Hi Adam. Many thanks. I've been doing a lot of reading and thinking, and think that I am beginning to understand some of these issues - which I think probably go beyond what an ‘average electrician’ would, or would need to, know (other than the ‘bottom lines’). Starting, with your specific points ....
The reason, John that we have to consult manufacturers data below 0.1 is due to:
->At sort of times any part cycles will be significant, thus an RMS I is less than true.
Indeed - I wrote a fair bit about this earlier in the thread. Even forgetting all the other issues below, if the duration of current is brief and not equal to a whole number of half-cycles, the calculated RMS fault current would not be totally appropriate and, as the duration becomes shorter (most dramatically when it get to less than a half cycle), the value of the integral of I² over time (which is obviously what actually interests us) will become appreciably dependent upon the point in the cycle at which the fault arises. However, I’m not sure that the manufacturers’ can do too much about this - given the random nature of the timing of the onset of the fault, I presume that they can but provide ‘worst case’ figures.
->As previously mentioned energy limiting class becomes relevant due to features designed into the device.
This is the bit which is new to me, and may well be the most crucial factor (although I’m yet to become sure how relevant it is at ‘usual domestic fault currents’) - see below
->The fault current doesn't just 'appear' all at once, the inductance of the supply will be such that it takes some tiny amount of time to attain its full value and by that time the breaker may have already started to open, this ties in with the point above.
Very true. However, since the manufacturer (and, usually, the designer/electrician) will not know the inductance of either supply or the circuit in question, I would again presume that the manufacturers probably have to provide ‘worst case’ figures (presumably assuming zero inductance), don’t they?
In fact the dorman smith loadmaster series of breakers from the 70's, ... If you look at the bottom you can see a section on maximum let through energy, if you calculate it back you'll find it equates to a t of 0.01 seconds. Remember though that this is an early and crude MCB from the 70s and would be certainly not be energy limiting class 3 as modern devices. ... I.e take 30A breaker, at 2ka it gives maximum I²t of 40,000 but if you have a fault of 360A it disconnects in 0.4seconds which is I²t of 51,840
Indeed. In fact, moving closer to the present time, BS EN 60898-1 imposes “
maximum let through (I²t)” figures for all MCBs. As you say, these figures are the “maximum permitted’ ones but I suppose those are the figures one has to use for ‘worst case’ calculations.
Moving to the education I’ve been subjecting myself to, one way of looking at my ‘seeing of the light’ is that I have realised the importance (in the fairly ‘extreme’ situations we are considering) of there being a ‘P’ (‘prospective’) at the start of ‘PFC’!
If the fault current arose ‘instantaneously’, remained constant and flowed for an even number of half cycles, then its calculated RMS value would presumably be a true reflection of the energy-producing capacity’ of that current (i.e. V*I*t would represent the energy expended during time t). However, as above, in reality most of those ‘assumptions’ will not be true. As I’ve said, in the case of the speed of onset of the fault current, and the part-cycles, I don’t think we (or the manufacturers) can do anything other than assume the ‘worst case’.
However, I think that my main realisation relates to the matter of the ‘constancy’ (or, rather, ‘non-constancy’) of the current flowing during time t. What we are actually interested in, of course, is the integral over time t of of I² (“I” being the ‘effective RMS’ value of the current) - which will simply be equal to I²t for a current of I which appears ‘instantaneously, remains constant throughout a period of t seconds and then instantly reduces to zero. I am now realising the importance of that “I” being the
Prospective Fault Current.
As I now see it, the reality (assuming worst-case inductance and part-cycle issues) is that there are two phases to the time period t. Initially, whilst the contacts remain closed, the (‘effective RMS’) current will, indeed, remain constant (at the calculated PFC). However, once the contacts start to open, current will then flow through the relatively high (and undoubtedly varying) impedance arc, causing the current to fall to below calculated RMS 'PFC'). As I now understand it, at least some ‘current limiting’ MCBs work by having mechanisms (sometimes a second set of contacts/arms) designed to hasten the onset of contact opening and hence the transition between the two phases of the period prior to disconnection (and maybe also measures to decrease arc duration and/or increase arc impedance. I suppose one way of looking at this is that, during this second (‘arc’) phase there is a temporary effective increase in loop impedance (to above Zs), hence a reduction in
actual fault current.
It is therefore apparent that (since ‘I’ is not constant) the simplistic assumption that the integral of I² over time t is equal to I²t is not true in reality, although it is as close as makes no difference for longer (say >0.1s) disconnection times (probably because the second, ‘arc’ phase of period t is only a very small proportion of the whole period). However, when one gets down to short disconnection times (say, <0.1s) the difference between the ‘simplistic’ and ‘true’ value of the integral starts increasing. Going back to:
I.e take 30A breaker, at 2ka it gives maximum I²t of 40,000 but if you have a fault of 360A it disconnects in 0.4seconds which is I²t of 51,840
...the point here, of course, is that although (literally) I²t calculates as 51,840, what we
actually want (the integral of I² over time 0 to t) will not be as high as that, since 'I' does not remain at 360A throughout the time period. I presume that if one had details of the variation of I during the period, the integration would produce a result less than 40,000.
What I’m not yet sure about is how relevant any of this is to the matters we’ve been discussing. Now that I have discovered that they exist, I’ve just been looking at a number of ‘current limiting curves’ and what I’ve seen so far (for Class 3 limiting devices) seems to suggest that ‘deviation from the simplistic’ only starts to have any appreciable effect with fault currents above about 2kA or 3kA - hence perhaps of somewhat doubtful relevance in an ‘average domestic installation’?
Do you think I’m starting to get there’?!
Kind Regards, John
