Derating of Low voltage Switchboard

Edit: our spec calls for temperature rise of 45k and the 70k in the equation is assumed to be the manufacturer tested temperature rise

Err possibly. ;-) 
Lets understand where those formulae come from - they hide a few assumptions which may  or may not be correct in your case.
I presume the busbar is plastic coated,or plastic parts are in contact with it, and that sets the 135C upper limit with the maximum current flowing for a long period. Its not the same as a fault rating, that can be quite a bit hotter if the ADS is prompt.
 
Here temperature rise is assumed linear with power, which is a bit dodgy, as convection increases the air circulation and then the rate of cooling with increasing temperature gradient.
Secondly that power dissipated is assumed to be proportional to the square of current, that is neglecting the fact that the resistance rises a bit when hot. 
Maybe these two cancel to a degree.

Are you using 60Hz ? At higher frequencies the magnetic forces push the strands of current apart more noticeably, so the more current flows near the outer surface than in the core. At 50Hz in copper that 'skin depth' is a touch under 10mm and more like 8.5mm at 60Hz so in really thick conductors less of the core is used. Flat bus-bars (thin compared to the skin depth)  don't have the same problem and the DC 50 and 60 Hz ratings are the same.

Then, only then  one must ask what is the thermal condition for the 4000A rating, and how much is that different in your use case.  I'm not too sure from your question what those conditions actually are..
Mike.

Nick Parker said:

Edit: our spec calls for temperature rise of 45k and the 70k in the equation is assumed to be the manufacturer tested temperature rise

I'm struggling to follow, but so far it's looking to me like the Manufacturer is starting from an ambient of 35ºC and a bus-bar temp of 130ºC - so a rise of 95ºC ?

(please say if I've got that wrong - I'm trying to learn here..)

If you're wanting to limit the temp rise to 45ºC (i.e. T_BB of 80ºC for a 35ºC ambient) that certainly would mean a very significant de-rating indeed). It sounds like you're trying to correct for a different ambient temperature as well ... not sure what figure you have in mind.

   - Andy.

I had the same problem, the OP needs to clarify the situation in terms of their assumed ambient and permitted rise, and why. 

But yes, when rating the bar at 4000A, Siemens assume an ambient of 35C, so to reach the permitted max bus temperature of 130C, a rise of 95 degrees occurs at 50Hz.

Now, either raising the ambient or reducing the upper limit, will curtail the current handling according to the assumptions give (temperature rise is assumed linear with power, and power scales with square of current.)

If the OPs assertion is that the new rise is limited to 45º instead of 95º, then new de-rated current is (noting that 45º/95º implies reducing the power by almost half; we might expect the current to be about reduced by a factor of 1/√2  or about 70% of the 95º value.)

4000* √(45/95) = 2.7kA  which is indeed a touch under 70%. 

Its also not very clear if the OP is using 60Hz or not.

Note that although the most heavily loaded sections of the bus might be a 130ºC,  normally one connects in a way that the terminations to insulated wires are not, so that 'normal' wires can be used, and their insulation is not cooked. Example pics from the catalogue gives an idea. these connection systems are more in socket set and disc cutter territory, not side cutters and long nosed pliers -  even the Stanley knife and hacksaw as used with SWA looks a bit inadequate  ;-) 

  

They also do 7kA stuff as well, you know for big jobs...

regards, Mike.

From this manual from Siemens,
Ambient temperature = 35
Temperature rise = 130-35 = 95

Calculation shown by siemens to derate for the ambient temperature of 40, which is 3893A from 4000A

Now I want to calculate the ampacity of the busbar for the permissible temperature rise of 45k at the ambient of 40 degree.

So the total derated ampacity is = derating due to different ambient X derating due to different temperature rise X derating due to different frequency.

now talking only about the derating due to different temperature rise:

sqrt (t1/t2) -> t1 is the 45k and t2 (I consider this is only 70k from IEC 61439 as the standard limits the temperature rise to 70k for terminals) as the calculation shown here by Siemens is an example and not sure about the actual temperature rise in the lab by the actual panel assembler (he is the panel assembler for siemens)

for derating due to different frequency, again this coming from IEC

From this manual from Siemens,
Ambient temperature = 35
Temperature rise = 130-35 = 95

Calculation shown by siemens to derate for the ambient temperature of 40, which is 3893A from 4000A

Now I want to calculate the ampacity of the busbar for the permissible temperature rise of 45k at the ambient of 40 degree.

So the total derated ampacity is = derating due to different ambient X derating due to different temperature rise X derating due to different frequency.

now talking only about the derating due to different temperature rise:

sqrt (t1/t2) -> t1 is the 45k and t2 (I consider this is only 70k from IEC 61439 as the standard limits the temperature rise to 70k for terminals) as the calculation shown here by Siemens is an example and not sure about the actual temperature rise in the lab by the actual panel assembler (he is the panel assembler for siemens)

for derating due to different frequency, again this coming from IEC

Hi Nick

hoping you can clarify 

- is your design using 60Hz then ?
I understand you have a hotter ambient (40C),
Why do  you need to limit Tbb to 70C ?

And surely the panel builders should know this as its their bread and butter ?

regds,
Mike.
 

Hi Mike, Thanks for your reply!

1) yes, my design using 60Hz

2) I'm not limiting tbb to 70C, but I assume that panel builder achieved a temperature rise of only 70k (type tested) as I dont have a temperature rise report yet

Yes, in my case, the panel builder is from China due to the management decision to use for commercial purpose.

Thanks for that - and I can imagine working with someone at a distance is a bit fraught with possible misunderstandings.
OK, so it really is 60Hz, so the figure does need scaling by a factor of 0.95.
You can do that at the start or the end. 

The bus bar hot spot temperature, Tbb is calculated by adding the the environment to the rise, (ΔT - 'delta' T )  , so a 40ºC environment plus a 70º rise means a more credible  Tbb of 110º C.
 

So the pre-derating ΔT was 130ºC - 35ºC =95º;

your  de-rated ΔT is 70ºC and as above if the ambient is 40ºC your  Tbb bus hot termp becomes 110º C  - is that the intention ?

In effect both the lower and upper temperature have changed, squeezing the permitted temperature rise. 

Assuming that is the intention,  the power dissipation is in the ratio  of 70 to 95, and the corresponding currents in the ratio of of square root of that. Oh, and the 60Hz thing
new current
0.95* 4000* √(70/95)= 3.26kA 

Note of caution,
That this whole current rating thing is all a bit smoke and mirrors, well, hopefully not too much smoke in this case, as the maker's nice round number 4kA rating is for some test arrangement  that is not mechanically quite the same as yours, with airflow not the same as yours ,heating from adjacent other bits of bus bar not the same as yours  etc. And as I noted at the top, these assumptions - that heat is proportional to the current  squared, and cooling is proportional to temperature gradient are similar to reality, but not quite true. And of course the current gets on and off the bus - it has not got a uniform current, so it is neither uniformly heated, or cooled.

Regards Mike.