2 applied to V, C, P 

 indicate their values at the sending end and receiving end of the line respectively. 



Let Vo be the disruptive critical voltage to neutral ; and let Q watts be the 



corona loss of power per line. Let 6 be the temperature in degrees centigrade of 



the atmosphere surrounding the line ; and h be the barometric pressure in inches 



of mercury. 



9 -9 6 A 

 Let 8 = —;— ; — ;- , and let 7 be the surface condition factor for the conductor. 

 273 + ti ' 



Further, let cos <j) be the power-factor of the load, let the efficiency of trans- 

 mission be denoted by i;, and the voltage regulation fraction from no to full load 

 by p. 



Write '=J-1, P = W, 



m=J{R + ipL) (K + ipS), 



and n= jUM 



\K + ipS 



Let the value of power be s pence per kilowatt hour, the value of conductor 

 material be q pence per lb., and the rate of interest and depreciation on the line 

 be r per annum. 



6. We will require to use certain identical relations connecting complex 

 quantities, and these are written down here for reference. 



(a + ix) + (5 + iy) = [a + b) + i {x + y), 

 {a + ix] - (b + iy) = {a - b) + i {x - y), 

 n {a + ix) = na + inx, 

 {a + ix) [b 1- iy) = (ab - xy) + i (bx + ay), 

 a + ix ah + xi/ . bx - ay 

 b + ly b' + y- o" + y 



(a + ix)' = (a- - .-r) + i (2««), 



]a + ix = — \]a + J/2 + a;= + i J _ a + Ja» + A, 



Ja^w = -- Ua ± jft2 + a;2 - ij - a ± Ja^ + xA, 



cosh (a + ix) = cosh a cos x + i sinh a sin x, 

 sinh (a + ix) = sinh a cos x + i cosh a sin x, 



, , X- x^ x^ 



cosh..= l + 2-, + 4] - g!-"--- 



Al3 /JgO ry-il 



. . tv t(/ lAy 



sinh ,r = a. + g^ + - + ^-- + . . . 



o2 



