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March 05, 2010

Transmission Line Losses

By: Aaron Datesman

I enjoyed the comments attached to this recent post about wind-to-hydrogen renewable energy. Some of the discussion involved losses on power transmission lines. I would like to elevate my response up to a blog post since, although this is sort of a dry topic, understanding it is actually somewhat important.

Partly due to history, and partly due to physics, the US electrical transmission grid is actually rather localized. The electrical energy we use is generated pretty near where we use it (also, pretty much just before we use it). This is a big problem if you propose to harvest energy in one place where it is abundant (for instance, via concentrated solar in Arizona, or via wind turbines in North Dakota) for use someplace else far away.

The historical portion of this surprising fact, I think, has to do with how the electric power industry evolved in the early 1900’s - generally as municipal utilities, many publicly owned. The physics contribution has to do mainly with transmission losses.

Now it’s not hard to dredge up the figure that transmission losses account for about 10% of the electrical energy generated in the US - that is, out of every 10W of power generated, we lose 1W getting that power to where it’s put to use. Because we use a lot of power, this represents a huge waste, but measured as a calculation of efficiency it’s pretty good - that’s 90%.

The more I think about this number, however, the more I hate it. The figure is remarkably deceptive. This is true because what it really measures is not efficiency; instead, it measures the total system losses measured against the total system generation. This provides no guidance about what the losses would be like if the distribution system were different - for instance, if it incorporated longer transmission lines. A useful figure would normalize to line length and utilized line capacity.

That’s complex-sounding but means something simple. From my desk at work, I can walk to a 150MW natural gas-fired power plant. It provides power to the Laboratory facilities, all of which lie within a radius of about one mile. Because the transmission distance is quite short, the transmission losses in this case are very small (<1%). Let's say that they are 0.5%, or 0.75MW.

Someplace in Nebraska or some other sparsely-populated state, however, there is certainly a small town or some energy-consuming facility which lies a great distance (say ~50 miles) from a power-generating facility. Maybe it uses 100kW of power. Due to the distance, the transmission losses in this case are quite large (I will estimate 35%, which is representative of the calculation coming up).

In aggregate, the example system comprised of Argonne National Laboratory plus a factory in Nebraska refining corn syrup suffers transmission losses of 785kW, or 0.52%. America is like this. The transmission efficiency looks high (losses of only 10%) because most of the power we use (normalized to capacity) travels only short distances (normalized to length). This does not mean that line losses per distance are low. Mostly it means that the lines are short - not at all adequate to carry power from North Dakota to someplace useful.

So, this is a nice, simple explanation, but is it true? To test it, this site has a useful model of an electrical distribution network. There is a little bit of math ahead, which I only include because I think some readers will like it.

Following the diagram and the text below it, Ohio Edison operates 5757MW of electrical power generation (let’s call it 6000MW). The source voltage is 18kV; this gives 300,000A of current in the generating facilities (rounding for convenience).

The ratio of the step-up transformer to the transmission line is 350/18, which we’ll call 20. This means that the current in the transmission line is 300,000/20, or 15,000A. Current is stepped down in this manner in order to minimize transmission losses, but they cannot be eliminated.

In order to calculate the transmission losses, we’ll assume that the transmission cable used for this application has a resistance of around 0.1 Ohms per km of length. This is at the low end of the range (so the loss estimate will be low) according to a couple of spec sheets I looked at.

This yields (P=I^2R) 22.5MW lost power per km of length, or 0.4% per km. That’s 0.6% per mile, or 10% of the total energy lost over a transmission distance of just 18 miles. After 115 miles, only 50% of the power remains.

This is the basis of my opinion that you really do lose a lot in the transmission lines, which has serious implications for how one might design distribution networks incorporating renewable energy sources.

Oh, OOPS: I wrote this post late last night, and managed to convince myself of something that isn't true. The conclusion that the lost power per unit of length is 0.6% per mile of length is correct. I then took that number and compounded it (like interest) to find the total loss, like this: 0.994^N=0.9, where N is the length in miles, to find the distance corresponding to 10% loss.

