HVDC vs HVAC line conductor saving

An HVDC line is preferred for large power over long distance because, after the break-even distance, the cheaper DC line (fewer conductors, less insulation, lower losses, no reactive power) outweighs the extra cost of converter stations.

Reasons

• Lower line cost: a bipolar DC line needs only 2 conductors instead of 3, smaller towers and narrower right of way. Terminal (converter) cost is high, but beyond the break-even distance (about 500–800 km for overhead lines, 40–80 km for cables) the total cost of DC is lower.
• No stability limit: AC power $P = \dfrac{V_1V_2}{X}\sin\delta$ falls as line reactance grows with length; DC has no reactance or load angle, so power is limited only by thermal rating.
• No reactive power or charging current: no need for line compensation; voltage stays nearly constant along the line.
• Lower losses: no skin effect, less corona, fewer conductors.
• Asynchronous link and fast power control by firing angle.

Mathematical comparison: conductor saving

Assumptions: same power $P$, same length $l$, same peak voltage to ground $V_m$ (same insulation), same total loss, same conductor material (resistivity $\rho$).

AC (3 conductors, area $A_{ac}$) and DC (2 conductors, area $A_{dc}$):

$$\begin{aligned} I_{ac} &= \frac{P}{3(V_m/\sqrt{2})\cos\phi}, \qquad I_{dc} = \frac{P}{2V_m} \\ \text{Loss}_{ac} &= 3I_{ac}^2\frac{\rho l}{A_{ac}} = \frac{2P^2\rho l}{3V_m^2\cos^2\phi\,A_{ac}} \\ \text{Loss}_{dc} &= 2I_{dc}^2\frac{\rho l}{A_{dc}} = \frac{P^2\rho l}{2V_m^2A_{dc}} \end{aligned}$$

Equating the losses:

$$\frac{A_{dc}}{A_{ac}} = \frac{1/2}{2/(3\cos^2\phi)} = 0.75\cos^2\phi$$

Ratio of conductor volume (material):

$$\frac{\text{Vol}_{dc}}{\text{Vol}_{ac}} = \frac{2A_{dc}l}{3A_{ac}l} = \frac{2}{3}\times 0.75\cos^2\phi = 0.5\cos^2\phi$$

Result:

At unity power factor, the DC line needs only half the conductor material of an equivalent AC line for the same power, voltage stress and losses; at lower AC power factor the saving is even greater. Fewer and lighter conductors also mean lighter towers and a narrower right of way, which is why HVDC lines are cheaper per km.