Compare HVAC and HVDC; 2/3 power loss

HVAC transmission sends power as three-phase AC through transformers; HVDC converts AC to DC at the sending end (rectifier), transmits DC, and converts back to AC (inverter). Each is best in a different range.

Comparison of AC and DC transmission

AC is cheaper for short and medium distances because terminals are simple; DC is cheaper for long distances (beyond the break-even distance) and for long cables.

Justification of the 2/3 loss

Assumptions: same power capacity, same conductor size and current $I$, same loss per conductor $p = I^2R$, same insulation (peak voltage to earth $V_m$, with $V_d = V_m$).

Same capacity:

$$\begin{aligned} P_{ac} &= 3\cdot\frac{V_m}{\sqrt{2}}\cdot I\cos\phi = 2.121\,V_mI\cos\phi \\ P_{dc} &= 2V_mI \end{aligned}$$

These are equal for $\cos\phi = 0.943$, so a 2-conductor bipolar DC line has the same capacity as a 3-conductor AC line.

Total losses:

$$\frac{\text{Loss}_{dc}}{\text{Loss}_{ac}} = \frac{2I^2R}{3I^2R} = \frac{2p}{3p} = \frac{2}{3}$$

Hence the HVDC line loss is only 2/3 of the HVAC line loss for the same power. In practice the saving is a little more, because the AC resistance is higher due to skin effect and AC lines have more corona loss.