The Graphs in Fig 3A4-6. What does the vertical part of the characteristic mean?

The vertical bit means anything between those values - pretty useless really.

I'd say ditch the graphs (they don't seem to be consistent with BS EN 60898 anyway - occasionally dangerously so) - and replace with tables of time/current (rather like the ones for RCDs) and energy let-though.
  - Andy.

AJJewsbury:
they don't seem to be consistent with BS EN 60898 anyway - occasionally dangerously so
 

Could you highlight where the inconsistencies are? Are you referring to Table 7?

OK  Andy, is that really what they mean? Please explain.

gkenyon:

AJJewsbury:
they don't seem to be consistent with BS EN 60898 anyway - occasionally dangerously so
 

Could you highlight where the inconsistencies are? Are you referring to Table 7?

Back to this old discussion - https://communities.theiet.org/discussions/viewtopic/1037/24502 - which seemed to conclude that BS 7671 was claiming that certain rating of certain types of MCB would open within 5s for a given current whereas both BS EN 60898 and manufacturer's data suggested it could take up to 8s to disconnect.

  - Andy.

davezawadi (David Stone):
OK  Andy, is that really what they mean? Please explain.

The vertical bits? - that's how I read them at least - there's a discontinuity between the thermal and magnetic parts - so when the current is right on the boundary between the two (the tiniest fraction below 5x In for a B-type for example) the thing could operate either in thermal mode and take over 10s to open, or it could be in magnetic mode and take (anything up to) 0.1s.

I know some mathematicians who would say that the vertical bit shouldn't really be drawn at all when there's a discontinuity - better to just leave a gap.

Given in BS 7671 land we're not really interested in disconnection times of over 5s, the whole graph is seems of limited use anyway.

   - Andy.

The vertical part is a mathematical error Andy, it should certainly not be there, see the spur thread. It certainly does not mean a range of values, and essentially should not be drawn like that. You are correct in that the graph is discontinuous and the mathematical reasons are as follows:
The two axes on a graph are related to one another by an equation, which may be very curious and complex. However, there is a proviso that the slope may never be infinite, which means that the relation between the axes is no longer present. There is no equation available that gives a "range of values" as the answer, it is not possible without cheating. The error is that the magnetic part is completely separate from the thermal part and they may never join. True there is a point where one takes the place of the other, but this point is not really defined. I also do not see why the vertical lines stop at 0.1 seconds, this is completely arbitrary and does not reflect the real operation. The rest of the curve over 5 seconds is very useful, it shows (as do the fuse graphs) what happens when the fuse is operated at less than the disconnection time (which is normal operation). You depend on this in your house DNO supply every day, and probably the cutout fuse too, it is "normal" not during fault operation.

Your reference to the old post Andy is the same answer from OMS as I have been giving, with slightly differing minor details. You should note that this is not a graph but an area plot, conceptually very different.

davezawadi (David Stone):
 The rest of the curve over 5 seconds is very useful, it shows (as do the fuse graphs) what happens when the fuse is operated at less than the disconnection time

Well, no it doesn't. In fact, none of the curves in Appendix 3, whether for fuses or mcb's, show that - quite simply because there's a range of operation (two bounds, lower and higher) that are described for most fuses and circuit breakers, either in, or as a result of, standard requirements, or from the required manufacturer's data. Both have their uses in design, and really need to be considered - for example, in selectivity studies and to prevent nuisance tripping due to inrush currents and similar. But I think you alluded to that in your reply to Andy in respect of circuit breakers.

The purpose of the data in Appendices 3 and 4 is mainly aimed at the worst-case limiting conditions discussed in BS 7671 to comply with, for the most part, Chapters 41, 42 and 43 of BS 7671, for the majority of smaller installations. Outside this scope, you need more information (and more standards).

gkenyon:

davezawadi (David Stone):
 The rest of the curve over 5 seconds is very useful, it shows (as do the fuse graphs) what happens when the fuse is operated at less than the disconnection time

Well, no it doesn't. In fact, none of the curves in Appendix 3, whether for fuses or mcb's, show that - quite simply because there's a range of operation (two bounds, lower and higher) that are described for most fuses and circuit breakers, either in, or as a result of, standard requirements, or from the required manufacturer's data. Both have their uses in design, and really need to be considered - for example, in selectivity studies and to prevent nuisance tripping due to inrush currents and similar. But I think you alluded to that in your reply to Andy in respect of circuit breakers.

The purpose of the data in Appendices 3 and 4 is mainly aimed at the worst-case limiting conditions discussed in BS 7671 to comply with, for the most part, Chapters 41, 42 and 43 of BS 7671, for the majority of smaller installations. Outside this scope, you need more information (and more standards).

