Short Circuit Rating of Switchborad/Busbar

Is this an academic exercise ?

I²t is not the only consideration, dynamic force is also a factor.

You cannot use a 31.5kA system on a 50kA fault level, since the first peak of the fault current can be 105kA, whose dynamic forces may be too much for the supports.

Even on the other option, why would anyone want a fault to persist for 2.5 s ? i have never come across any discrimination system which needs such a long delay in LT.

There are a large number of threads in CR4 on this subject, please search using'busbar' in the seasrch window here.

It would be also nice to register on CR4 .. it is free.

A busbar rated with a short time withstand of 50 kA for 1 sec would withstand 31.5 kA for 2.52 seconds for sure going by the I2t calculations. But, as rightly said by KVS, I would be more worried about the dynamic withstand in this case too, which, definitley is not decided only by the bus bar size and/or the Short time withstand ratings.

On your second query, a strict NO-NO. A lower short time with stand rated bus bar / switchgear can NEVER be subjected to a higher short circuit current albeit for a lesser duration. So, even on a thermal withstand criteria this cannot and should not be done.

A conductor cross section is dependent on magnitude of fault current through the conductor, its duration and temperature range. Final temperature range is composite and takes into account ambient temperature.

Formula for conductor sizing is:

xsection = fault current X sqrt of time / constant of the material being used.

I fail to understand how does the relation 'square of current X time' got reffered to in your query.

Neglecting grading for discussion, as a general expression Main (primary protection) is rated 0.5 second, Back up protection 1 second and for important installations for eg. oil, gas, primary substations etc. equipment is rated 3 seconds.

Not only ambient temperature, for mechanically loaded conductors short circuit rating becomes less and you have to design the supports in cosideration of forces during short circuit.

busbar shall be sized based on symmeterical and peak fault level.

both the factors shall be considered