This discussion is locked.
You cannot post a reply to this discussion. If you have a question start a new discussion

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.
  • The temperature of the c.p.c. isn't always taken to be the live conductor temperature - where it's not incorporated into the same cable, or bunched with the same, it's taken to be ambient temperature (30 degrees). It's all incorporated into the "k" value. E.g. check tables 54.2 vs 54.3.


    There is a formula for calculating "k" for various initial and final temperatures (together with lots of other factors - e.g. the heat capacity of the conductor's material) - I think it's in one of the guidance notes or commentaries - but my memory isn't what is was and I'll have to search it out (unless someone else here has it to hand).


    BS 7671 does seem to like using the maximum permitted conductor operating temperature rather than the actual (design) temperature - e.g. see the NOTEs to table 41.2 etc - I have challenged this but they seem to persist in that view - perhaps it's just to guard against someone increasing the load at a later date and just presuming the c.p.c. size etc is OK. So while using something closer to the (lower) actual temperature is an interesting academic exercise, you'd got to question whether the results would satisfy BS 7671 requirements.


       - Andy.
  • An interesting question!


    The CPC itself shouldn't be carrying any significant current, but it may be warmed by virtue of being snuggled between a couple of live conductors (T&E) or in the same cozy conduit, or it could be cool by virtue of being the conduit itself or armour.


    I'd stick with the "adiabatic" as in BS 7671. The rest is above my pay grade. ?
  • It may help to realise that  12t has the same units as Joules per ohm you are just looking at the heating in joules of a given mass of copper - the 12t *R/heat capacity.

    Clearly a colder start either leads to a colder final temp, or allows a bigger energy dissipation. The problem, as alluded above, is that you do not really know the start temp - or at least the reg writers do not, so they assume worst case. However, if you know better for your specific case then you can make use of the extra margin.

    I suggest if you do you also leave a copy of the sums next to the layout diagrams, or for ever after each inspector who sees it will try and fail it.


  • Thanks All.


    In my case I wasn't looking at CPC sizing - just to confrm if the cable was adequately protected by the MCB based on an energy let-through basis (reg 434.5.2)


    I would be interested to see the alternative calcuation methods for the k value, or any other method of adjusting for a lower starting temperature if anyone has these.


    Jason.
  • If it helps at all I've taken this from Paul Cook's Commentary on the IEE Wiring Regulations 16th Ed (OK I know it's old, but the underlying physics won't have changed)


    k = √ ( (σc ( β + 20 ) x 10 -12) / ρ20 ) ln ( (θf + β) / (θi + β) ) )


    (hopefully I've got the brackets right)


    Where σc is the volumetric specific heat capacity of the conductor at 20°C. (e.g. 3.45 x 106 J/Km3for copper)

    β is the reciprocal of temperature coefficient of resistance of the conductor at 0°C (e.g. 234.5 K for copper)

    ρ20 is the electrical resistivity of the conductor at 20°C (e.g. 1.7241 x 10-8 Ωm for copper)

    θf is the final temperature (°C)

    θi is the initial temperature (°C)

    ln is the natural logarithm (loge)

      - Andy.


    (edited to try and get my Greek letters correct)
  • 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
  • I am not sure what finishing temperature is permissible.

    The last rows of tables 54.2 or 54.3 might be a reasonable starting point - i.e. 160°C for thermoplastic (e.g. PVC) insulation, 250°C for thermosetting (e.g. XLPE) insulation.

      - Andy.
  • here is a spreadsheet

    Looks good - at least it seems to reproduce 143 and 176 (rounded off) when I plug in the values for 30/160 degrees and 30/250 degrees - so it agrees with BS 7671 table 54.2 for copper.


       - Andy.
  • Thanks chaps - excellent work and very interesting!


    I knew I could rely on the greater minds than mine on here to come up with the answer!


    Jason.