---
title: "HVDC vs HVAC line conductor saving"
subject: "Power Electronics"
chapter: 7
key: "semester_7/power_electronics:hvdc-conductor-saving"
source: https://www.bctengineer.com/q/semester_7/power_electronics/hvdc-conductor-saving
site: BCT Engineering
---

# HVDC vs HVAC line conductor saving

Power Electronics · Chapter 7: HVDC power transmission

- Asked in: 2080 Bhadra, 8 marks; 2080 Baishakh, 8 marks (asked 2 times)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/power_electronics/hvdc-conductor-saving
- Whole chapter: https://www.bctengineer.com/md/semester_7/power_electronics/chapter-7

## Question

Why HVDC line is preferred over HVAC line to transport large power over a long distance? Make a mathematical comparison between HVAC and HVDC lines to justify line conductor saving in HVDC line.

## Short answer

HVDC is preferred for long-distance transmission due to lower line cost and losses beyond the break-even distance. For the same power, voltage, and total loss, the required DC conductor material is only 0.5 cos²φ times that of AC. At unity power factor, HVDC needs just half the conductor volume, saving material and tower costs.

## Answer

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:**

| Power factor of AC line | $A_{dc}/A_{ac}$ | DC conductor material as % of AC |
|---|---|---|
| 1.0 | 0.75 | 50% |
| 0.9 | 0.61 | 40.5% |
| 0.8 | 0.48 | 32% |

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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which quantities are held equal in the conductor-saving comparison?
   A. Same power, length, peak voltage to ground, total loss, and material
   B. Same current and different power
   C. Same area and different loss
   D. Same rms voltage only
   Answer: A. Equal power, length, insulation (peak voltage), total loss and resistivity let the conductor areas be compared. (Key point: Assumptions)

2. Equating losses, what is A_dc/A_ac?
   A. 0.5 cos^2(phi)
   B. 0.75 cos^2(phi)
   C. 1.5 cos^2(phi)
   D. 0.75 cos(phi)
   Answer: B. (1/2)/(2/(3 cos^2 phi)) = 0.75 cos^2(phi). (Key point: Area ratio)

3. Including the number of conductors (2 vs 3), what is the DC to AC conductor volume ratio?
   A. 0.75 cos^2(phi)
   B. 0.5 cos^2(phi)
   C. (2/3) cos(phi)
   D. cos^2(phi)
   Answer: B. Vol ratio = (2/3)(0.75 cos^2 phi) = 0.5 cos^2(phi), i.e. 50% at unity pf. (Key point: Volume ratio)

4. As the AC line power factor falls, what happens to the DC conductor saving?
   A. It decreases
   B. It stays the same
   C. It increases
   D. It becomes zero
   Answer: C. The DC material ratio 0.5 cos^2(phi) shrinks as cos(phi) falls (40.5% at 0.9, 32% at 0.8), so the saving grows. (Key point: Effect of power factor)

## Related in Power Electronics

- [Why HVDC over HVAC: mathematical comparison](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Ahvdc-vs-hvac-comparison) — Power Electronics, chapter 7, asked 4×
- [HVDC power loss is 2/3 of HVAC](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Ahvdc-two-thirds-loss) — Power Electronics, chapter 7, asked 2×
- [HVDC advantages and power transfer capacity](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Ahvdc-power-transfer-capacity) — Power Electronics, chapter 7, asked 2×
- [Compare HVAC and HVDC; 2/3 power loss](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Acompare-ac-dc-two-thirds-loss) — Power Electronics, chapter 7
- [HVDC two conductors vs HVAC three conductors](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Ahvdc-two-vs-three-conductors) — Power Electronics, chapter 7, asked 2×

## Related in other subjects

- [Infinite bus and HVDC vs HVAC comparison](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Ainfinite-bus-hvdc-vs-hvac) — Power System Analysis I, chapter 1
- [HVDC for long distance and B2B significance](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Ahvdc-long-distance-b2b) — High Voltage Engineering, chapter 1
- [HVDC vs HVAC and HVDC scope in Nepal](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Ahvdc-hvac-compare-nepal) — High Voltage Engineering, chapter 1