well in a T an E cable, if the live cores are warmer than ambient , the CPC will be as well.
singles in rattling about in trunking or conduit may well be a quite different temps so your R1 and R2 correction are not really correct. Equally even if things are tightly grouped even unloaded cable may actually be heated by adjacent cables.
You can say even less about the stuff that is external and may be shared with other consumers, and is just as likely to be  running hot or cold on the day you test.
However the assumption is just that, an assumption that it is all hot - if you can justify that it never will be, maybe you can relax the test limits, but there will be few cases where a fail becomes a pass, and to be honest if there are, I'd consider it a marginal design anyway.
Mike

Late edit, Sorry, that was rubbish. The assumption is that on the day you measure it is all cold of course - a low resistance day if you like, but that you may need the fuse or whatever to still operate at full speed on another day when it is all hot, so 125% more resistive and when   the fault current when hot is 80% of the cold test result. Moral keep your algebraic wits about you.

 Mike

should it not be only applied to the R1+R2 ,as the ZE part may be at a different temperature

It did used to be written that way in BS 7671, but it seems to have disappeared. I guess there's an argument that while the supplier's conductors (the Ze part) may well not be entirely cold, it may not be exactly at full load either - say you did a Ze test during the day in early summer where there's little heating or air conditioning load, the DNO's conductors might well be cooler than say late afternoon in in mid winter, when it's dark and a lot of heating is in use. So some adjustment for the supplier's conductors may be justified - although perhaps not quite as much as 20% - but as we don't really know what, 20% is probably a good rule of thumb and errs on the side of safety.

   - Andy.

The biggest elephant after all that is that the day after tests, the DNO may replace the street transformer or main feeders and you would be none the wiser.
Some countries that have rather wilder electrical installations than the UK require an earth fault trip/ giant RCD at the incomer for just that sort of reason, and in many cases over and under-voltage lock off as well.

Mike.

Newfutile said:

we apply this to the whole maximum ZS  ,should it not be only applied to the R1+R2 ,as the ZE part may be at a different temperature and possibly wont be loaded up as much.

You can if you like. BS 7671 says, just below this method in Appendix 3 (Page 410 of BS BS 7671:2018+A2:2022):

NOTE: The above is one method of correcting for the effects of temperature difference; other methods are not precluded.

So, you could, for example, subtract a Ze reading from Zs, temperature correct the remainder using the correction factor for temperature coefficient of resistance from ambient to 70 deg C (roughly, multiply by 1.2), and add Ze again and compare the result with Tables in Chapter 41 (rather than the tables in OSG and GN3 which have the corrected values in them) ...

BUT Ze (and sometimes Zs) readings aren't all that accurate, so it might not make a lot of difference in the round.

gkenyon said:

So, you could, for example, subtract a Ze reading from Zs, temperature correct the remainder using the correction factor for temperature coefficient of resistance from ambient to 70 deg C

Not so sure about that. I think R1+R2 would have to be measured separately. You may well find Zs-Ze is far from any reasonable notion of R1+R2, it could even work out as a negative number. Raising R1+R2 to conductor operating temperature and adding Ze is probably more applicable to a design exercise. However, in testing, if you are over the 0.8* Zs7671 but under the value of Zs7671 and Ze is relatively high, there may be merit in digging deeper. 

mapj1 said:

The biggest elephant after all that is that the day after tests, the DNO may replace the street transformer or main feeders and you would be none the wiser.

That happened in our street a few weeks ago, but one could hardly fail to notice. My first thought was whether they might have dropped the voltage, but 241 V in my office just now, so apparently not.

The new transformer's labels mention its neighbours, so they must be connected in some sort of ring or grid, in which case if you changed the voltage at one, you would have to change the lot.

lyledunn said:

Not so sure about that. I think R1+R2 would have to be measured separately.

BS 7671 does not require that, nor advise that.

lyledunn said:

You may well find Zs-Ze is far from any reasonable notion of R1+R2, it could even work out as a negative number.

I agree, that is why I mentioned errors in measurement.

lyledunn said:

aising R1+R2 to conductor operating temperature and adding Ze is probably more applicable to a design exercise. However, in testing, if you are over the 0.8* Zs7671 but under the value of Zs7671 and Ze is relatively high, there may be merit in digging deeper. 

I think there are circumstances that would lead to "does not compute" between any of the methods.