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Adiabatic Equation - different starting temperature

I have recetly had to do some calcs with the adiabatic equation, and this got me wondering on the following:


As-written, this assumes an initial conductor temperature of the max operating temp of the condictor for that cable type, so for a 90 degree Thermoplastic cable it's 90 degrees.  This is clearly a worst case scenario for a heavily loaded cable bit in most cases cables are operating at much lower temperatures than that.  In my use-case, the design current was approx 0.6A, so the cable is likely to be barely above ambient, so there would be a good 60 degrees of additional 'headroom' for an energy let-thorugh before hitting the stated final temperature for the cable type.

Has anyone expanded this calcuation to account for this?  If you were just the wrong side of the line and needed some 'help'  then this could maybe do it for you.  It could be a bit complicated though - factors that occur to me are:

 



  • You would need to know what the worst-case operating temp of the conductor is under the design current - and this could be raised at a point where it passed through some insulation

  • Then you would need to work in the specific heat capcity of the conductor material and the heat losses through the insulation and sheathing (although these could probably be neglected for a short duration fault).

  • That would then allow you to calcualte the energy (in Joules) needed to raise the conductor temp from operating temp to max temp

  • Then work that back to give you the I2t figure equivalent.


Anyone seen this done or worked it through?


This is just an interesting thought experiment for me....I didn't need the headroom in my example, and arguably if you are that close then you should probably go up a conductor size anyway....


Jason.
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  • If Andy has got his brackets in the correct place (I am sure that he has) and I have transcribed them correctly, here is a spreadsheet which shows the effect upon k² and assuming that S, t and I are constant, I²t.


    The choice of starting temperature could be anything between the nominal ambient, 30°C (no load)  and 70°C/90°C (full load) but I am not sure what finishing temperature is permissible.


    Enjoy!

    Adiabatic.xlsx
Reply
  • If Andy has got his brackets in the correct place (I am sure that he has) and I have transcribed them correctly, here is a spreadsheet which shows the effect upon k² and assuming that S, t and I are constant, I²t.


    The choice of starting temperature could be anything between the nominal ambient, 30°C (no load)  and 70°C/90°C (full load) but I am not sure what finishing temperature is permissible.


    Enjoy!

    Adiabatic.xlsx
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