Cable Derating Factors - Single circuit, multiple cables in duct

Before getting buried in the details of the regs view,  if its not your day job & second nature, it is worth stepping back and seeing that there are a few ways to dice this -

Firstly how well do you know your load ? Is it constant power 24/7, or is it modulated on and off over time - depending how fast this occurs it may be faster or slower than the cable heating time. If the mains voltage is high does the load draw more current, like a resistor, or less like a building full of electronics with switch mode supplies containing more or less constant power. The regs assume the former, as the worst case, but nowadays it is not always true.

Secondly the route and space available

Heavy SWA rapidly gets awkward to install - its worth looking at bend radii carefully not to mention the sizes you are considering weigh in at about 10kg per metre so if it needs to be installed anywhere that it cannot be dropped into or dragged into place by vehicle it can be tricky.  Dividing it down over parallel cables is one solution, - 240mm2 is a lot more flexible than 300mm2 for example, but the terminations rapidly get bulky.  There is a reason that beyond a certain point, ( and if your route is convoluted, or overhead for any great distance you may have reached that ), where installing as AWA singles tied in trefoil or quadrifoil to a tray is the easier method - it is less likely to give the installer a hernia. Killing someone by a poor choice at the drawing board stage is not a good start. Also make sure there is enough space at the ends for termination

parallel cables heat each other, same circuit or not, and unless you want a fire, this needs to be thought about, and spacing things by a cable diameter or two and allowing air to circulate works wonders.

finally Length and voltage drop - self explanatory but for a long run, it is sometimes worth having a short (well few metres) tail of one cable, then a joint to something with greater cross-section for the long, and hopefully straighter  run. There is also the economy of losses over the life of the installation - but it depends how that is budgeted relative to construction costs.
M

The derivation of Cc is given in the Commentary on IET Wiring Regulations if you have access to a copy (I would recommend a read to any designer working on your scale of project) but in short it's an adjustment for the temperature rise due to small overloads being different for buried cables due to a lower ambient temperature. The Cc value in the Regs is in fact a conservative value allowing for different cable types. Notably if you assume a lower ambient soil temperature, Cc gets "worse", but 0.9 covers the usual cases down to 15°C.

You could if you wanted calculate Cc with project-specific values and still conform to BS7671 (since Cc as 0.9 is in the informative Appx 4, but the actual requirement is 433.1)... But unless your Client will be happy to show your design calculations to anyone reviewing the design for the life of the installation, it's probably not worth arguing, and at last check Amtech/Trimble (yes, other software exists) don't allow it do be varied so you'll be doing it by hand. Note that this way, Cc will likely not be 1.0, but may be greater than 0.90.

Alternatively if you really do know your load well, it is fixed and it cannot suffer small overloads, such that overload protection can be omitted, so can Cc. (Mike's already written more about that)

Meanwhile as already said, even if the cables are feeding the same load the grouping factor will be for three circuits.

As for cables in the same duct (they're a bit big for it though!) there isn't a tabulated solution for multiple cables in a duct in Appx 4 so you need engineering judgement, some other set of tables, or to calculate from first principles (BS EN 60287). Or, more practically, use separate ducts for each cable (or trefoil/quad bundle).

Chris Horne said:

As these are all feeding the same load am I correct that the Grouping Factor C_g is still 1.0?

Not quite (as Mike as already mentioned from a physical point of view) - from a regs point of view it's worth looking at the descriptions that go along with Cg - e.g. the heading for table 4C1 - 'Number of circuits or multicore cables'  (OK while the wording still isn't 100% especially for the case of single core cables in parallel, it does follow the general logic that what you're counting is how many multiples of the (loaded) conductors described in the installation method you have e.g. if you have 6 and the installation method says 3, then Cg is for "2 circuits".

Which suggests I need to derate the cable by 0.9

The way I think of it is that tables for buried in the ground reference methods (e.g method D etc) have already been increased to take advantage of the lower ambient temperature - the 0.9 factor puts them back closer to "normal conditions" (which makes the assumptions used for overload calculations valid again).

If you want to argue that your overload protective devices have a smaller than the usual 1.45x margin, so you can safely run the cables a little bit harder, than that might well be valid - but arguably it should be equally applied equally to above ground cables as underground ones. So maybe more a matter of applying 0.9 and then applying some other factor to adjust for your choice of protective device (which may or may not come out to be 1/0.9).

    - Andy.