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short circuit cable temperature considerations

short circuit cable temperature considerations

short circuit cable temperature considerations

(OP)
Hi,

When sizing a cable you need to take into consideration among other things short circuit temperature performance.  Here is Australia we use AS3008 to size cables for 600v or lower (apparently very similar/interchangeable to european standard IEC 267??? - I can't remember the number).

I remember doing a course where the presenter said it was pretty unusual for a cable size calculation to be impacted by short circuit temperature considerations - so I have never given it much thought but the other day I decided to check if a 2.5mm2 PVC cable was OK connected to a switchboard with a 6kA fault level (pretty common scenario) to my surprise it was not!!!  Can you guys check this is right?  My calc as follows:

formula (I^2)t = (k^2)(s^2) where I is the fault level (amps), t is clearing time (secs) k = 111 based on copper PVC going to 160 degrees and s is size (mm2) of cable (2.5).  Assuming a 20A C type MCB, clearing in 0.01 seconds. I get:

s = 5.4mm2 minimum cable size.  Which suggests although 2.5mm2 meets nominal current load and voltage drop considerations it is too small at a rather smallish fault level of 6kA.

My only other thought that would make 2.5mm2 OK is that the MCB limits the let-though fault energy the cable is exposed to, to less than the energy the cable can deal with under fault conditions.  In this case for 2.5mm2, (I^2)t let though must be less than: (111^2)(2.5^2) = 77006 A^2s.

Checking a datasheet for a Terasaki Din-T 10kA C20, they have a graph showing that the MCB will only let through about 20000 A^2s of energy at 240/415V.  Given this is less than 77000, does this mean the circuit breaker makes it safe to install a 2.5mm2 cable at a 6kA fault level?

Anyone know of any standards or books/resources that demonstrate this calculation better?  It seems some MCB manufacturers don't publish let-though energy so you can't assume a MCB will protect a cable in this instance without it....can you?


 

RE: short circuit cable temperature considerations

But the cable won't be damaged by a fault at its source end.  If the fault is in the cable it is damaged anyhow.  Look at what happens for a fault beyond the end of the cable, a through fault.  It is the through fault condition that you have to be concerned with, and your small conductors have a tendency to be very limiting on the amount of through fault current.

RE: short circuit cable temperature considerations

I did a math check of your calc and agree if you assume 75C initial temperature.  Specifically, with Tinitial=75C,  Tfinal = 160C, copper conductor of area 54. mm^2, my calculations give get k=111, I^2*T = 361400, T = 0.01 seconds.

I don't know how this applies to your particular cable. Good point by davidbeach that the 6ka would only be relevant as a through-fault.   

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RE: short circuit cable temperature considerations

That was 5.4 mm^2, not 54.2 mm^2

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RE: short circuit cable temperature considerations

Of course both dpc and electricpete are right.
According to IEC 60865-1 Short-circuit currents Calculation of effects
Smin=SQRT(Ith^2*Tk)/k where Smin is the minimum required conductor cross section, Ith=Thermal equivalent short-time current
Tk is the total fault duration [or sum of durations if there are more than one connection and breaking times]
According to DIN VDE 100 Part 540  k depends upon conductor and insulation material.
For copper conductor and PVC insulation  from ambient [30 oC] k= 143 and from rated[ 70 oC] k=115.
Ith=I"k*sqrt(m+n)  where I"k is the initial symmetrical short-circuit current.
m=factor for heating effect of the D.C. component, n=factor for heating effect for a.c. component.
m depends on Tk , frq, kappa where
kappa=factor for calculation of peak short-circuit current kappa=1.02+0.98*exp(-3*R/X) [according to IEC 60909].
For low voltage system R/X=0.05 approximate then kappa= 1.9
According to IEC 60865-1 Fig 12 a m=1.8
n depends upon I"k/Ik and Tk .For frq=50 Hz and Tk=.01 n=1 approximate.
So for I"k=6 KA  Ith=6*1000*sqrt(1.8+1) =10000 A.
Smin=10000*sqrt(0.01)/115= 8.7 sqr.mm
 

RE: short circuit cable temperature considerations

Quote (7anoter4):

Of course both dpc and electricpete are right.
Now, I'll admit that dpc usually has things right, but even before he posts in the thread?

RE: short circuit cable temperature considerations

I am very sorry, indeed. I meant not dpc but davidbeach of course!Mea culpa, I am sorry.

