# Why do power lines sag when they are heated up?

I was reading some information about the 2003 power blackout in the Northeastern US.

Beginning early in the afternoon of August 14, 2003 big transmission lines began to fail in First Energy's operating area, several because the utility had not kept up with tree-trimming, so that as heavily loaded lines heated up, they sagged into brush and shorted out. As one went down, the next would become too loaded, sag still more, and short, and so on. All that, the result of a serious infringement of operating standards and no small matter in its own right, would have remained a local problem if First Energy and the midwestern power regulator had quickly recognized what was going on and had promptly cut service to enough customers to keep the whole system from getting overloaded.

From "A Coal Power Ban Is a Necessity." Coal. Ed. Michael Logan. 5 Aug. 2010

What about overheating causes power lines to sag? I understand that increasing the load on the line will increase the line's temperature due to the resistance in the cables. Why does this increased heat cause the lines to sag though?

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I'm not sure why this merits two downvotes. If something about the question isn't a perfect fit for the Physics.SE community or needs improvement, I'm happy to fix it. –  nhinkle May 9 '11 at 17:13
Unfortunately, that "A Coal Power Ban Is a Necessity" link requires an Oregon State Univ ID code to access. –  nibot May 10 '11 at 16:15
@nibot, I just went and looked for a copy somewhere freely available but couldn't find any. I don't believe I would be permitted to upload a copy of it publicly. I'm sorry. –  nhinkle May 10 '11 at 16:30
It is apparently an excerpt from "Kicking the Carbon Habit: Global Warming and the Case for Renewable and Nuclear Energy" by William Sweet, 2006. –  nhinkle May 10 '11 at 16:34
It is interesting that kind of the opposite is the problem in winter. When huge ice buildup makes the lines too heavy to be carried by the towers, so that they fail. I didn't talk to somebody who is working exactly with this, but I would move a lot of reactive power over the lines to heat them up. Another interesting tidbit is that power lines can move more power in (reasonably) windy conditions, as the wind cools down the conductors. Funny stuff :-). –  Kurtovic Jul 13 at 12:16

The conductor material (copper, aluminum, whatever) expands when heated. When the temperature increases, the length of the power line between two towers increases due to thermal expansion, and the line sags because of the increased slack.

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Overhead high voltage lines are almost always Aluminium + a steel core. Copper is very expensive, corrodes and is mechanically weak. –  Martin Beckett Jan 25 '12 at 4:30
Although some utilities still have copper lines still in use from 70+ years ago. I don't think First Energy does though. –  ja72 Jan 30 '12 at 20:28
There is an additional mechanism of creep which is accelerated when heat up. So running at high temperatures for a few hours a day, may add up to a catastrophic failure in a few years. –  ja72 May 9 '14 at 20:24

There is thermal expansion of metals, and in a power line the length will become greater than the installation one. Gravity takes up the slack and lowers the lowest point of the line. The shape taken by suspended strings/cables with only their own weight is called a catenary, and the length depends on the constants of the solution ( alternative analysis in the catenary link).

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Besides the thermal expansion noted elsewhere (which is correct), heat causes a different kind of failure in power lines. Heat anneals the aluminum used, causing it to loose strength and eventually fail.

The standard cables used are called ACSR (Aluminum Conductor Steel Reinforced) and the strength of the cable is shared between the steel core and the aluminum strands. Above 93°C the aluminum used (AL1350-H19) looses its heat treatment and it's breaking strength goes down. Eventually with some extra wind, or other loading conditions it might fail. Possibly the lower strength lowers the resistance to fatigue and thus aeolian vibrations might make the cable fail. More reading here and here.

Also what happens sometimes is at the ends of the conductor there are connectors that carry the current and those may fail if operated at high temperatures (runaway heat condition) as their sealing compound inside "melts" away allowing for corrosion to enter in the the steel supports of the connectors.

These have sparked the need for high temperature conductors such as ACSS, ACCR and others. Southwire has some nice write up like here. Operating temperatures can be 120°C or over 200°C with some of the more exotic (and expensive) cables used today.

Also, high operating temperatures accelerate creep, which is a gradual expansion of the cable with time. As creep progresses the cable will sag more and it might impact a tree or structure (bad). The effect is not linear, and the higher the temperature creep moves much more quickly and can become the dominant effect of sag within a few years.

Maybe additionally the increased sag increases the swept area of the conductor (becomes longer between the supports) making it more susceptible to wind and ice loading.

PS. I used to work in the transmission line industry and your question is very welcome here.

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I haven't been on track what the industry does in the ice loading scenario. Are the ice levels monitored or modeled ("guessed") so that a quick response can come by increasing the reactive power (my guess) to increase the losses? I'm sorry that this is a question-comment, but I guess the answer will be short. –  Kurtovic Jul 13 at 12:30
There are US standards for wind and ice depending on location. On top of that there are additional safety factors in order to take into account other knowns. All loading factors end up as a lbs/ft value to be added to the weight of the cable. –  ja72 Jul 13 at 13:58
Some older information to be found in home.eng.iastate.edu/~jdm/wind/… –  ja72 Jul 13 at 14:03
Nice resource, it describes well what is going on mechanically for a lot of scenarios. The thing that I'm missing is the mitigation strategies for critical situations, like what to do from the power flow management point of view for the given power line. Particularly "can the ice laden doomed power line be saved by high losses", there is a hint to it in the ampacity chapter ..will be monitored continuously, as will local weather conditions..then the conductor may be rated at a higher ampacity during that time period. Thanks! –  Kurtovic Jul 13 at 15:25
The only thing you can try to control is the temperature of the conductor. When loaded with wind and ice sag increases and when the temperature goes it the sag increases further. So forestry control is important to maintain clearances, as well as making sure the tensions do not exceed the support limits. –  ja72 Jul 13 at 17:58

During summer due to heat, the intra molecular space increases and the substance expands. As the substance expands, the weight of the conductor increases resulting in the increased sag.

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This doesn't add anything new to the answer given by Keean –  gonenc Jul 13 at 11:56
The weight doesn't increase when it expands. No new mass is added for there to be an increase in weight. –  Jim Jul 13 at 13:20

## protected by Qmechanic♦Jul 13 at 13:00

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