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.

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.