Table 4D1A has cables that when reference method F is used starting at 25mm^2, I cannot find a suitable explanation as to why 25mm^2 single insulated cables are okay to use at this CSA and not any less.
If I used 25mm^2 cable from this table the insulation is still the same as a smaller cable from the same table.
is there any justification that when the cable gets to 25mm^2 it somehow becomes acceptable to use?
You are maybe thinking about it in slightly the wrong way - there is a limited amount of space in the regs for tables, and there are not experimental results available for all cables in all configurations - actually to do well it is quite hard to test a cable - slitting and resealing it it to add thermocouples and running many samples in a controlled environment at different currents.
It does not mean that you can only use cables in the tabulated types in the tabulated installation and routing methods, just that there is only guidance for a representative sub-set, that is the ones that have been repeatedly tested and agreed upon. Generally cable on trays is multicore in the smaller sizes but of course it does not have to be.
Of course when you do your own design you will have to decide how close to the edge you want to sail and if one installation method is close enough to another for your purposes. So if perhaps you wanted 16mm2 on a tray, you could probably use the figures for 16mm method C for example and add on a similar percentage as the equivalent ratio of methods C to F for 25mm2.
IS10101:2020 (the Irish Regs) is as per 7671 in this regard but provides table 52C as an example of simplification of the the requirements of Section 523, in particular regulation 523.2, which is much the same in both documents.
For reference method F single phase, 52C reads; 23, 31, 42, 54, 75, 100A for 1.5, 2.5, 4, 6, 10 and 16mm2 respectively and 19.5, 27, 36, 46, 63 and 85A for 3-phase.
There is no indication as to why 1.5 to 16mm2 is omitted from the comparable table to 4D1A in the Irish Regs but I reckon Mike is right, he usually is!
In effect you are using the change in resistance of the cable over temperature, and I'd caution that it is indeed easy if you do not mind being 10- 20% out with the deduced temperature rise;-)
First you assume uniform current distribution and heating, which will be fine in small diameter cables, but you also assume the temperature coefficient of resistance is linear with absolute temperature and classic phonon dominated Debye model, i.e there are no lattice dislocations from impurities in the copper or worse changes of state, which is indeed true for pure soft copper, but not for all cable types. Try it with steel or brass conductors and be amazed.... Less seriously very modest amounts of impurity in copper have quite a serious effect on the residual resistivity ratio (RRR). (more info here http://cds.cern.ch/record/2723215/files/2006.02842.pdf?version=1 )
These sort of errors you can eliminate by measuring the resistance with a low current and putting the cable in an well stirred oven or oil bath, when the cable sample is at say 80C, then that is the resistance of that cable at 80C but it is no longer an easy experiment.
And again with larger cables and layouts where flow and return AC currents are non-adjacent, you need to be careful of the inductive element to the voltage drop as that is not contributing to heating.
I'd be happy with it as a quick and dirty estimator method, I'd be most disappointed if any of the figures in the official tables were derived that way without cross checking to proper temperature probe measurements.
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