Cable Temperature

Why not provide a link?

Also, If you are going to measure the DC resistance of a cable you are presumably going to do it at a time when there is no (significant) AC current flowing in it, so it is likely to be close to ambient temperature (commonly taken as 20°C).

On the other hand, the current-carrying capacity of a a cable will be worst-case conditions when it is hot, so it is logical to specify the resistance when hot.

What did <...the IEC cable catalogue...> publisher say during the telephone calls made on this topic?

The publisher spoke in French and the poster never understood a word he said, so he asked here, Merci pour votre appel

For XLPE and HR PVC insulated cables, the recommended max operating temperature is 90degC. This explains why AC resistance @ 90 degreesC.

Can I understand, when the tabulated current ampacity for the particular cable flows through the cable, temperature will be within 90 degree celcius?

But how to find the time limit for the cable before which the temperature of the cable reaches up to 250 degree celcius during short circuit

The maximum current ratings of cables depend upon the ambient temperature and the installation arrangements of each cable and its neighbours where they cross and also, particularly, run parallel. The time limit for the cable in the installation arrangement can be calculated using the applicable national electrical code, and the circuit protective device(s) can then be chosen to suit, giving a cable that is fully protected when installed in accordance with that code.

A full protocol for working all this out is given in British Standard 7671, as an example of one nation's electrical standard; other standards are applicable in other jurisdictions.

If in doubt, consult a qualified Electrical Engineer.

The catalog provides a formula for SC withstand. If the required duration is less, the cable can withstand higher magnitude of SC current.

It follows the relation 'Isquaredxt' is constant. That is, for a reduction in current, the increase in SC duration would be substantial (exponential).

The time to reach 250'C from 90'C maximum working temperature is found by assuming the cable conductor loses no heat during short circuit but all current² x resistance heating is absorbed by the mass x specific heat capacity of the cable [this is called adiabatic heating]. This calculation must take into account the initial resistance @ 90'C & increase in resistance of the cable as its temperature rises.

BS7671:2018 clause 434.5.2 gives formula t = k²*S²/I² where t = seconds for temp to rise from rated continuous current value to maximum short-circuit value: S = cross-section of conductor in square millimetres: I is rms AC fault current in amperes: k is coefficient according to material and initial & final temperatures. For 90'C rated thermosetting insulation & final temperature 250'C with standard copper conductor, k is given as 143 in table 43.1

As an example, this is a graph of short circuit withstand times for various mm² copper PVC insulated 70'C rated cables compared to fuse maximum operating times......Note that, with this fuse protection, the danger for the cable comes if short-circuit current is too low - maybe if you over-estimate short-circuit current with no margin on cable withstand time.

Your local regulations may give different rules, so this is just an example from UK regulations.

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