# How does DC transmission require several times less wire than AC?

In this YouTube video (scrolled to 5:55) there's a claim that replacing an AC high voltage transmission line with a high voltage DC transmission line allows for having seven times fewer powerlines (the video shows how seven lines evaporate, then one line appears and the cutting in the forest gets narrower).

How is that possible? I've read the Wikipedia article and it claims that

The power delivered in an AC system is defined by the root mean square (RMS) of an AC voltage, but RMS is only about 71% of the peak voltage. The peak voltage of AC determines the actual insulation thickness and conductor spacing.

but that doesn't explain seven times less power lines.

How is such massive (seven times) saving possible when switching from AC to DC transmission?

• Our teacher always said that for AC all useful energy is carried by the electric and magnetic fields. Everything that goes through the wire is losses. – Federico Russo May 18 '12 at 9:56
• @FedericoRusso, that is true for all electrical energy, not just AC. The electric and magnetic field is the real source of power, the electric field really forms the heart of it in pure DC. – Kortuk May 19 '12 at 3:53
• There's a good wikipedia article about high voltage DC systems. They're most cost effective when you need to send a lot of power a very long way - the AC/DC conversion equipment is quite complicated and some of the losses in AC transmission are proportional to the length of cable (e.g. capacitive losses to ground). If I was making up examples for a HVDC equipment vendor I'd base them on very long power lines. en.wikipedia.org/wiki/High-voltage_direct_current – Will Feb 12 '15 at 11:33

A significant factor, and probably the major one here, is the increase in voltage. They are comparing apples with pears and then some.

Power = Vrms x Irms.
BUT resistive line losses are proportional to I^2.
So if you increase voltage by a factor of "N" then current for the same power drops by a factor of N and losses drop as N^2, as

• Power = V x I = (V x N) x (I/N)
Losses at I are proportional to I^2
Losses at I/N are proportional to (I/N)^2 = I^2 / N^2.

Their original AC lines are 500 kV.
Their DC line is 800 kV.
N = 800/500 = 1.6
N^2 = 1.6^2 = 2.56 .
To get to 7 x you need a factor of 7/2.56 = 2.7

For the same number of wires you will need 2.7 x the area or about 1.65 x the diameter. And/or lower resistance material. Maybe more copper and less aluminum.

Then there is a loss of capacitive losses from AC.

A significant factor is that ABB have been around a long long time and 'know their stuff'. It won't be magic - just applied engineering - and the claim will be true as presented - but there will still be some smoke and mirrors. How BIG is that new tower? How visible are the wires ... ?. The fact they are doing it means thy believe they can make more money and save the customer money or equivalent in the process.

• 800 kV vs. 500 kV RMS (you said kW, but I think you meant kV) would certainly be the deciding factor. +1 for actually doing the math! – Kevin Vermeer May 18 '12 at 21:44

There are three main factors at work that make DC power transmission more efficient.

1. Peak voltage. As you say, AC transmission lines have to be designed for the peak voltage, but the useful power is related to the RMS voltage. These differ by the square root of 2 since they are are sines. Power is proportional to the square of the voltage. The same transmission line can carry twice the power at a steady DC voltage that is the same as the peak AC voltage.

2. Skin effect. With AC, the outer edges of the cable carry more of the current. This makes the cable appear to have a higher resistance at AC than it does at DC. I don't know what this ratio is at 60 Hz for typical transmission lines. Of course those transmission lines were sized with this in mind. This is why sometimes you see a cluster of 3 cables instead of one bigger one. With DC the one bigger one would work fine, which is presumably less expensive. There is another issue of keeping the field strength in the surrounding air down, so three lines isn't necessarily only to reduce skin effect.

3. Radiation and capacitive loss. Even 60 Hz radiates, and there is always some capacitive coupling to ground and between the conductors. Radiation is pure power loss, and reactive impedance causes currents in the wires that don't transfer power but cause loss and eat into your max current budget. I don't know how big either of these effects are with normal transmission lines. I do know that AC lines are crossed over at regular intervals of some miles. This makes them essentially twisted pair to reduce the net external field.

7x sounds rather high to me. Without a clear accounting of what factors were considered and some justification for the numbers chosen, I'm not ready to believe it. Some amount of extra efficiency in the transmission system is definitely there though. Note that while DC is more efficient to transmit, AC is easier and more efficient to convert between different voltages and currents. The system needs to be designed for the best total end to end result.

DC systems do exist, so that fact that most transmission lines are AC probably means that economics doesn't favor DC except in niche situations. It seems (I don't have direct knowledge) that DC is used today for long distances and when going between different grids. In the first case, the better transmission efficiency dominates at long distances, and in the second case DC doesn't require the ends to be phase synced.

One example of the former case is the Hydro Quebec transmission to New England. That's a long haul, but there is also a large power conversion station at the receiving end not too far from my house. It's definitely not trivial to receive the DC power and make it usable to the local grid. You can see this for yourself at 42.57047°N 71.52434°W. The cut thru the forest towards the northwest is where the DC lines come in. That cut also includes a 3 phase AC line which was previously existing before the Hydro Quebec project. The east-west lines just south of that plant is a major AC transmission line of the local grid.

• It's some pretty amazing stuff, huge oil-submerged stacks of electronics to handle the voltage and AC/DC conversion in the jungle. en.wikipedia.org/wiki/Inga%E2%80%93Shaba_HVDC – joeforker May 19 '12 at 4:17
• This picture always looked like something out of Star Wars, down in the guts of the Death Star. – tcrosley Feb 12 '15 at 18:00

I'm not sure about seven times. I recall from my university days that 25% of all power plants exist to heat wires and cables (I'm pretty sure you can find more accurate information on the web). AC power distribution suffers from two main adverse effects:

• Reactive power: real power systems are never strictly resistive, i.e. their power factor is less than 1. This leads to useless reactive energy "sloshing around" heating wires. Remember that it is active power that does useful work, but it's apparent power that flows in wires, so wires have to be sized for apparent power. Expensive power factor correction is commonly employed to counteract this effect, but it's never completely effective. See AC power.

• Skin effect: it's actually pretty serious even at 50 or 60 Hz. It reduces effective conductive area of the wire. Many powerline wires are made of steel core wrapped in aluminium. Resistive losses in the steel core are actually negligible.

There're other effects related more to overhead power transmission than to AC such as corona discharge, phase imbalances that require transposition of phases (not a factor in cables IIRC), the need to heat wires in cold weather to prevent ice buildup, etc., but these have a comparatively small effect on efficiency.

The designing of DC transmission system is based on Peak value of the voltage , but the designing of AC transmission system depends on the R.M.S value. Therefore, the limit of the AC transmission system must multiply by 1.4 to transmit the same amount of power

• Yes, that was outlined in the question and it is not enough to explain the massive increase of power. – sharptooth Feb 12 '15 at 11:27
• The economical comparison between the AC and DC connection types is significant due to the overall cost. The total cost of transmission lines for both connection types involves main equipment and components, right of way (ROW), conductors, insulators, and operational costs which include line losses. Therefore, building a DC system requires less space compared to an AC system with the same rating, and for long distance DC systems is more economic and less expensive compared to AC. Improved energy transmission facilities would introduce to existing power plants a more efficient utilization. – Hasan Alrajhi Feb 12 '15 at 11:35