Formula to figure out the cooling time required for xformer loaded above nameplate?

[tortuga]

To all you EE's out here:
I am doing a little research on transformer loading above nameplate rating.
I am looking for formulas to figure out the cooling time required for xformer loaded above nameplate.

In this interesting thread i stumbled across a interesting quote :
http://forums.mikeholt.com/showthread.php?t=128639&highlight=mount+overload

Heat build up is what causes all transformers to fail (excluding short circuits). Theoretically, you could overload a transformer by 200% for 12 hours then turn it off for 12 hours, and it would last for its normal life expectancy. In reality it takes longer for a transformer to cool down then it does to heat up, so the period of loading would more likely be 200% for 8 hours followed by <50% load for 16 hours. There are formulas to figure out the amount of cooling time required based the ambient temperature and the actual loading profile.

I am wondering where I find some of these formulas?

(I have checked through some MFR data sheets, and looked through several manufacturers specs on sizing transformers and found some interesting stuff short of a formula.
I have glanced at a few dusty engineering text books as well.)

I found an article here however it is $225.
Thanks in advance for any formulas,tips, links or ideas etc.

 

[weressl]

To all you EE's out here:
I am doing a little research on transformer loading above nameplate rating.
I am looking for formulas to figure out the cooling time required for xformer loaded above nameplate.

In this interesting thread i stumbled across a interesting quote :
http://forums.mikeholt.com/showthread.php?t=128639&highlight=mount+overload



I am wondering where I find some of these formulas?

(I have checked through some MFR data sheets, and looked through several manufacturers specs on sizing transformers and found some interesting stuff short of a formula.
I have glanced at a few dusty engineering text books as well.)

I found an article here however it is $225.
Thanks in advance for any formulas,tips, links or ideas etc.

The theory proposed in the quote is faulty. If that would be the case, we can overload the transformer to any limit and just by resting it for the same time period no shortening to it's life expectancy would occur. Two things are to keep in mind: heat is generated by I^2*t, and that thermal damage is irreversible.

The only rule of thumb I recall is that every 10 Centigrade temperature rise the remaining insulation life is halved. So if you have a 40 year life expectancy of the insualtion, a 10C rise would result in 20 years life expectancy and a 20C would result in 10 years and a 30C in 5 years remaining and so on. Even though this rule of thumb is incomplete as it does not talk about the length of time the overload/temperature is sustained, it is the closest to any useful information I've ever seen or heard of. I also heard this to be aplied to cable overloading.

 

[texie]

I'm no transformer expert, but it seem to me that there would be vast differences between oil/liquid cooled, cast coil, etc.

 

[don_resqcapt19]

The theory proposed in the quote is faulty. If that would be the case, we can overload the transformer to any limit and just by resting it for the same time period no shortening to it's life expectancy would occur. Two things are to keep in mind: heat is generated by I^2*t, and that thermal damage is irreversible.

The only rule of thumb I recall is that every 10 Centigrade temperature rise the remaining insulation life is halved. So if you have a 40 year life expectancy of the insualtion, a 10C rise would result in 20 years life expectancy and a 20C would result in 10 years and a 30C in 5 years remaining and so on. Even though this rule of thumb is incomplete as it does not talk about the length of time the overload/temperature is sustained, it is the closest to any useful information I've ever seen or heard of. I also heard this to be aplied to cable overloading.

What is that 10 degree rise based on? Is it over the stated maximum design temperature or some other value?

 

[Hv&Lv]

That would be a complicated algorithm with all the variables involved... How about some pretty charts instead?
http://www.usbr.gov/power/data/fist/fist1_5/vol1-5.pdf

 

[jim dungar]

The theory proposed in the quote is faulty.

No it is not.
It was correct for the post in which it was given.

For those looking for the math, I suggest IEEE STD C57.96-1999, IEEE Guide for Loading Dry-Type Distribution and Power Transformers.

An outline of methods that may be used to determine short-time loads with no sacrifice of life expectancy is given in 3.2. Methods for determining constant loads and short-time loads with moderate sacrifice of life are given in Clause 4. All the methods given in the preceding clauses are based on the equations, assumptions, and empirical data presented here, which give results that are of the right order of magnitude and that are in general agreement with tests and data from several independent sources.

