Disconnection time formula?

Perhaps because, as has been pointed out by John, such faults do not give rise to electric shock hazard.
Possibly it is just a mathematical exercise for you.
No, it was an exercise in looking at what happens in long cable runs under fault conditions

77A equates to a Zn of 2.99Ω.
The Zs would not be compliant (1.37 for C16 before the derating factors).
Not compliant with what regulation?
 
Indeed - but, as my graph illustrates, in the case of 4mm² cable and a C16, it will always comply, no matter how long the cable. I rather suspect that the same would be true with most credible combinations of cable size and MCB type/rating.

Kind Regards, John
What is not credible about using 1.5 or 2.5mm cable with a C16?
 
Yes for 4mm, but if you look at 2.5mm cable and 1.5mm cable in the otherwise same scenario things look a bit different! Both (depending on install method etc) have a CCC in excess of 16 amps.
Well, looking first at 2.5mm ...[Edit: THIS GRAPH IS INCORRECT - see post #68 below]

upload_2018-7-11_20-21-40.png


[Edit: THIS IS ALL BASED ON THE INCORRECT GRAPH ABOVE, AND IS THEREFORE ALSO INCORRECT - see post #68 below]As you can see, even with what are undoubtedly substantial underestimates of 'overheating times', those time remain longer than the C16 disconnection times up to over 400 metres - and that would be unrealistic, given that there would then be a voltage drop of about 115V at 16A.

This is all tending to support my view that you are probably talking about a potential problem which is extremely unlikely to ever arise with any realistic/credible cable/breaker combination.

Kind Regards, John
Edit: Errors Indicated - see post #68 for (hopefully!) corrected version
 
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What is not credible about using 1.5 or 2.5mm cable with a C16?
See my recent post. I haven't got around to looking at 1.5mm² yet, but with 2.5mm², the (underestimate of) 'overheating time' is longer than the C16 disconnection time up to a cable length which would result in a >115V voltage drop at 16A.

In other words, what is not credible is using 400m of 2.5mm² cable to supply 16A, and the situation would be even worse with 1.5mm². Up to cable lengths for which the VD is even half-acceptable, the 2.5mm² cable remains more than adequately protected by a C16, and I imagine that the same will be true of 1.5mm² (although obviously a shorter cable length for an acceptable VD).

If one didn't need to supply as much as 16A (hence lower VD), then a lower-rated MCB could be used, in which case 'things would get better'.

Kind Regards, John
 
No, it was an exercise in looking at what happens in long cable runs under fault conditions
Could it have been to get you to realise that the answer would be - not much.

I wonder why they chose 77A and a C type MCB. Could it be because 77 is just under the 80 Ia of a B type and the C type is unusual?
77A and 15s is about the same for a B type (maybe a couple of seconds less, still over ten).

The example is no different than an appliance overloading the circuit to 77A (if it could happen) for which it would be compliant.

Not compliant with what regulation?
I did say "would not be compliant for a C16".
The Zs is not compliant for a C16 MCB.

It has been said that some of us disagree that merely adding an RCD in that situation is an acceptable solution.
 
According to my calculations a 77amp fault current with 2.5mm cable would take 13.9 seconds* to overheat and reading the graph (C16) would take about 15 seconds to disconnect.

A 77amp fault current with a 1.5mm cable would take 5 seconds to overheat (still about 15 seconds to disconnect).

So I'm thinking there must be an error in your graphs? Maybe plot time against fault current instead of length and things will be clearer?

*or more, as discussed...
 
According to my calculations a 77amp fault current with 2.5mm cable would take 13.9 seconds* to overheat and reading the graph (C16) would take about 15 seconds to disconnect.. .... So I'm thinking there must be an error in your graphs?
Whoops, sorry - I think that the 4mm² graph is OK, but for the calculation of 'overheating time' for 2.5mm² I forgot to change the CSA (i.e. still used a 4mm²) - watch this space for a corrected version.