Actually, it's simpler. Since the resistance increases at the same rate as the length (0.2Ohms for 2km, etc.), the loss just scales as length as well. So the benchmark comparisons actually are 17mi for 10% loss and 83mi for 50% loss. The overall point remains correct, but the specific numbers were wrong. I apologize for the error.

(What led me to over-think this question is the answer you get using this method to calculate the loss over, say, 300mi: 180%. Of course this is impossible - you can't lose more than you started with - from which I concluded that the physics actually should involve constant bites in percentage terms from a diminishing total. This is incorrect. When the line losses start to get pretty large, I think a slightly more complex analysis of the distribution network must be invoked. Since this doesn't alter the conclusion, which remains correct, I'll omit further explanation.)

— Aaron Datesman

Posted at March 5, 2010 01:12 AM

For long distance transmission, you want HVDC lines. Typical losses are about 3% per 1000km.

Posted by: Dunc at March 5, 2010 06:40 AM

Aaron, thanks for delving into the electrical energy issue so deeply. Your post today explains why it's less expensive to ship the coal by rail to the generating facility than it is to make the electricity at the coal mine. It also has a lot to do with the recent hype about very local fuel cell generation (the Bloom Box) - in addition to being run on a variety of energy sources, including those that are crop-based, which was the emphasis in the material I saw about it, it also minimizes transmission losses by being so close to the user.

Turning to larger issues:

a) Will carbon dioxide emissions, which are substantially involved in anthropogenic global warming, be regulated by a cap-and-trade or carbon tax or other international binding regime, in order to ameliorate (because it is already too late to prevent) further climate change? My guess is (and I am following the pessimism of the host at someassemblyrequired dot com, who aggregates news, some of which pertains to this) - not during the foreseeable future, however long that is. Fasten your seat belts.

b)And here's something to think about - and let me begin with an analogy from real life. A relative of mine received an inheritance from her parents and built a house. A few years after moving into it she lost her job, and took up another pursuit which might have replaced the income, seemed to her like it was always on the verge of doing so - but actually didn't. In order to stay in her house, which was in an upper-middle class neighborhood with rising property values, she refinanced the mortgage. And again. And again. And then --- foreclosure and bankruptcy. She is about to move into subsidized senior housing. She lived beyond her income for years - now she has to adjust to much more modest circumstances (let us not even mention that, as a recipient of subsidized housing, she is STILL living beyond her income).

We too are living beyond our energy income. We - i.e. the industrialized countries of the world - are drawing down the fossil fuel stores of the world, and all our ways of doing things imply a much larger throughput of energy than is sustainable - not only transportation and heating/cooling of living spaces, but manufacture, and particularly and most poignantly industrialized agriculture. Will it be possible to find a "glide path" down from where we are to a sustainable steady state? Or will we have a bumpier landing - maybe a very, very bumpy landing?

I don't know. Nobody knows. G-d only knows.

May the Creative Forces of the Universe stand beside us, and guide us, through the Night with the Light from Above (metaphorically speaking.)

Posted by: mistah charley, ph.d. at March 5, 2010 08:21 AM


You are a fine teacher and I'd say have great potential as a testifying expert (assuming no drooling problem or the like).

mistah charley, ph.d.

"Or will we have a bumpier landing - maybe a very, very bumpy landing? . . .I don't know. Nobody knows. G-d only knows."

A few weeks ago, while I was thinking about my wonderful late mother, who I was missing, I saw a picture on the web of the Andromeda galaxy taken from NASA's fancy WISE camera in orbit. It struck me as really beautiful, almost spiritual, though of course I was in that mood. Out on the plains, far away from the light created by cities, a person can see the Milky Way pretty well on a clear, dark night, and it's quite a sight. The stars that surround us form an illuminated haze that cuts across the whole sky, and it makes a person realize how important stars must once have been. You know, before television.

