Question

1. ”The Rio Madeira transmission link in Brazil, with an overhead length of 2,385km, is the world’s longest power transmission line. The 600kV high-voltage direct current (HVDC) bipolar line was brought into commercial operation in November 2013 and is capable of transmitting 7.1GW of power.” a. What is the current in this line when it is carrying maximum power?. b. If the resistance of the wires in the line is about 2.4 x 10−2 ohms per kilometer, how much energy goes to heating the wires of the line when it is operating at maximum power? What percent is this of the maximum power? c. There has been some discussion of a similar line between Seattle and Boston. If the design parameters (voltage, maximum current, resistance per kilometer of wire) were the same, what percent of the transmitted power would be lost to heat in the Seattle Boston line? The distance from Boston to Seattle is 4870 kilometers.

Answer 1

P = VI ==>

I = P/V = $I = 7.1 gW/ 600kV = 7.1 \times 10^{9}/600\times 10^3 = 11833.333 A \\ R_{net} = 2.4 \times 10^{-2}\times 2385 = 57.24 \Omega \\ \implies P_{heating} = I^2*R = 8.02 W \implies \% = 8.02 \times 100/7.1 = 113\% \\ \\ For \ new \ line ==> R = 2.4 \times 1-^{-2}\times 4870 = 116.88 \Omega \\ \implies P = I^2R = 16.37 gW \implies \% = 1637/7.1 = 231\%$