Transmission line energy loss/length.

[Vic Sandler]

Here are some figures from this article.
Wiki: Electric Power Transmission

For example, a 100 mile 765 kV line carrying 1000 MW of energy can have losses of 1.1% to 0.5%

Unless I made a mistake, that would be approximately 100W to 200W loss per foot.

Transmission and distribution losses in the USA were estimated at 6.6% in 1997 and 6.5% in 2007.

That's some 6 to 13 times as much as the percentage loss in the example above, but it doesn't tell me what is the line length or energy transmitted. Does anyone know what is the number of Watts lost per foot (or the same thing in any other units) for typical real transmission lines?

 

[meBigGuy]

I get different numbers. 1% of 1000MW is 10MW and 100 miles is 528000 feet. More like 20W per foot.

Also, it is 1000MW of POWER.

 

[Vic Sandler]

You're right. It's because I entered 10GW instead of 1GW in my calculator and didn't check the result. But is 20 Watts a typical real world number? It uses a figure of 1.1% for the power loss instead of the average 6.5%.

 

[jim hardy]

There's heat loss, corona loss,,,,

and at the end of the line there's probably transformers and lights for the switchyard if you want to count them in.

Rule of thumb: Any individual line might lose ~3% when fully loaded

A search on "utility transmission line loss" turns up several industry papers.
http://large.stanford.edu/courses/2010/ph240/harting1/

http://www.aep.com/about/transmission/docs/transmission-facts.pdf

 

[Vic Sandler]

Rule of thumb: Any individual line might lose ~3% when fully loaded

The wiki link I provided said 6.5% and the article you linked to said 6.8%. The 3% figure you a referring seems to be just the resistance loss, or just the corona loss. But none of this answers my question.

 

[jim hardy]

The wiki link I provided said 6.5% and the article you linked to said 6.8%. The 3% figure you a referring seems to be just the resistance loss, or just the corona loss. But none of this answers my question.

I take it the question was:

Does anyone know what is the number of Watts lost per foot (or the same thing in any other units) for typical real transmission lines?

from the Stanford.edu link above,

Measured Values

In a paper from the American Electric Power (AEP) company published in 1969, the authors make an estimate that the amount of power loss from non-corona based effects is about 4MW over 100 miles in a 1GW transmission system. [7] Converting to metric units, this gives a loss of about 25MW or 2.5% over a 1000km transmission line. This number is consistent with the resistive loss given in a contemporary, self-published report from the AEP. [11] In this report, the resistive loss was listed as between 3.1MW/100 miles and 4.4MW/100 miles, depending on the wiring configuration. This corresponds to between a 1.9% and 2.8% power loss over 1000km.

Corona Loss

Corona loss is the other major type of power loss in transmission lines. Essentially, corona loss is caused by the ionization of air molecules near the transmission line conductors. These coronas do not spark across lines, but rather carry current (hence the loss) in the air along the wire. Corona discharge in transmission lines can lead to hissing/cackling noises, a glow, and the smell of ozone (generated from the breakdown and recombination of O2 molecules). The color and distribution of this glow depends on the phrase of the AC signal at any given moment in time. Positive coronas are smooth and blue in color, while negative coronas are red and spotty. [5] Corona loss only occurs when the line to line voltage exceeds the corona threshold. Unlike resistive loss which where amount of power lost was a fixed percentage of input, the percentage of power lost due to corona is a function of the signal's voltage. Corona discharge power losses are also highly dependent on the weather and temperature.

4mw/100 miles sounds like ~7.57 watts/foot. Remember there's three wires.
Perhaps there's a genuine power systems guy somewhere on the forum who'd have a better suggestion.

 

[Vic Sandler]

The problem with the 7.5 Watts per foot figure that you calculated is that it was for a configuration in which the loss was roughly 2.5%. I also calculated the loss per foot for a configuration given in the wiki article. However, from both articles we know that the average loss is 6.5%. The problem with the 6.5% figure is that we don't know the configuration. It is easy to get the loss per foot for an example configuration, but what is the loss per foot for a typical (6.5% loss) configuration.

To give a concrete example of what I mean, take these figures from the Stanford link:

4MW (loss) over 100 miles in a 1GW transmission system.

That's .4% loss. Since the average loss is 6.5%, this is not a typical situation. 6.4/.4 = 16 so I figure that there would be 6.4% loss over 1600 miles in a 1GW transmission system. That would then give 7.5 Watts loss per foot and also give a typical 6.4% loss. However, is 1600 miles a typical length in real world situations? Is 1GW a typical load?

 

[jim hardy]

From that Wiki article:

Transmission and distribution losses in the USA were estimated at 6.6% in 1997[10] and 6.5% in 2007.[10] In general, losses are estimated from the discrepancy between power produced (as reported by power plants) and power sold to end customers; the difference between what is produced and what is consumed constitute transmission and distribution losses, assuming no theft of utility occurs.

As your Wiki article mentions , losses are a lot less at high voltage.

From that AEP article , page 4 :
http://www.aep.com/about/transmission/docs/transmission-facts.pdf

LINE LOSSES - MW/100 MILES
sorry about the columnization - lost when copy&paste
Resistive Corona* Total
765 kV LINE @1000 MW LOAD: --------- ------- -----------
Original 4-conductor (“Rail”) bundle 4.4 6.4 10.8 ( 1.1%)
Newer 4-conductor (“Dipper”) bundle 3.3 3.7 7.0 (0.7%)
Current 6-conductor (“Tern”) bundle 3.4 2.3 5.7 (0.6%)
Planned 6-trapezoidal cond. (“Kettle”) bundle 3.1 2.3 5.4 (0.5%)

500 kV LINE @1000 MW LOAD:
Typical 2-conductor bundle 11.0 1.6 12.6 (1.3%)

345 kV LINE @1000 MW LOAD:
Typical 2-conductor bundle 41.9 0.6 42.5 (4.2%)

In between the power plant and the customer are switchyards, transformers and lots of lower voltage distribution lines. You can't ascribe all the 6% to the high voltage lines.
So there's no "One number fits all" for transmission lines.

However, is 1600 miles a typical length in real world situations? Is 1GW a typical load?

And no, power plants are situated close to their intended loads. While the whole US is interconnected most power travels less than a few hundred miles from plant to consumer.
Sixteen hundred miles is a LONG transmission line. A quarter wavelength at 60hz is what, 775 miles? When a line approaches that length it starts acting like an antenna. You don't want your power radiating off into space.
Longest one I know of personally is the 500KV line that brings coal power from Southern Company's plants in Alabama and Georgia to South Florida. It's probably 350 miles. When you drive alongside it on US 27 you'll see every few miles two of the wires swap positions on the pole to reduce antenna effects. That's called transposing, it effectively makes them a twisted pair just like in audio work.

1 GW sounds a lot for one line.
The plant where I worked was ~2.2 gw, which is comparable to US side of Niagara Falls.
Power left us on three lines and was mostly consumed within 250 miles.
When long lines are highly loaded you start having problems from inertia effects - the rotating inertias at opposite ends can begin harmonic torsional oscillations between one another.So one GW isn't an inordinate load . But moving that much power over more than a very few hundred miles while not unheard of is not commonplace.

I'm afraid that's the best answer I can offer. Maybe there's some genuine power guys on board.