Unlike the Milky Way, the Andromeda galaxy captured in all its glory by WISE is barely visible to the naked eye even from a place like that where the stars show so much of themselves. Wikipedia says the Andromeda galaxy is 2.5 million light years away, and that it contains a trillion stars, which makes it more than twice as big as the Milky Way. I thought about that as I looked at that spectacular picture NASA was nice enough to provide. A trillion stars in that one beautiful galaxy, our neighbor among the galaxies, of which there are apparently a few hundred billion in the whole universe. (Ridiculous, isn't it?)

When I'm able, I reflect on that in an attempt to momentarily stop being so OCD about trying to understand if there is a way to prevent "the very, very bumpy landing" that looms ahead. For me, finding that kind of peace of mind has become a challenge, but it's pretty obvious from religion and literature that such challenges preceded climate change, just as they preceded the specter of nuclear holocaust. This is the human condition.

So I thank you for reminding me of the Creative Forces of the Universe that guide us with the Light from Above through the Night. That made me think of this. For a person like me at home in remote places which can feel as close to the heavens as anything on earth, your words don't even seem metaphorical.

Posted by: N E at March 5, 2010 10:47 AM

Be very wary of "bloom boxes" or other miracle cure energy sources that will be popping up in the news with exponential frequency in the next few years. As a mechanical engineer with a focus in alternative energy, I can tell you that there are no magic solutions just on the horizon. There are a handful of proven "renewable" energy resources (renewable because many of them incorporate natural gas and conventional sources into their production). Solar, wind, tidal, and geothermal are the big ones, with many smaller variations thereof. There are others that are still only in design stages. It is impossible for there to be a new energy source that no one has thought about yet, and will also be implementable in the near future. Energy consumption is a large pie, and there will have to be a lot of slices from many different areas to replace oil. It's very unlikely that they will be developed in time to avoid a very, very bumpy landing.

Posted by: Gordon Browning at March 5, 2010 12:53 PM

Be very wary of "bloom boxes" or other miracle cure energy sources that will be popping up in the news with exponential frequency in the next few years. As a mechanical engineer with a focus in alternative energy, I can tell you that there are no magic solutions just on the horizon. There are a handful of proven "renewable" energy resources (renewable because many of them incorporate natural gas and conventional sources into their production). Solar, wind, tidal, and geothermal are the big ones, with many smaller variations thereof. There are others that are still only in design stages. It is impossible for there to be a new energy source that no one has thought about yet, and will also be implementable in the near future. Energy consumption is a large pie, and there will have to be a lot of slices from many different areas to replace oil. It's very unlikely that they will be developed in time, even the commercially proven ones like solar, to avoid a very, very bumpy landing. This is a hard reality, but the sooner we get used to it the better. Major energy shortages will be a part of life in 1 year, not 10 or 20.

Posted by: Gordon Browning at March 5, 2010 12:56 PM

The Andromeda Galaxy image from the Wide-field Infrared Survey Explorer, or WISE, can be seen at tinyurl dot com slash ygnzkz5. My most glorious views of the stars were in the years I lived in Wise county, Virginia. Yesterday I was looking at the blog of someone I knew then, who still lives in the next county over. There was a quote from the Talmud:

"Do not be daunted by the enormity of the world's grief. Do justly, now. Love mercy, now. Walk humbly, now. You are not obligated to complete the work, but neither are you free to abandon it."

N E's comment reminded me of the Galaxy Song from Monty Python's The Meaning of Life, which can be seen at tinyurl dot com slash yfldg5m. And that reminded me of the film's deepest explanation of how to find life's meaning, "People are not wearing enough hats", tinyurl dot com slash 6qba8l.

Posted by: mistah charley, ph.d. at March 5, 2010 01:04 PM

The stars, the Talmud, synchronicitous cognates for acronyms, Monty Python, and hats---it doesn't get better than that!

Posted by: N E at March 5, 2010 03:04 PM

Hi Aaron. Your revised figures are not too far off for AC transmission, though it is possible to upgrade networks to get slightly lower losses per mile. (Basically if your line has higher peak capacity, so that normal transmission is a lower percent of that peak capacity, than your AC losses are a bit less.)

