HVDC advantages and power transfer capacity

HVDC transmission uses a rectifier at the sending end, a DC line, and an inverter at the receiving end. For large power over long distances it is cheaper and more efficient than HVAC, because the line is cheaper and has no stability or reactive-power limits; the high converter cost is recovered beyond the break-even distance.

Why HVDC for large power over long distance

• Lower line cost: a bipolar DC line needs only 2 conductors instead of 3, smaller towers and a 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.

Advantages of HVDC over HVAC lines

1. Only 2 conductors (bipolar) or 1 conductor with earth return (monopolar); lighter towers, narrower corridor.
2. No charging current, so there is no limit on the length of underground or submarine cables.
3. No skin effect; the full conductor area is used.
4. Less corona loss and radio interference for the same voltage.
5. Fast and accurate control of power flow by firing angle; it can damp oscillations in the connected AC systems.
6. Can link AC systems of different frequencies or not in synchronism (e.g. 50 Hz and 60 Hz).
7. Does not raise the fault level of the connected AC systems; DC line faults are cleared quickly by converter control.
8. In a bipolar link, one pole can continue to operate with earth return if the other pole fails.

Mathematical comparison of power transfer capacity

Assumptions: same conductor size and current rating (same rms current $I$ per conductor), same insulation, i.e. the same peak voltage to ground $V_m$; three-phase AC line with 3 conductors; bipolar DC line with 2 conductors at $\pm V_d$, $V_d = V_m$, $I_d = I$.

$$\begin{aligned} P_{ac} &= 3\cdot\frac{V_m}{\sqrt{2}}\cdot I\cos\phi = 2.121\,V_m I\cos\phi \\ P_{dc} &= 2V_d I_d = 2V_m I \end{aligned}$$ $$\frac{P_{dc}}{P_{ac}} = \frac{2V_m I}{2.121\,V_m I\cos\phi} = \frac{0.943}{\cos\phi}$$

Per conductor:

$$\frac{P_{dc}/2}{P_{ac}/3} = \frac{V_m I}{0.707\,V_m I\cos\phi} = \frac{1.414}{\cos\phi}$$

Interpretation:

• At $\cos\phi = 0.943$, $P_{dc} = P_{ac}$: a DC line with two conductors carries the same power as an AC line with three conductors of the same size and insulation.
• At unity power factor, $P_{dc}/P_{ac} = 0.943$, but per conductor the DC line carries $\sqrt{2} = 1.414$ times as much power, because the DC conductor works continuously at the peak voltage $V_m$ while the AC conductor's rms voltage is only $V_m/\sqrt{2}$.
• So for the same power, DC needs one conductor less and its loss is about 2/3 of that of the AC line.