Task $3$

A three phase $11$ kV aluminium cable is to be designed to transmit $2\mathrm{.}465$ MVA over a distance of $1$ km for $2190$ hours per year $($diversity of $\frac{1}{4}$ of $24$ hours, $7$ days per week$).$ The cost of aluminium $2448$ per tonne and a density of $2700k\frac{g}{m^3}.$

The interest and depreciation charges total $10\%$ per annum and the energy costs $6\mathrm{.}693$ p per kWh $($day unit cost$).$

As before from tables, the resistance of one kilometre of conductor of cross$-$sectional area of $100m{m}^2$ aluminium conductor is $0\mathrm{.}2780\frac{}{k}m,$ so the resistance in $m{m}^2$ of conductor is $0\mathrm{.}278100\frac{}{m}\frac{m^2}{k}m.$

What is the most economical conductor cross$-$sectional area?