However the major point is that if you are transmitting electricity long distances it is crazy to use AC. In that case use High Voltage Direct Current (HVDC) lines which lose about 3% of energy per 1,000 kilometers. In the U.S. massive use of wind would probably never require sending power more than 1,500 miles - which translates in a 7.25% loss. in addition you lose about 1.5% converting from AC to DC, and the same back. So your loss from DC transmission is 10.25%. You still have losses from local AC transmission and distribution of around 10%. So a DC electric system would have peak losses of 20.25%. If U.S. grid efficiency was upgraded to that of the western EU, that could be lowered to 15% to 17%. However a DC transmission system would distribute varying amounts of power, so average losses would be a bit less, simply because a lot of power would travel much shorter distances, mostly 500 miles or fewer. SO HVDC combined with an upgrade AC system used to support wind and other renewables would lose about 12% to 17% depending, with 17% being unrealistically high and 12% being unrealistically low.

Compare to Hydrogen. The best electrolyzers on the market run at about 85% efficiency. However they only work on distilled water, and you have to compress (and often chill) the hydrogen to store it. So net efficiency is about 81%. Most commercial fuels cells get 70% efficiency or worse. So we already have about 33% round trip loss. However we have to transport the hydrogen. Hydrogen is light, but is at one atmosphere it has much less power per cubic foot that natural gas. So at minimum to transport it via pipeline you have to compress it more than natural gas. Most proposals for hydrogen pipelines suggest liquefying it. So you are going to consume substantial energy transporting it.

There are very high priced pieces of equipment that can get better efficiency that this. But there are high price pieces of equipment that can get better results for electricity transmission too. The bottom line is that HVDC system integrated with AC will have much lower losses than any plausible hydrogen system with today's technology. And the capital costs for these lines are lower than for hydrogen pipelines too.

Posted by: Gar W. Lipow at March 5, 2010 05:59 PM

@ mistah charley, NE - Thanks for the compliments. I'm confident that they will ruin my life.

Regarding living beyond our energy income, I think I don't agree. It's not a snappy comparison, but what we're doing is more like shredding the paychecks we earn from a no-show job while spending our trust fund and tossing away matches on the rug when we light our bong.

The sun provides plenty of energy through light, wind, and tides. We could go a long way toward meeting even our wasteful current levels of consumption with renewables if we chose. These are the paychecks we're shredding.

The trust fund represents the fossil reserves. This isn't income, it's savings. It's what the sun gave us in the past.

The matches on the rug are the possibility or likelihood that the global warming feedbacks are large and positive. If they are, then we are coming really close to burning the house down.

(With drugs that we buy using trust fund money.)

But I think we could fix this, for instance by breaking up the agricultural monopolies, moving people back on to the land, and paying them handsomely for biochar production. And I also think we have the ideas necessary to start cashing the paychecks we shred and quit drawing down the trust fund.

Posted by: Aaron Datesman at March 5, 2010 06:08 PM

OK, sorry I missed you had discussed HVDC in comments in the other post.

To make up for that a bit, here is a link to a pdf of a recent study on transmission for increased wind. Although this study tops out at 30% of power from wind, this seems to imply to me that transmission can stabilize rather than destabilize the grid. Past a certain point we have to add storage, but transmission decreases the amount of storage needed, and storage is expensive.

Posted by: Gar Lipow at March 5, 2010 06:37 PM

Aaron - and everyone else. Thanks for the information. My concept of our energy grid is now more accurate.

Posted by: steve the artguy at March 5, 2010 09:02 PM

Aaron, Mistah Charley, N E, Gar Lipow - and all of you wonderful smart guys - I've learned so much the past few days about electricity and related stuff I fear my head may explode at any moment (but in a nice way). I promise not to make a mess. (And Aaron, I like your website too.)

This has been more than just educational for me - it has been encouraging... I especially like connecting the conversation back to metaphysics - that life is so much more than just facts and figures (at least sometimes) (although a nice figure can be nice) - a good story on a starry night is a special delight!

