Effect of parameters on conductor and insulator cost

Line current is $I = \dfrac{P}{\sqrt{3}\,V\cos\phi\,N_c}$ per circuit. Conductor size depends mainly on current, while insulator size depends only on voltage.

(i) Power to be transmitted and length of line

• Conductor cost: larger $P$ means larger current, so a larger conductor area (for thermal limit and to keep losses low); conductor cost per km rises roughly in proportion to $P$. Longer $L$ increases voltage drop and loss, so for long lines a larger conductor (or higher voltage) is needed, again raising conductor cost per km.
• Insulator cost: per km it does not depend directly on $P$ or $L$, because insulation depends only on voltage. Indirectly, large $P$ and long $L$ push the design to a higher voltage, which increases insulator cost per km.

(ii) Voltage level

• Conductor cost: current $\propto 1/V$, so conductor area and conductor cost per km fall as voltage rises (loss $\propto 1/V^2$ for the same conductor). At EHV, however, minimum size or bundling may be fixed by corona, so the fall stops.
• Insulator cost: number of discs, string length, cross-arm length, tower height and clearances all increase with voltage; insulator cost per km rises roughly in proportion to $V$ (or faster at EHV due to switching-surge design).

(iii) Number of circuits

• Conductor cost: for the same total power, each circuit carries $1/N_c$ of the current, so each conductor is smaller, but there are $N_c$ times as many. Total conductor cost per km is roughly the same or a little higher (smaller conductors cost more per unit current), while losses for the same total aluminium are similar.
• Insulator cost: number of strings is proportional to $N_c$, so insulator cost per km roughly doubles from single to double circuit. Double-circuit towers are taller and heavier, but cheaper than two separate S/C lines.

These opposite trends give an optimum (most economical) voltage and number of circuits for each $P$ and $L$.