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

# HVDC two conductors vs HVAC three conductors

Power Electronics · Chapter 7: HVDC power transmission

- Asked in: 2076 Chaitra, 8 marks; 2072 Kartik, 8 marks (asked 2 times)
- Video: [Comparison between HVAC and HVDC transmission system](https://www.youtube.com/watch?v=l9nHs8e0WUg) — The Learning Curve
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/power_electronics/hvdc-two-vs-three-conductors
- Whole chapter: https://www.bctengineer.com/md/semester_7/power_electronics/chapter-7

## Question

In which circumstance, HVDC transmission line has advantages over the HVAC transmission line? Prove that a HVDC line with two conductors can transmit same amount of power as transmitted by HVAC line with three conductors of same size. What type of power electronic converter is used in HVDC line and why?

## Short answer

HVDC is advantageous for long-distance bulk power, submarine cables, and asynchronous ties. With same conductor size and insulation, a 2-conductor DC line transmits equal power to a 3-conductor AC line at power factor 0.943 because P_dc/P_ac =0.943/cosφ. The converter used is a line-commutated 12-pulse thyristor bridge, chosen for high power, natural commutation, and harmonic cancellation.

## Answer

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.

## Check yourself

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

1. Which situation favours HVDC over HVAC?
   A. Short overhead line between two nearby cities
   B. Linking two AC systems of different frequency
   C. Low-power distribution to households
   D. Any line shorter than 100 km
   Answer: B. HVDC can tie asynchronous or different-frequency systems; it is also chosen for bulk long-distance power and long cables. (Key point: When HVDC is favoured)

2. In the proof, what is the AC three-phase power with phase voltage rms Vm/sqrt2?
   A. P_ac = 3(Vm/sqrt2) I cos(phi) = 2.121 Vm I cos(phi)
   B. P_ac = 2 Vm I
   C. P_ac = 3 Vm I
   D. P_ac = Vm I cos(phi)
   Answer: A. Three phases each deliver (Vm/sqrt2) I cos(phi), totalling 2.121 Vm I cos(phi). (Key point: Proof of equal power)

3. What converter is used in conventional HVDC and how is power reversed?
   A. Diode bridge; by reversing the line current
   B. Line-commutated thyristor bridge; by changing firing angles (alpha < 90° rectifier, > 90° inverter)
   C. Chopper; by changing duty ratio
   D. Cycloconverter; by changing frequency
   Answer: B. The thyristor bridge is rectifier for alpha < 90° and inverter for alpha > 90°, so power direction changes via firing angles. (Key point: Converter type)

4. What is the advantage of 12-pulse operation with Y-Y and Y-delta transformers?
   A. Cancels the 5th and 7th harmonics, reducing filter size
   B. Doubles the DC voltage rating
   C. Removes the need for thyristors
   D. Eliminates reactive power
   Answer: A. The 30° phase shift between bridges cancels the 5th and 7th harmonics on the AC side. (Key point: Why 12-pulse)

## Related in Power Electronics

- [HVDC vs HVAC line conductor saving](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Ahvdc-conductor-saving) — Power Electronics, chapter 7, asked 2×
- [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×
- [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
- [When HVDC is economical; equal transmission capacity](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Ahvdc-economical-bulk-power) — Power Electronics, chapter 7
- [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×

## Related in other subjects

- [T/F: HVDC converter reactive power need](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atf-hvdc-reactive-power) — Transmission and Distribution System Design, 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
- [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
- [Criteria for choosing HVDC or HVAC](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Ahvdc-hvac-choice-criteria) — High Voltage Engineering, chapter 1