Kind Regards, John
 
According to my calculations a 77amp fault current with 2.5mm cable would take 13.9 seconds* to overheat and reading the graph (C16) would take about 15 seconds to disconnect. ... So I'm thinking there must be an error in your graphs?
Whoops, sorry - I think that the 4mm² graph is OK, but for the calculation of 'overheating time' for 2.5mm² I forgot to change the CSA (i.e. still used a 4mm²) - watch this space for a corrected version.
OK, I think this one is right ....
upload_2018-7-11_21-39-33.png


Up to a length of about 250m (fault current down to about 47A), the (underestimate of) 'overheating time' and the C16 disconnection time are virtually the same (so that the true 'overheating time' is undoubtedly longer than the C16 disconnection time throughout that period). Since one cannot see the separate curves below about 275m, this magnified version makes things clearer ...
upload_2018-7-11_21-49-5.png

(the wiggles in the C16 curve are due to inaccuracies in my reading from the published graph).
The nearest point I had to your 77A wa the point for a 150m cable length. The fault current then (assuming 0.35 loop impedance at DB) was 75.4A, with a disconnection time I read from the graph as about 14 secs and an (underestimate of) 'overheating time' was about 14.5 secs - so pretty close to the figures you mention. The apparent anomalies at the very start of the graph arise because one cannot get sensible disconnection times from the graph once current becomes high enough for magnetic tripping

So, interpreting the (corrected!) graph, the 'overheating time' is, in general terms, at least as long as the C16 disconnection time for cable lengths up to about 250m (i.e. fault currents down to about 47A), at which length the VD at 16A would be about 43V.

I don't think this alters my views about the relevance of all this to credible real-word situations.

Kind Regards, John
 
Could it have been to get you to realise that the answer would be - not much.
I think my graphs (after correction) have illustrated that no problem such as envisaged is going to arise unless the cable gets so long that VD (at a current equal to the In of the OPD) is ridiculously high.

Kind Regards, John
 
Supplies for things 100's of metres away from the nearest source are not at all unusual in a temporary event or other temporary scenarios (credible real world situations).

The supply may only be for a small load, such as LED lighting, or small device charging and so volt drop less of an issue (and a private-supply generator is likely to be set up to output a higher voltage than the nominal).

16A breakers and 2.5mm cable do seem to be coordinated right enough, until the length means the cable could handle the fault current anyway, too long and ADS would just fail altogether. 2.5 is the norm for 16A-plug/socket distro cable although 1.5 is used too, and smaller for the final connections to equipment, and adapters. The 1.5 curve is not so good. Similarly 6mm/32A protection (typical for hired distro cables) would seem to be able to handle fault currents at any length.

@EFLImpudence ^ C type breakers are the norm with hired-in distro boxes, not unusual at all (and swapping them out on the hoof John could be problematic for a few reasons). I have thought of having "16A ceeform plug => B6 breaker => 16A socket" assemblies for this very reason (to keep disconnection times down for remote locations with small loads).

@EFLImpudence the Zs limit for C16 breakers with RCD protection is 1667ohms, per regulation 411.4.9
 
Supplies for things 100's of metres away from the nearest source are not at all unusual in a temporary event or other temporary scenarios (credible real world situations). The supply may only be for a small load, such as LED lighting, or small device charging and so volt drop less of an issue ...
Fair enough. The issues which concern you really only arise if the cable is so long that its resistance/impedance is too high for magnetic tripping of the MCB to occur - see below ***.
... (and a private-supply generator is likely to be set up to output a higher voltage than the nominal).
The fault currents we have been using for our calculations assume a 230V supply. If the supply voltage is higher than that, then fault currents will be higher, hence disconnection times shorter (and a longer cable length required before magnetic tripping ceases to happen.

*** On reflection, I wonder if you are not approaching this all in the wrong way. As above, the issues which concern you really only arise if the cable is so long that its resistance/impedance is too high for magnetic tripping of the MCB to occur - which is the very situation in which adiabatic calculations cease to be valid (i.e. over-estimate conductor temperature rise). However, this situation, in which 'fault currents' are relatively low is essentially what we normally think about in relation to 'overload' situations ...

