DC Cabling Current Carrying Capacity - Continuous vs Momentary / Finite Period Assessments Query

Well, firstly the tables in the annexes to BS 7671 are all relating to very specific installation assumptions  - and therefore implied assumptions about airflow and conduction of heat to the environs (itself at particular temperature), and also to steady state loading. Inrush current of up to ten times the steady state rating is common in some motor start applications.
The tables are there to allow the safe and conservative design of systems that do not exist, so that they definitely run at acceptable temperatures and should give no problems with an estimated 70 year lifespan.

Of course you already have a system, that I hope you would have mentioned if it was suffering signs of thermal distress, so presumably there are factors in this installation that help it along.  So there are some questions - is the air temp controlled in your facility, what is the design load duty cycle, what is the longest burst on time, and what is the design life of the installation.

Note that cables (but not perhaps the things at the ends of them) can be run quite a lot hotter than the 70C core temperature, but the lifespan shortens from decades to years, roughly halving with every 8 degree rise.

In terms of time constants - things can warm up quite slowly as illustrated here.

https://electrical.theiet.org/media/1704/establishing-current-ratings-for-cables-in-thermal-insulation.pdf

Mike

PS

When you do overload a cable... the power dissipated is equal to P=I²R, so the temperature rise increases roughly in line with the square of the current*, so assuming you have a cable rated at 27A and its running at 70 degrees copper temp (yeah, just assume), the temperature rise normally is 40 degrees (from an ambient air of 30), say you put a load of 32A on this cable, that's an overload of factor 32/27 = 1.185, the temperature rise in this case will be (1.185)²x40=56.2 add that to the 30 start point and you get a conductor temperature of 86 degrees which won't start any fires, but the lifetime of PVC cable halves for each 8 degrees its overrun, so pvc cable run 24/7 at its tabulated rating lasts 23 years, this one only lasts 23/4 = 5.75 years before it starts to crack, very few installations  run their circuits at full load 24/7 though.

Now if you have that the load for only 8 hours a day the expected life time for the cable at its tabulated rating is 69 years.

Even if you did put a 10.8kw shower on the end of the 27A cable, I'm not sure any fires would start... the ageing rule breaks down at about 120 degrees when the cores start to melt through the PVC and things tend to go bang... and this is quite a way off the 451F/233C point at which even paper paper catches light  ! (With a nod to Ray Bradbury)

*We assume that the rate at which a cable can shed heat into the surroundings doesn't go up as the temperature difference between the cable and surroundings increases, which is not really correct, but I'm not sure quite how it changes and I see no reason to complicate the numbers further

some of the figures are taken from an IET  paper dealing with thermal ageing that used to be available at 
http://www.iee.org/Publish/WireRegs/Commentary-UpdateApr04.pdf - sadly its gone in one of the website re-shuffles. so here is a copy ;-)
PDF

The concept of "thermally equivalent" currents is not unknown and is detailed in one of the GNs (I'd have to check which) - basically is is valid to have a "design current" (Ib) that's equivalent to the medium/long term effect of the load, rather than just using the peak current (we sort of take that approach anyway, as we often disregard starting currents). I believe that's all acceptable under BS 7671. The time periods aren't that long though (typically minutes for small cables, maybe tens of minutes for larger ones (I suppose you might just get into hours for very large c.s.a.s)) - so that may or may not be sufficient justification on it own.

BS 7671's cable data is based on a large number of assumptions - and as it's "informative" rather than "normative" it's not strictly part of the standard and so other approaches are permitted. You could for instance decide that a shorter working lifespan for the insulation is acceptable, you could run the conductors hotter (it's interesting to look at the rating for automotive cabling - where the design lifetime is closer to 10 years rather than 70), or use different insulation that survives higher temperatures. That does have knock-on effects though - conductor resistance would be higher, so increased voltage drop, increased loop impedance, and the need for higher temperature terminals ... but that can often be dealt with.

   - Andy.

Is the "attached pdf" just 2 pages on a single sheet? engx.theiet.org/cfs-file/__key/communityserver-discussions-components-files/4/Commentary_2D00_UpdateApr04.pdf

yes - the standard it is lifted from is/was IEC 943, but now subsumed by the more recent

IEC 60943.Guidance concerning the permissible temperature rise for parts of electrical equipment in particular for terminals. 

The technical approach (and numbers)  remain essentially the same, but its almost 60 pages and about £300 more than the free PDF ;-) 

Mike.

Hi Andy,

Thank you for your reply, most helpful.

My main issue is that there is pressure being bought to bear by the client on the project to consider and accept the alternate calculation methodology, which I have no issue with in principle, but the substantiation they present to support their alternate calculation is 2x documents that I am struggling to readily accept.

When I have calculated the UPS to Battery Panel (BP) dc cabling, protected by a 800A mccb, the post Ca/Cg adjusted It is 980A, the 2x 150mm 1C cables per pole can achieve an Iz of 864A therefore there is a notable shortfall. The alternate calc provided by others indicates that 2x 150mm 1C cables per pole can accommodate an Iz (or Ikb as they note it) of 1040A for a period up to 600s (10mins).

The UPS systems are each 1200kvA / 1000kW, ultimately supported by 4x BP / Battery systems, which are to provide min. 10mins autonomy. The system will either be in a normal float charge state where the current apparent is minimal but the dc voltage is at its highest or under discharge 

To further muddy matters there are a few other issues apparent that I have raised i.e. the primary mccb and string fuses in the BP are not fully rated to the potential dc voltage apparent, the string cable sets are also protected by 800A fuses but cabled via 1x 95mm 1C cables per pole, there is no clear discrimination between the devices in the BP, it goes on. All of this erodes my confidence in the original systems design and therefore makes me reluctant to continue to accommodate and match such with any newly added elements.

Simon

Hi Mike,

Thank you also for your reply, this is my first time posting in the forum so well impressed with the prompt and helpful replies apparent.

I have added some further info below to my reply to Mike, in addition the project ER calls for a design life expectancy of 15 years, I am presuming that the original installation was under the same premise.

Simon

ISL said:

dc cabling, protected by a 800A mccb, the post Ca/Cg adjusted It is 980A, the 2x 150mm 1C cables per pole can achieve an Iz of 864A therefore there is a notable shortfall.

I've only dealt with much smaller systems, but in those battery fuses (and CBs) are often selected to provide only fault protection - (overload protection either not being necessary due to the nature of the load (i.e. the inverter in the UPS in your case) or is dealt with downstream) - in such cases the fuse is often 2 or 3 times the expected design current, but the cables are still sized according to the actual current (Ib) rather than the protective device (In). If your actual currents are lower, there may be some margin there.

10 mins is a reasonably short time for such large cables - it might be worth a quick back-of-an-envelope calculation to see what the adiabatic temperature rise would be (if you know the per metre resistance, and current, you can calculate the energy that goes to heat the conductor, then apply that to the heat capacity of copper to work out the temperature rise) -  that might prove to be either reassuring or justify your doubts.

Discrimination between devices in series on the same circuit typically isn't a concern - if the end effect is the same (it all stops working) whichever device opens first, you're not really loosing anything. If one device opening in preference to another means that some loads, especially critical loads, could continue, that's a different matter. BS 7671 doesn't demand discrimination in all situations - just provides means of achieving it, if it's required. 

   - Andy.