 

RE: short circuit cable temperature considerations

(OP)
Thanks guys - some good points - still not sure I am confident with where it leaves me - some further points to consider:

(1)davidbeach - great point about the through fault being the only real concern but, consider this: A cable is sourced from a 6kA switchboard and terminates at a load where fault level has dropped to 3 kA.  The cable is sized so that it can withstand 3kA for 0.01s (i.e. fault at load end).  A bolted fault then occurs half way up this cable where fault level is 4.5kA and it clears in 0.01 seconds.  Because the cable was only sized to withstand 3kA the cable catches fire at some point above the fault.  If the whole cable had been sized for 6kA, the fire would never have happened.  Also what if the fire didn't happen but the cable was damaged due to high current and the sparky simply repaired the cable at the fault area - we now have a damaged cable in use.  Is this a valid reason to size the whole cable for 6kA instead of 3kA ?
(2) 7anoter4 - thanks for the calculation.  I have never seen that formula quoted in Australian standards.  Somewhat worrying that it resulted in a larger conductor size than the (I^2)t = (k^2)(s^2) equation we are supposed to use here...
(3) Does anyone agree with my reasoning that a fault current limiting mcb will protect the cable even at 6kA given that it's let through energy is less than the smaller conductor cope with?

Thanks again guys - more comment on the above would be appreciated.
 

RE: short circuit cable temperature considerations

The equation I used which matched your results is derived here.  
thread237-238191: Time to delta T
(in particular see the ABB attachment in last post of the thread for the simplest form of the equation).

It assumes sinusoidal current.  

In contrast, 7anoter4's equation seems to be modeling a fault current with a sinusoidal component plus an exponentially decaying dc component of current... which is what would usually be expected for suddenly-occuring fault fed through an inductive source impedance.  

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RE: short circuit cable temperature considerations

Cable isn't likely to catch fire, but it will likely suffer insulation damage.  But since the cable is already damaged and needed to be replaced anyhow, no additional risk or cost.  After all, those withstand ratings are for damage of the insulation, not fusing of the conductor itself.  Insulation damage occurs far sooner than conductor damage, but the whole thing is of no further use if the insulation in damaged.

RE: short circuit cable temperature considerations

(OP)
electricpete - thanks for the calculation links.  So, generally speaking, is it OK to use the simplified case for LV protection calcs (i.e assume no decaying dc component).

davidbeach - I take your point but I was thinking if you sized the cable to withstand the source side fault level it would be OK to reuse all/portions of the cable after a fault that occurred along the cable (e.g. cut and rejoin at site of fault) rather than just throw the whole thing away after a fault.  This way the insulation would be fine to reuse.  Rather than insulation that just cooked itself due to undersizing.  Again I think this would usually be theoretical if a current limiting circuit breaker is used as let-though energy is small enough - but would need that confirmed?

RE: short circuit cable temperature considerations

It seems to me that are some differences between IEEE and IEC mainly on permissible temperature [rated and short time].In this case, as electricpete did, one has to recalculate k [from Smin=Ith*sqrt(Tk)/k].I'd prefer  to follow IEEE 80 way.
A= ALPHA * RO * 10 ^ 4 / TCAP
B=Ln(1+(T1-T2)/(K[oC]+T2))
Where :
T1= Short time max. permissible temp.[oC]
T2= Rated temperature [oC]
ALPHA= Resistance thermal coefficient
K [oC]=1/ALPHA-20
RO=specific resistance at 20oC[ohm.cm]
TCAP=Volumetric Heat Capacity [J/cm^3/oC]
k=100*sqrt(B/A)
Covering Material
       PVC         XLPE     EPR
T2     75            90           90  
T1     160         250          250
Conductor Material
                Copper      AL
ALPHA   0.00393    0.00403
K[oC]        234           228
RO            1.724         2.862
TCAP         3.422       2.556
 

RE: short circuit cable temperature considerations

If you're willing to reuse possibly damaged conductor go right ahead and do so.  I have no feel for conductor sizes in mm2, but 6kA fault current suggests something rather small, as the lowest level panel rating I've encountered is 10kA.  I'd just figure on replacing anything small.  I might be more interested in splicing in a repair on larger conductors, but then there is generally not a fault damage concern for many installations.

RE: short circuit cable temperature considerations

(OP)
Thanks for the data 7anoter4.

Cheers davidbeach.  The system described was just for examples sake.  I take your point where you would just replace a 2.5mm2 cable (very small - used for general light and power) - but I was interested in the answer for a generic case where fault levels may be more around the 40kA mark and conductors up to maybe 500mm2 (capable of 800 amps).  Our standard doesn't seem clear if you should size to withstand fault at source as well as load end - so I'll just assume both to be safe - which should be fine with a fault current limiting circuit breaker anyway.

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