HVDC two conductors vs HVAC three conductors

HVDC has advantages over HVAC when large power is to be sent over a long distance (beyond the break-even distance), and in some special cases.

Circumstances favouring HVDC

1. Bulk power over long overhead lines (beyond about 500–800 km).
2. Submarine or underground cables longer than about 40–80 km, where AC charging current would use up the cable rating.
3. Linking two AC systems of different frequency, or not synchronised (asynchronous tie).
4. Where fast power-flow control or stability support is needed, and to avoid raising fault levels.
5. Where right of way is limited (fewer conductors, smaller towers).

Proof: 2 DC conductors carry the same power as 3 AC conductors

Assumptions: all conductors same size (same current $I$), same insulation level (peak voltage to earth $V_m$).

AC three-phase line, phase voltage rms $V_m/\sqrt{2}$:

$$P_{ac} = 3\cdot\frac{V_m}{\sqrt{2}}\cdot I\cos\phi = 2.121\,V_mI\cos\phi$$

Bipolar DC line, $\pm V_d$ with $V_d = V_m$, $I_d = I$:

$$P_{dc} = 2V_dI_d = 2V_mI$$

Ratio:

$$\frac{P_{dc}}{P_{ac}} = \frac{2}{2.121\cos\phi} = \frac{0.943}{\cos\phi}$$

For the usual power factor $\cos\phi = 0.943$ (or close to it), $P_{dc} = P_{ac}$. So a 2-conductor HVDC line transmits the same power as a 3-conductor HVAC line with the same conductor size and insulation. In addition, its line loss is only $2I^2R$ against $3I^2R$, i.e. 2/3.

Converter used in HVDC and why

• Line-commutated, fully controlled three-phase thyristor bridge converters, usually connected as 12-pulse units (two 6-pulse bridges fed by Y-Y and Y-Δ transformers).
• The same bridge works as a rectifier ($\alpha < 90°$) at the sending end and an inverter ($\alpha > 90°$) at the receiving end, so power can be reversed by changing firing angles.
• Thyristors are available in very high voltage and current ratings and can be series-connected into valves; they use natural commutation (no extra commutation circuit).
• 12-pulse operation cancels the 5th and 7th harmonics, reducing filter size.
• Newer schemes also use voltage source converters (VSC) with IGBTs, which allow independent reactive power control and connection to weak networks.