Jkffcott — Electrical Design of A. C. High Tension Transmission Lines. 75 

 and the root mean square value ol' y is 



J jj' i/dt = j¥TW^- 



Under the assumptions made, this is the effective vahie of the current so far as 

 power loss in the line throughout the year is concerned. 



And similarly for other cases, the effective value of the current must be 

 estimated from the load and time diagram. 



For present purposes the average power loss throughout the year is taken as 

 C-E as a first approximation. If desired, more exact figures, resulting from the 

 determination of the electrical performance of the line, iu eluding leakage and 

 corona effects, may be used afterwards for greater accuracy. 



Let us suppose copper is the material chosen for the line. 



Then E = — - — ohms. 

 A 



CH 

 Hence power loss per line = G-B = -04.3 — - watts ; and the annual value of this 



power is '.SVC C- -^ s pence. 



The weight of copper is 20,.300 AI lbs. The annual charge for interest and 

 depreciation on the copper is therefore 20,300 Alqr pence. The total annual cost 



in pence is then '376(7- -j s + 20,300 Alqr, and this is to be a minimum. 



Hence "-. + 53,900 Aqr is to be a minimum. To satisfy this requirement we 



find A is given by 



■^ - 53,900 qr = 0, 

 A- 



or A' = •0000185C--, 



qr 



or A = -00436' J- • 



\ qr 



If ^ = 15 pence per lb., r ='8 per cent., s = one penny per unit, we obtain 

 A = -00392 C. 



Similarly for other values of q, r, s. 



This equation gives us the most economic sectional area of copper conductor, 

 and it will be noted that the current density in the conductor is quite small, so that 

 there is no risk of overheating. 



If aluminium be used for the line, we have E = -^ ohms. The weight of 



C's 

 aluminium is 6120 ^Hbs. Hence we find that -j + 10,000 ^^r is to be a 



minimum. Therefore ^ = -010C. — for aluminium conductor. 



Sqr 