The most responsive chord to me in this latest thread is Aaron's analogy back to basics - that we could "break up the agricultural monopolies, move people back on to the land, and pay them handsomely for bio-char production."

I love it! (Of course we would have to reclaim much of the good land we've paved over, but it could be done...) (There isn't anything we can't do, etc.)

I'm struck by how (in the minds of so many) our future depends on figuring out ways to maintain the status quo without having to give up anything - as if "getting back to basics" is totally and entirely out of the question. Impossible! No one will ever do that!

But in fact, long term "getting back to basics" will trump, eventually, any technological breakthrough we discover that, for awhile at least, seems to be an "economical" substitute for fossil fuel and coal. For all the reasons you gentlemen know so well there will always be other costs and consequence for anything we do - which doesn't mean we don't do anything - but the sooner we get back to basics the better it will be (so my children and grandchildren won't be any more spoiled by cheap fuel then they already are).

Please keep up the good work Aaron and all of you, and thanks again Jonathan for hosting this inspirational and informative discussion. (If the web is going to help to save us, A Tiny Revolution will have done more than it's part - even if "Everyone Failed You" about your Coffee Party joke. (Sometimes you are just too smart) (for me).

Posted by: Grandpa Ken at March 6, 2010 10:46 AM

>"break up the agricultural monopolies, move people back on to the land, and pay them handsomely for bio-char production."

OK. Again, a switch to organic agriculture could play a major part in reducing emissions, and would be sustainable in other ways besides global warming. And biochar could play a modest role in that. But not as much as is sometimes assumed. Not all forms of biochar are stable. Some deteriorate and release their carbon fairly quickly. Not all forms of biochar increase soil fertility. Some actually can reduce plant growth. And there seems to be a tradeoff. The ones that are the best at storing carbon long term are worst in terms of helping agriculture. Also to some extent adding charcoal to the soil can reduce the ability to absorb other carbon. In spite of all this, managed carefully biochar is a net benefit. But it is not a magic bullet any more than any other single technology is.

Actually Aaron is right on in his larger point. We absolutely have the technologies to live sustainably now - to phase global warming emissions, to keep our freshwater use within the budget the earth provides, to build our homes without spewing pollution from cement factories or cutting down forests, to do everything we need and most of what we want non-destructively. But it is not going to happen without radical transformation in our social and economic system. As long as we pour capital investment into stupid wars, and bases to allow us the power to get into future stupid wars we are not going to invest where we need to invest. As long as we leave investments to banksters and derivatives traders rather than making a decision as a people to put money for critical infrastructure. Although even a tiny revolution would be nice, we don't necessarily have to wait for a revolution for the changes we need. But we damn well do need a mass movement that forces fundamental changes down the throats of corporate and government elites, that wins at least some degree of real democracy.

Posted by: Gar Lipow at March 6, 2010 01:05 PM

Gar Lipow

It's too bad it's so hard to get mass movements going nowadays. We don't seem to have any emergency brake, and maybe that could be one. But it takes time for mass movements to build, and they don't seem to start building until things are very bad for people on a day-to-day level. People collectively don't have a sense of consequences a decade from now, let alone a century from now.

I think the mass movement would help because elites are invested in perpetuating their "way of life" even if that way of life needs to end. Our government was structured by the Framers with the opposite problem in mind: stopping the mob (the people)from ending a good way of life. Elites think the world will end if the elite ends, and they are consequently able to justify enormous sacrificese to quash threats to the elite. that's the problem we now have. For me, the easiest place to see elite insanity is nuclear doctrine (Read the 1987 book To Win a Nuclear War: The Pentagon's Secret War Plans by Michio kaku and Daniel Axelrod to get an understanding of just how batshit crazy the ruling National Security elite was during the Cold War.) But I get the feeling from the scientists and economists and pollsters and statisticians that this insanity increasingly shows itself in many areas.

Posted by: N E at March 7, 2010 02:10 PM

@Gar - Can you give me some sources you've read on biochar? Some of the points you mention on this topic are new to me.

Posted by: Aaron Datesman at March 8, 2010 02:45 PM