... it is the assumption of BS7671 that a cable is adequately protected, with any degree of overload, if the In of the MCB is no greater than the 'tabulated' CCC of the cable (as installed), Iz. Hence, for example, a cable is deemed not to suffer harm (undoubtedly, with a large safety margin) if a current of 1.45 x In flows for up to an hour - or for any other current for the period of time that the MCB would allow to flow before operating (per the graphs we look at).

If we were talking about someone plugging multiple fan heaters into the end of a 2.5mm² 16A radial of any length, we would call that 'overload' and would be happy that a 16A (or 20A, or 25A if installation method allowed) MCB would provide adequate protection to the cable - so surely the same applies if a similar current flows because of an L-N fault (short) at the end of that radial?

In other words, it would seem that BS 7671 has probably already done the work for you, and has deemed that any cable of any length will be safe from harm, no matter what currents flow, provided it is protected by a (satisfactorily functioning) MCB with an In no greater than the 'tabulated' CCC of the cable.

...the Zs limit for C16 breakers with RCD protection is 1667ohms, per regulation 411.4.9
For what it's worth, all of 411 is about protection against electric shock in TT installations. The 1,667Ω limit arises from the requirement for the RCD to operate if 'touch voltages' of exposed-c-ps are ≥50V. As I said before, if one merely wants an RCD to operate in the case of an L-E fault then a Zs limit of 7,667Ω is adequate.

Kind Regards, John
 
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411 is ADS, not limited to TT supplies
411.4 is about TN supplies
411.5 is about TT

411.4.9 is about using RCD's in a TN installation to satisfy disconnection times
 
411.4.9 is about using RCD's in a TN installation to satisfy disconnection times
Yes, you're right, I misread the reg numbers - my apologies. However, the 'required disconnection times' relate to protection against electric shock, which is nothing to do with your concern about melting cables.

The more I think about it, the more it seems to me that what I wrote in my last post about cable protection was correct. Even though you are talking about excessive currents due to 'short circuits', when those currents are less than those which will produce 'immediate' disconnection (magnetic tripping in the case of an MCB), then the situation is entirely the same as what we normally regard as 'overload' - and in that situation, as I said, it is considered that the OPD's, t/I curve is such that a cable of any length will be provided with adequate protection (i.e. will come to no harm), provided only that its CCC (as installed) in no less than the In of the OPD. If you accept that, then none of your calculations are required.

Kind Regards, John
 
There is also the point that you could lengthen the cable to reduce the short circuit current at the end.

Of course,though, there are an infinite number of short-circuit current values between the end of the cable and the point at which it becomes 160A, the Ia of a C16, including ~9s for 100A.

I am not sure what that shows other than John must be right in that this is all covered by the CCC of the cable being greater than the In of the OPD.
As B, C and D types graphs are all the same up to 80A (Ia of B type) and there are no requirements for larger cable CCCs for C and D types, it must be satisfactory.

I am still puzzled by the original course question as to why 77A was chosen with a C type (unless I was right and it was to confuse {or prove lack of confusion} by being so close to 80A).
 
There is also the point that you could lengthen the cable to reduce the short circuit current at the end.
Indeed - and I think that that, coupled with my graphs, show how inappropriate it is to use an adiabatic calculation for currents which last for more than a small number of seconds. The graphs appear to show that as one increases the cable length beyond a certainly length (200-300m with the examples I showed), as the fault current decreases further the 'overheating time' (as calculated, incorrectly, assuming adiabatic conditions) becomes progressively less than the C16 disconnection time - leading to skenk's concerns.

However, it is pretty ridiculous to imagine that decreasing the fault current can result in the cable becoming increasingly 'at risk' - so what appears to be happening in my graphs is almost certainly simply a reflection of the fact that the ('inappropriate') adiabatic calculations are underestimating the 'overheating time' progressively more and more as the current decreases (and duration of current increases).
I am not sure what that shows other than John must be right in that this is all covered by the CCC of the cable being greater than the In of the OPD. As B, C and D types graphs are all the same up to 80A (Ia of B type) and there are no requirements for larger cable CCCs for C and D types, it must be satisfactory.
Quite so.

Kind Regards, John
 

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