To what extent does HV protection mitigate LV faults?

This is a bit of a nuanced question. As AJJewsbury mentioned below if you looking purely at overcurrent tripping scenario's then its a matter of using the winding ratio's to assess your fault levels. However you need to understand the HV protection relay pick up and TMS settings, from which you can find the tripping times. There are also all the different fault scenario's to consider and protection types across the transformer. Its also worth noting that in the Arc flash guidance 2 seconds is used as the maximum arc period for calculation. Do you have more info to hand?

as our learned colleagues have noted, this will become clearer when you run the numbers. the fault currents will likely be dominated by the impedance of the transformer, which should be on its rating plate.

I find the most onerous scenario is a single-phase-to-earth fault. I'm not sure if what I'm about to write applies to your challenge but, inside a substation, the metalwork earth and the transformer LV neutral earth are sometimes separated. that means that the fault loop includes the soil around the substation, which increases resistance, reduces fault current, and makes it harder for the HV protection to see an LV fault. if the casing of your LV switchboard is connected to the LV neutral earth somewhere, then you at least won't have that problem

 A quick observation re. the arc flash thing that may not be obvious. 
As there is some voltage drop accross the arc - after all there has to be some I*V that is heating up the ball of hot plasma, the currents are somewhat lower than the dead short 'bolted fault'.
Breaking times are therefore longer than the dead short case.

Also the worst case arc energy may be approximated by half the PSSC times half the open circuit voltage that was there before you dropped something that struck the arc.  There are very many other combinations of more V and less I  or more  I and less V, but unless the supply has some non linear roll off of voltage with current, the upper bound in watts available to generate the fireball is the half and half figure. This can then be assumed at any given distance to be smeared out over a sphere (or part of one see below), to give so many watts per square cm, and the upper bound for a survivable "instant suntan" for bare skin is normally taken as 5 watt seconds per square cm.  This highlights the need forthe shortest breaking time, and the greatest distances for maximum protection. 

Note that the expansion of the flash into a sphere (so area =4.pi square metres at 1m distance ) assumes that it is an arc in free space, not one in a box where the energy is reflected off the sides and back of the box, in from of an open box, the intensity may be 3- 4 times more intense in the cone of the direction where the box lid is removed and of course nothing at all in the directions where the box is blocking.

This simple geometry method is attractive but tends to over-estimate the exposure and a more rigorous approach that takes into account the energy limiting action of the ADS as it opens, and the gap length over which the arc must be struck,  is described in the very comprehensive Eaton White paper https://www.cablejoints.co.uk/upload/Arc_Flash_Clothing,_Arc_Flash_Protection,_Arc_Flash_PPE___A_Practical_Approach_to_Arc_Flash.pdf

(This in turn is based on  IEEE Standard 1584, which incidentally with a bit of care can be used to show that almost anything single phase 230V in a box protected with a 63A fuse or less is safe at fore-arm length distances, so working on most final circuits and domestic probably wont need any arc PPE.) But of course above that it gets 'interesting', rapidly. 

Mike

PS actually an arc at lower current, that burns for ever and never goes out, due to being below the ADS threshold is technically worse, but fortunately  not a realistic situation.

 A quick observation re. the arc flash thing that may not be obvious. 
As there is some voltage drop accross the arc - after all there has to be some I*V that is heating up the ball of hot plasma, the currents are somewhat lower than the dead short 'bolted fault'.
Breaking times are therefore longer than the dead short case.

Also the worst case arc energy may be approximated by half the PSSC times half the open circuit voltage that was there before you dropped something that struck the arc.  There are very many other combinations of more V and less I  or more  I and less V, but unless the supply has some non linear roll off of voltage with current, the upper bound in watts available to generate the fireball is the half and half figure. This can then be assumed at any given distance to be smeared out over a sphere (or part of one see below), to give so many watts per square cm, and the upper bound for a survivable "instant suntan" for bare skin is normally taken as 5 watt seconds per square cm.  This highlights the need forthe shortest breaking time, and the greatest distances for maximum protection. 

Note that the expansion of the flash into a sphere (so area =4.pi square metres at 1m distance ) assumes that it is an arc in free space, not one in a box where the energy is reflected off the sides and back of the box, in from of an open box, the intensity may be 3- 4 times more intense in the cone of the direction where the box lid is removed and of course nothing at all in the directions where the box is blocking.

This simple geometry method is attractive but tends to over-estimate the exposure and a more rigorous approach that takes into account the energy limiting action of the ADS as it opens, and the gap length over which the arc must be struck,  is described in the very comprehensive Eaton White paper https://www.cablejoints.co.uk/upload/Arc_Flash_Clothing,_Arc_Flash_Protection,_Arc_Flash_PPE___A_Practical_Approach_to_Arc_Flash.pdf

(This in turn is based on  IEEE Standard 1584, which incidentally with a bit of care can be used to show that almost anything single phase 230V in a box protected with a 63A fuse or less is safe at fore-arm length distances, so working on most final circuits and domestic probably wont need any arc PPE.) But of course above that it gets 'interesting', rapidly. 

Mike

PS actually an arc at lower current, that burns for ever and never goes out, due to being below the ADS threshold is technically worse, but fortunately  not a realistic situation.