I agree with you, the Appendix 3 curves do not provide the information required to do a selectivity study.

So what are they for then?  You are suggesting that they may be used for the adiabatic equation to determine energy let through or to look at disconnection times.
 
The question is are they in the best format for the intended use.  Well given that the range of application has an upper bound of 5 second and a lower bound of 0.1 seconds presenting them as log log curves seem to me to be over complicating things.  It also makes getting accurate readings from the graphs very difficult as it is hard to estimate values between axis divisions on a logarithmic scale.

The following comments only apply to fuses because, as David Stone has pointed out, the graphs have no real meaning for mcbs (or any other device that uses a magnetic trip for high fault current protection such as mccbs).

Over the required range the five given points for times (5, 1, 0.4, 0.2, 0.1) can be plotted on linear scales.  This makes it much easier to determine the values between the given points.  I am not aware of any equation the accurately models the graph, I have tried various methods (Cubic Splines, BSplines and Polynomials together with some 'home brew' efforts) and whilst they work to some extent they are not perfect for all devices.

Given that the values plotted have a significant uncertainty there is not much error in taking a value from a graph that simply links the points by straight lines.

I have developed an application that calculates the disconnection time using various equations.  Taking as an example a BS 88-2 (E) 315 A Fuse, at a fault current of 2500A gives:

Newton Difference    BSpline         Linear Interpolation  between 5 sec & 1 sec
         2.37                     3.13                                         3.1

Try reading the value from the Appendix 3 graph - well it's somewhere between 2 and 3 - remember the scale between divisions is logarithmic!
 
IMO the result from the relatively simple linear equation is adequate for most purposes.

Regards
Geoff Blackwell

Hi Geoff,
I think I may have been slightly less than clear on the point, I meant current is less than causes fault type disconnection. Sorry if anyone was confused.

There is a severe mathematical problem plotting things on logarithmically scaled graphs (and we do it a lot for all kinds of things) in that the reason to use these scales is that they in many applications allow us to plot a straight line, which we can the use. It doesn't work for fuses or MCBs does it? Whoever chose to use this scaling has not really been very helpful, they need to calculate the underlying function they wish to plot and scale the axis using a suitable function. There is no need for this to be a log, exponential, or any other easy curve. It may mean they need to make their own graph paper but this is trivial nowadays with computers.

Now fuses, as excellently described by Mike follow an I²t heat characteristic whilst adiabatic and will need some heat loss correction at longer times. It would seem that the fuse plotted on log time against a log square law current might produce a fairly straight line. Log current is probably incorrect, and so the graphs are curved.

The MCB also depends on heat, but well outside the adiabatic region, so the current axis will be a modified square law, probably a square plus a thermal loss part which will be probably connected to temperature to a fourth power and an operating environment offset in absolute temperature.  The magnetic part has a threshold, the ampere-turns to cause disconnection, and another factor of current controlling the acceleration of the contact mechanism, so energy let through.

Whilst various kinds of curve fitting can improve the situation, a straightforward equation is the way to go for accuracy, but probably not for general electrical use. It is unlikely that a discrimination study needs more than the equation, after all, there are more factors, such as how many times a fuse has been stressed before, which will have an effect on the real performance. It is likely that we have these graphs because no one has thought it worth the effort to produce linear lines, and in fine detail, it might be quite difficult. Curve fitting is, in my view, a dangerous game unless the underlying characteristics are known, various kinds of regression analysis should be most accurate if the degree is chosen to match the underlying characteristic, but then determining this is difficult as I say above. B-splines or other spline types have all kinds of nasty end effects and become complicated to use when end connection slopes are taken into account. Linear interpolation of a curve is pretty poor, one takes one's pick depending on the effort and time available.

Graham, I do not understand what you mean. Circuit breakers and fuses give curves for 0.1 to 10,000 seconds. Time to trip or fuse under various "overcurrent" conditions can be very useful, particularly for mechanical loads on motors. BS7671 applies in all installation areas, it may not present data for higher current installations, but has all the principles and regulations for all sizes of jobs. It is true I consider the circuit breaker data on the graph grossly misleading, and it has obviously misled Andy, but manufacturers data can also have the same defect. I wonder if you think that operating a fuse at greater than its "fusing" current is in some way incorrect, the continuous rating of a circuit may be very different from short term conditions, for example for motors starting with a high inertial load, or large incandescent lamps or heating elements.

davezawadi (David Stone):
Graham, I do not understand what you mean. Circuit breakers and fuses give curves for 0.1 to 10,000 seconds. Time to trip or fuse under various "overcurrent" conditions can be very useful, particularly for mechanical loads on motors. BS7671 applies in all installation areas, it may not present data for higher current installations, but has all the principles and regulations for all sizes of jobs. It is true I consider the circuit breaker data on the graph grossly misleading, and it has obviously misled Andy, but manufacturers data can also have the same defect. I wonder if you think that operating a fuse at greater than its "fusing" current is in some way incorrect, the continuous rating of a circuit may be very different from short term conditions, for example for motors starting with a high inertial load, or large incandescent lamps or heating elements.

