An effective 900mm2 vs 240mmm2 seems one heck of a de-rating (!) - or the 240mm 4 core is undersized, what are you assuming about cooling and ambient temps in the ducted section, vs assumptions in the open air run ? - and related you do not mention the design current ?
In terms of cable ratings there is nothing magical about the fact it is a substation so the same rules apply as if it was a sub-main to a building.
Note that the current ratings in the BS7671 annex are guidance and for a few example situations, they are not the last word in possible cable selection, mounting methods  and rating, and there are corner cases that are not a good fit to these 'reference methods' There are additional documents, based on work originally done by ERA that fill some of the gaps that may be worth looking at.

An article about that
electrical.theiet.org/.../

regs Mike

mapj1 said:

what are you assuming about cooling and ambient temps in the ducted section, vs assumptions in the open air run

I think I can see what's going on here.

240 sq mm 4-core in free air has a current-carrying capacity of 516 A for three-phase operation (70 deg C conductor temp - Table 4D4A). When you look at ducts, this drops to 280 A. This is simple physics.

However, if this cable really is running near 500 A for 150 m, isn't this a problem for volt-drop ?

When going up a conductor size, this doesn't help much in the duct, and when you parallel you end up with a grouping factor issue ... which, as we've seen before, can really mess things up.

Overall, the simple laws of physics apply and if you enclose cables they will get hotter, but as mapj1  says there are other models to use; however, I still think there will be a big difference between "in ducts" and "free air", made worse with grouping for parallel cables.

516 A for three-phase operation (70 deg C conductor temp - Table 4D4A). When you look at ducts, this drops to 280 A.

I wondered that, but even then I struggled to get to needing 3 lots of 300mm in parallel even at the full 500A unless they are tied together and the bundle thermally insulated ;-) (oh and assume the soil type is desert sand..)

My suggestion to the OP is that the ERA papers that consider  bigger ducts and cables on brackets where cables are more thermally independent are probably worth a browse to see how that affects things.
And then there are tall ducts with vented tops (or even a grid top like a boot scraper) so that hot air is not trapped and that is more like cable on a wall. The nos in the regs are similar to to the solid/ unvented case where really it is a cable in a pipe.

I agree though that if it is the full 500A   then volt drop over 150m, won't be stellar with 240mm2  (~ 0.2V per amp per km call it 100V per km  at 500A >>  15V on your 400V over 150m ) though I suppose depending on what is fed by it, maybe OK - but I agree it leaves precious little slack for voltage drop in whatever final wiring is at the far end and may not clear the transformer end protection especially promptly in a fault. Of course all this is guesswork on my part as we don't know the design current or duty cycle or even what LV fuses protect the cable leaving the Tx .... 
Mike

I have seen a range of 'solutions' to this over the years mostly retrofitted and most would be classed as bodges.  These include: forced air cooling of the ducts (diificult to arrange and requires substantial space and power); filling the ducts with water and arranging a flow to waste (once set up effective but cost of water cannot be neglected) and there is the risk of flooding the switch room if there is a leak.  Cables need to be suitable for long term immersion too.

The best answer is to redesign the last few metres to avoid the need for ducts or failing that transition to bigger cables for the ducted portion.  Easy to say but you would need a substantial marshalling / joint chamber fitted with busbars and appropriate separators/insulation. 

If this is all indoors and dry could you use busbar chamber in a pupose made cable trench/ duct.  These tend to have higher ratings as the bars are normally bare though you would have to take account of the restricted ventillation..  

gkenyon said:

240 sq mm 4-core in free air has a current-carrying capacity of 516 A

Hi Graham, Think you've read the wrong column 516A is for a two core cable. A 4 core CCC is 445Amps.  

It might be worth accepting the use of oversized cables for the entire run. This will save significant money at todays electricity pries, especially if the load is a long hour one.

I suggest calculating the losses and the annual cost thereof, and putting the upsized cable to the client as an option.

Presumably you have looked at the actual soil conditions, rather than the conservative defaults in Appx 4. By my reckoning, assuming typical values for the UK, if you've gone up a size for volt drop etc., you're getting closer. Conversely, with a cable run that long followed by a need for burial I assume this is outside... is the cable ladder arrangement protected from solar gain / do your calculations allow for it?

You could also consider direct burial, encasing the duct in concrete (reducing the STR, given that it appears to be under the foundation anyway) or casting cable pits in and outside the substation so you've only got the cable entry to worry about. Or indeed keep the cable entry above ground and go through the wall.

If you're sizing for 70°C at the terminals, might be worth allowing the conductors to run up to 90°C in buried sections as long as they're far enough away from the terminations.