# The Naked Scientists Forum

### Author Topic: How much power is lost in transmission cables?  (Read 19777 times)

#### chris

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##### How much power is lost in transmission cables?
« on: 05/03/2009 21:17:05 »
I was asked by someone on the radio if the number he'd heard as the amount of power left over after transmission losses had been taken into account - 30% - was realistic. I answered that 60% transmission losses sounds very unlikely and that since the power station is a heat engine and is therefore only about 30% efficient anyway, perhaps that's where he got that figure.

But does anyone have any figures for exactly how much energy we lose in transmission across the grid, and some accurate figures for power station efficiency?

Chris

#### Vern

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##### How much power is lost in transmission cables?
« Reply #1 on: 05/03/2009 21:56:28 »
This Wikki article has the losses at about 8%.  I'm surprised that the article shows the UK losses to be greater than in the US. The reason for the 50 cycle power in the UK was to provide more efficient distribution. Theoretically 60 cycle distribution should suffer more radiation losses due to the higher frequency.

Losses

Transmitting electricity at high voltage reduces the fraction of energy lost to Joule heating. For a given amount of power, a higher voltage reduces the current and thus the resistive losses in the conductor. For example, raising the voltage by a factor of 10 reduces the current by a corresponding factor of 10 and therefore the I^2R\,\! losses by a factor of 100, provided the same sized conductors are used in both cases. Even if the conductor size is reduced x10 to match the lower current the I^2R\,\! losses are still reduced x10. Long distance transmission is typically done with overhead lines at voltages of 115 to 1,200 kV. At extremely high voltages, more than 2,000 kV between conductor and ground, corona discharge losses are so large that they can offset the lower resistance loss in the line conductors.

Transmission and distribution losses in the USA were estimated at 7.2% in 1995 [2], and in the UK at 7.4% in 1998. [3]
« Last Edit: 06/03/2009 04:57:55 by Vern »

#### lyner

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##### How much power is lost in transmission cables?
« Reply #2 on: 05/03/2009 23:00:28 »
As well as radiation losses, there is the greater problem of Power Factor penalty due to cable capacitance at 60Hz compared with 50Hz.

#### chris

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##### How much power is lost in transmission cables?
« Reply #3 on: 06/03/2009 11:45:31 »
SC - can you explain that a bit more - I don't understand.

Chris

#### Vern

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##### How much power is lost in transmission cables?
« Reply #4 on: 06/03/2009 12:06:42 »
Non linear loads such as induction motors can cause the voltage and current to get slightly out of phase. When peak voltage happens at a different time than peak current, there is Power-Factor loss.

Quote from: Wikki
In a purely resistive AC circuit, voltage and current waveforms are in step (or in phase), changing polarity at the same instant in each cycle. Where reactive loads are present, such as with capacitors or inductors, energy storage in the loads result in a time difference between the current and voltage waveforms. This stored energy returns to the source and is not available to do work at the load. Thus, a circuit with a low power factor will have higher currents to transfer a given quantity of real power than a circuit with a high power factor. A linear load does not change the shape of the waveform of the current, but may change the relative timing (phase) between voltage and current.
« Last Edit: 06/03/2009 12:08:57 by Vern »

#### syhprum

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##### How much power is lost in transmission cables?
« Reply #5 on: 06/03/2009 20:30:45 »
We keep French industry running by sending them power via DC cables under the English channel.

#### lyner

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##### How much power is lost in transmission cables?
« Reply #6 on: 07/03/2009 09:50:06 »
Verne: The load does not need to be non linear. It just needs to be reactive. This may be an inductive (a big motor) or capacitive (as with long transmission lines).
When volts (V) and current (I) are out of phase by angle theta, the effective power transmitted is
P = V I Cos(theta)
This means that higher voltages and higher currents are needed to transmit a given power if theta is not zero.
This is a reason why it is worth all the losses in converting to Dc and back for long transmission lines.
Another reason for the channel links using DC is that the two ac systems do not need to be synchronized.

#### Vern

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##### How much power is lost in transmission cables?
« Reply #7 on: 07/03/2009 12:59:34 »
Yes; I agree on the reactive losses.

I didn't realize the channel link was DC; that was a good move since we now have the technology to convert lots of power back and forth between AC and DC.

#### syhprum

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##### How much power is lost in transmission cables?
« Reply #8 on: 07/03/2009 14:50:18 »
They started of with Mercury arc rectifiers but now they have gone over to more modern semiconductor devices.
The voltage is a quite modest 200 Kv but larger installations go up to 1 Mv.

#### Vern

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##### How much power is lost in transmission cables?
« Reply #9 on: 07/03/2009 15:21:44 »
Maybe we should consider DC for the new link to the new "green" power sources in the western US deserts and badlands. I think I'll email that suggestion to the powers that be.

#### chris

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##### How much power is lost in transmission cables?
« Reply #10 on: 07/03/2009 16:34:44 »
The sub-sea cables need to be DC because otherwise the energy lost to moving dissolved ions around, owing to the changing electric field, would be sufficient to render the cable useless.

Chris

#### syhprum

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##### How much power is lost in transmission cables?
« Reply #11 on: 07/03/2009 16:59:19 »
Chris

The cables are coaxial, no electrical field escapes.

#### Bored chemist

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##### How much power is lost in transmission cables?
« Reply #12 on: 07/03/2009 17:14:29 »
While the lower losses (and thinner insulation) are benefits from using DC transmission, I think the major reason that the cable is DC is that France uses 60Hz and the UK uses 50Hz.

A straight AC connection would be impossible.

The fact that the cable is under water has nothing to do with it- you could easilly use a coaxial cable which doesn't have much of a radiation field.

Incidentally, I think that theFrench generally send us power rather than the other way round but I may be mistaken. It's certainly a two way link.

#### lyner

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##### How much power is lost in transmission cables?
« Reply #13 on: 07/03/2009 18:50:49 »
Quote
I think the major reason that the cable is DC is that France uses 60Hz and the UK uses 50Hz.
Of course they don't. The UK and their mates are the ones with 60Hz.

#### syhprum

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##### How much power is lost in transmission cables?
« Reply #14 on: 07/03/2009 20:34:33 »
The UK and virtually all of Europe use 50Hz, It is just a little jingoistic joke that if a trawler breaks the cable France grinds to a halt (the circuit was only 200MW last time I checked)
Correction

The power is now 2000MW and the voltage plus and minus 270Kv (540Kv total)
« Last Edit: 08/03/2009 21:52:31 by syhprum »

#### Bored chemist

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##### How much power is lost in transmission cables?
« Reply #15 on: 08/03/2009 10:55:24 »
OK, I messed up. Our French friends also use 50 Hz, but phase syncronisation would still make things more difficult.
The thickness of the insulation you need for an AC cable is rather higher and I think that may be a significant factor.

#### erickejah

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##### How much power is lost in transmission cables?
« Reply #16 on: 08/03/2009 21:38:39 »
What is the DC voltage being send through the(or those) coaxial(s) cable(s)?

#### lyner

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##### How much power is lost in transmission cables?
« Reply #17 on: 09/03/2009 15:15:00 »
270kV, apparently (Wikkers)

The phase synchronisation is, indeed, a serious problem - particularly during times when the load is a lot higher on one side than the other. It would require an impractical amount of effort to keep them in sync and, unles they were always in sync, it would take far to long to get them in step when you wanted them connected.

#### The Naked Scientists Forum

##### How much power is lost in transmission cables?
« Reply #17 on: 09/03/2009 15:15:00 »