Design a DC transmission line that can transmit 300 MW of el

Design a DC transmission line that can transmit 300 MW of electricity 117 km with only a 2% loss. The wires are to be made of aluminum and the voltage is 680 kV. What should be the minimum transmission line diameter?

The correct answer is between 1 and 2 cm.

Solution

loss of power, P = 2% of 300 MW

= 0.02*300*10^6 W

= 6*10^6 W

Let R is the the resistance.

Apply, P = V^2/R

==> R = V^2/P

= (680*10^3)^2/(6*10^6)

= 77066.66 ohms

now use, R = rho*L/A

A = rho*L/R

pi*d^2/4 = rho*L/R

d^2 = 4*rho*L/(pi*R)

d = sqrt(4*rho*L/(pi*R))

= sqrt(4*2.65*10^-8*2*117*10^3/(pi*77066.66))

= 0.0003200 = 0.32*10^-3 m or 0.320 mm