 

[mike_kilroy]

I will post two formulas that show how to calculate this tomorrow when I get access to office. the theory is such that they work for any device with a thermal time constant. there are 2 parts to this question: 1) rms equiv load & 2) thermal time constant temp rise.

If one just concentrate on 1) they can get into wrongly quoting a comment like Jim's: of course if u load to 200% for 10 hours & then 0% for 10 hours, the rms equiv load is 100% - BUT if the device's thermal time constant is 16 minutes, it reached max temp in probably 12 minutes and continued heating until it melted down in 25 minutes. So without watching BOTH equations, you will get wrong answer.

1) is just Jim's thing for rms: Xrms=[(t1*X1^2+t2*X2^2+...+tn*Xn^2)/(t1+t2+...+tn)]^.5

2) is like Xmax_temp=Xrated*e(-1/t) something (need my book to copy it down

 

[jim dungar]

I will post two formulas that show how to calculate this tomorrow when I get access to office. the theory is such that they work for any device with a thermal time constant. there are 2 parts to this question: 1) rms equiv load & 2) thermal time constant temp rise.

It is all about heat buildup leading to insulation degradation.
Don't forget the impact of ambient temperatures (during overload and during cool down period) and of the heat transfer characteristics of the cooling medium (i.e. forced air cooling).

 

[weressl]

What is that 10 degree rise based on? Is it over the stated maximum design temperature or some other value?

The ROT comes from the insulation material manufacturers data. The reference or base temperature is the maximum recommended operating temperature for the insulation class.

 

[petersonra]

You can always turn a fan on the xfmr while it is overloaded. I have been told by several xfmr manufacturers that just a floor fan blowing on a machine tool xfmr will give you as much as 25% extra capacity without damaging the xfmr any.

I have seen a chart on the subject of heat versus xfmr life on one of the manufacturer's web sites. you might wan to just call their tech support number. they are pretty good at putting their hands on this kind of ifor IME.

 

[zog]

The concern is not so much the tempature but the difference between the core tempature and ambient, or the inside and outside of the windings. The difference in expansion rates from a high delta T is what causes the most damage if I recall.

 

[weressl]

The concern is not so much the tempature but the difference between the core tempature and ambient, or the inside and outside of the windings. The difference in expansion rates from a high delta T is what causes the most damage if I recall.

The concern IS the temperature, that is what causes damage to the insualtion material. The rate of rise does not cause concern except under short circuit conditions.

 

[Hv&Lv]

I can see where the formulas would work for indoor transformers, where the ambient could be controlled in some way, whether by static temperature,fans or water. Outside transformers would be almost impossible to calculate without assumptions that would invariably be wrong.

 

[mike_kilroy]

What is that 10 degree rise based on? Is it over the stated maximum design temperature or some other value?

Just google "10 degree C insulation life rule of thumb" and you will see this. it comes up with a zillion references to it. works as a rule of thumb for any device that gets hot.....

I apologize for delay in posting the formulas we used to use all the time for rms overload and max temp one shot rise (based on ambient of course) formulas.... it has been very hectic here this week with our HSUS animal rescue work (was in national news) and now largest Hamfest in the world starting tomorrow thru the weekend here in Dayton. I will get to my books and post formulas and explainations of them 'soon.' AC8V.

 

[zog]

The concern IS the temperature, that is what causes damage to the insualtion material. The rate of rise does not cause concern except under short circuit conditions.

I didn't say rate of rise, I said the difference between core and ambient, or the "max rise" limit. The higher the differential becomes the larger the difference in expansion from the inside of the winding is to the expansion on the outside of the winding, almost like compressing the winding, which can damage the insulation.

The max tempature is important too but usually the max rise is the limiting factor.

 

[weressl]

I didn't say rate of rise, I said the difference between core and ambient, or the "max rise" limit. The higher the differential becomes the larger the difference in expansion from the inside of the winding is to the expansion on the outside of the winding, almost like compressing the winding, which can damage the insulation.

The max tempature is important too but usually the max rise is the limiting factor.

You did not 'say' "rate of rise", but that is what causes the temperature differential.