To what extent does HV protection mitigate LV faults?

It all depends on the numbers.. 

The general principle is that a fault (of negligible impedance) on the LV will result in a certain size of fault current (depending on the characteristics of the supply and the length/size of conductors feeding the fault) - and that fault current will result in a corresponding overcurrent on the HV side - the size depending on the ratio of the windings (e.g. a 1000A fault current on the secondary of a 2:1 transformer would see 500A flow on the primary side). So it's then just a matter of seeing how the HV protective devices respond to that magnitude of current.

   - Andy.

Presumably it's more nuanced than this? Otherwise why would an LV switchboard have an ACB

why would an LV switchboard have an ACB?

Generally only when the PSSC on the LV side is high enough, that nothing less than an ACB will reliably break it. It is unusual in the UK - some bosky 'death or glory' fuses on the LV side are more common. These never blow unless the fault is at the level that would destroy something, but that is what they do.

That fault current in turn, is set by the transformer, and its internal impedances, and to some extent also by the impedance in the HV external loop. However, by the miracle of transformation, ohms on the HV side have far less effect on the PSSC than any similar resistance in the LV loop ;-) 

Any ACB on the HV side is normally only protecting against gross faults within the transformer itself, and perhaps a dead short on its output somewhere before the LV ADS. 

It might provide some coverage for slightly lower current LV faults, i.e. big short circuits but further downstream within the LV network, but it is not sensible to rely on it.
The problem is that without a lot of info about the transformer, the ACB set-up and the various loop impedances for that specific installation, there is no general rule. 

Mike.

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.

The HV protection will be designed to protect the transformer, and the tails up to the first LV protection. As with the DNO protecting your first 3m, anything after that may be protected but unless you talk to the designer it is not guaranteed.

However because of the impedance of the transformer coupled with transformation ratios, what looks like a HUGE current at LV may well look like a mere overload current at HV. To compound this some HV protection only provides protection for fault current, relying on the LV side and other devices for overload. Becaue we don't want the HV protection operating at the drop of an LV hat (selectivity etc, particularly given that the HV protection could well be based on HV fuses or time-limit fuses), the upshot is that HV protection for the LV components will be slooooow.

Furthermore, assuming a delta-wye winding, LV earth faults appear to the HV system as phase current, so unless it's a close in and solid fault, may not even register at HV at all.

As others have noted, this means that the energy released (damage caused) before the fault is cleared could be considerable. This is why alternative protection schemes are fitted for more valuable transformers / at risk locations, such as Restricted Earth Fault (REF), which is a bit like an RCD facing backwards to trip very quickly on transformer LV winding earth faults which are very hard to detect at HV but cause a lot of damage if unchecked.

In principle it may be possible, subject to practical limitations like fuse sizes / setting ranges, to provide backup protection for the main LV protection, perhaps and ideally that is done. But it needs coordination and all of the information to be available at the right time, e.g. LV switchboard withstand rating.