The graphs in BS 7671 are only the RHS of the "area" described by the range of real fuses (or circuit breakers) that come off a production line. So, whilst they are useful for some things, they are not useful for others, such as selectivity, or determining whether a "keen" fuse towards the LHS of the range will operate due to a motor starting under load. Compare the time/current characteristics of fuses shown in BS 1362, which show the whole area for 3 A and 13 A fuses:

Linked from https://pat-testing-fss.blogspot.com/2014/02/whay-13-amp-fuse-does-not-seem-to-blow.html

They are certainly peculiar graphs.

Normally one would find the desired prospective current along the abscissa, go up to the line, and then turn left to find the trip time at the ordinate. As stated above, if one is in the magnetic trip area, it does not really work.

However, one might wish to be assured that a PFC (at the end of a final circuit) is sufficient to operate ADS within the correct interval, in which case go the other way and the graphs may be more useful.

Odd that they do not have a range of values as with the ones supplied by manufacturers.

It makes sense to have a logarithmic rather than linear scale where you want to be able to read off values reasonably accurately at different scales, accommodated on a single graph. For example sometimes we are interested in slight overloads that trip in the order of 1000s. If time was on a linear scale of 0-1000, that graph would be useless for reading of values that occur in in 10s or less for example.

That is true if you want to put many devices on one graph.  However, you still have the difficulty of reading a value to contend with.  My point is that if we want to actually use this data maybe a graph of this sort is not the best way.  Simply providing data for each device for the five points given plus simply equation to obtain intermediate values might be better.

t = t1 + ( (t2 - t1) * ((I2 - I1) / (I2 - I1)) ) I think that is right but I am converting from a different form so check it before use.

Regards 

Geoff Blackwell

I did NOT suggest putting time on a linear scale, just a useful one. The BS1361 fuses have a particularly wide range Graham, because they are not really there for overload protection, just short circuit protection (or severe fault). Because of the range, one can see why this might be.
Graphs with straight lines or proper accurate equations and matching scaling are more useful. Looking at fuses, the adiabatic current ratings of fuses are set by the physics Mike outlined. They should not have huge ranges, just reasonable manufacturing tolerances. If one wishes to see the entire envelope, fair enough, but we wish in most cases to examine the worst-case time/current value. Quicker fusing is not a problem for faults to overloads, it is the longest time that is dangerous. Next time I have a spare few minutes I will attempt to produce an equation and axis scaling which produces straight lines.
Geoff, you do have an error but it is interesting (I2 - I1) / (I2 - I1) always equals 1! I think you were attempting linear interpolation, between 2 points, but this is not it. I will leave the correct answer to the student!

 

David

t = t1 + ( (t2 - t1) * ((I2 - I1) / (I2 - I1)) )  should have been t = t1 + ( (t2 - t1) * ((Ix - I1) / (I2 - I1)) ) 

The error is that I put I2 where it should have been Ix.  The result is now the same as my application produces.  This application also graphs all of the equations and by inspection the given result is probably correct.

Putting the values in for the 315A fuse

t = t1 + ( (t2 - t1) * ((Ix - I1) / (I2 - I1)) ) 

5 + (( 1 - 5) * ((2500 - 2000)/(3050 - 2000)) )

5 + ( (-4)*((500)/(1050)) ) = 3.1 seconds as required

t1 = 5 sec
t2 = 1 sec
I2 = 3050A (current that gives 1 sec)
I1 = 2000A (current that gives 5 sec)
Ix = 2500A (current used for my example)

IMO for most practical engineering use this is as accurate as it needs to be.  Cables only come in a limited number of sizes!

Regards
Geoff Blackwell

You are not the student Geoff. 10/10!!

You are correct of course about cable sizes, but I would like to change those graphs. I think your result is at least as accurate as we need, and we could also make the MCB graphs rather better without the "instant trip" vertical by adding the calculation from the let-through energy and available PSCC. I will write something down.

Regards
David