Earthing Conductor Size- Good?

[Cookie]

Alright, so what do you think of these CPC sizes in relation to the phase conductors?


90*C insulation, TN-C-S supply


MCB / Live / CPC / Multiplier

15 - 2.08mm2 - 2.08mm2 - X 1

20 - 3.31mm2 - 3.31mm2 - X 1

60 - 13.30mm2 - 5.261mm2 - X 0.3955

100 - 26.67mm2 - 8.367mm2 - X 0.3137

200 - 85.01mm2 - 13.30mm2 - X 0.1564

300 - 177mm2 - 21.15mm2 - X 0.1195

400 - 304mm2 - 26.67mm2 - X 0.0877

500 - 456mm2 - 33.62mm2 - X 0.0737

600 - 760mm2 - 42.41mm2 - X 0.0558


0.3, 0.1 and 0.05 multiplier difference ever encountered in the UK?

 

[Cookie]

Sorry for the way the forum compresses the table. That wasn't my intent.

 

[DefyG]

Where have the figures come from as obviously not standard UK cable sizes?

 

[Cookie]

NFPA 70, National Electrical Code. I can link the tables if it will help.

 

[DefyG]

NFPA 70, National Electrical Code. I can link the tables if it will help.

Thanks but don't think it will as I/we work to standard UK cable sizes and BS 7671.
Typically, a 100A supply would be 25mm and earth size determined by tables /calc from BS 7671 and/or adiabatic equation!

 

[Cookie]

Right, but the physics are still the same. I'm wondering if these CPCs are ok or not from a theory perspective.

 

[DefyG]

If they are tabulated in the NFPA document I guess someone somewhere in the US has previously done the calculations to prove they are?

 

[Cookie]

If they are tabulated in the NFPA document I guess someone somewhere in the US has previously done the calculations to prove they are?

Well, that would be an assumption...

 

[DefyG]

Well, that would be an assumption...

It would just as we in the UK assume the tabulated values in BS 7671 have been calculated and vetted by others before going to print. We don't go out of our way to prove them wrong but might need to verify a conductor by use of adiabatic calc!
Not really sure what your point is, if non standard sizes seems meaningless!

 

[streamer]

It would just as we in the UK assume the tabulated values in BS 7671 have been calculated and vetted by others before going to print. We don't go out of our way to prove them wrong but might need to verify a conductor by use of adiabatic calc!
Not really sure what your point is, if non standard sizes seems meaningless!

@DefyG I've just googled the sizes and it seems they are the metric equivalent of AWG (American wire gauge) system so it seems they are standard American sizes. Every day's a school day!

 

[Cookie]

It would just as we in the UK assume the tabulated values in BS 7671 have been calculated and vetted by others before going to print. We don't go out of our way to prove them wrong but might need to verify a conductor by use of adiabatic calc!
Not really sure what your point is, if non standard sizes seems meaningless!

These are standard sizes for North and South America.

The ratio between live and earth is huge, so much so my point revolves around the uncertainty that that the CPC will survive a fault.

 

[DefyG]

Non standard to the UK so meaningless to me and I'm sure other UK electricians as I am not upto speed with the US regulations on conductor sizes or calculation using a US adiabatic formula!
Have you tried calculating yourself to prove the sizes are ok or not?
Need more information in any case.
Perhaps the US regulations do not allow for protection of the cable in the event of a fault?

 

[Cookie]

Non standard to the UK so meaningless to me and I'm sure other UK electricians as I am not upto speed with the US regulations on conductor sizes or calculation using a US adiabatic formula!
Have you tried calculating yourself to prove the sizes are ok or not?
Need more information in any case.

Truth be I'm not sure how to go about calculating them as there is nothing explicit in the NEC about it. Closest thing is the formula for tap conductors. Which I guess could work in theory.

Perhaps the US regulations do not allow for protection of the cable in the event of a fault?

That has gone through my mind, and thats what I'm trying to figure out to be honest.

 

[Cookie]

This applies to tap conductors, but nothing in regards to the CPC.

 

[pc1966]

0.3, 0.1 and 0.05 multiplier difference ever encountered in the UK?

Not as "rule of thumb" design, typically ours is 0.5 or a few smaller ones in the case of T&E which are normally limited to the 6-50A region.

Those cable sizes are mostly OK provided your breaker operates fast (i.e. magnetic trip) and your PFC is moderated for the smaller sizes. Running adiabatic calculations for k=100 (typical copper 90C thermoplastic) I get:

MCB​	Live​	CPC​	Multiplier​	I2t limit​
15​	2.08​	2.08​	1​	4.33E+04​
20​	3.31​	3.31​	1​	1.10E+05​
60​	13.3​	5.261​	0.3955​	2.77E+05​
100​	26.67​	8.367​	0.3137​	7.00E+05​
200​	85.01​	13.3​	0.1564​	1.77E+06​
300​	177​	21.15​	0.1195​	4.47E+06​
400​	304​	26.67​	0.0877​	7.11E+06​
500​	456​	33.62​	0.0737​	1.13E+07​
600​	760​	42.41​	0.0558​	1.80E+07​

Looking at some let-through curves for Hager 100A-250A MCCB (just to hand) it is showing about 5E5 at 5kA PFC, and 4E6 at 40kA PFC. Hence short runs on a 40kA board for your CPC at 200A and below are at risk, even for a high but not unheard of "domestic" fault of 5kA, your 60A and below is at risk.

Of course, depending on the length and so on, it might be OK. But to me it is really marginal as if you have Zs and/or fault impedance that fails to hit the magnetic trip region then those MCCB let-through values are in the 6E6 to 6E7 region and a risk of burning them out even at the highest size in that table.

 

[Cookie]

Can you explain what 5E5 and the number in the I2R column mean?

US breakers do not always trip magnetically either due to the run length or high pickup. Some older breakers did not have a magnetic trip.

You make a valid point about high current, I was thinking about low current from long runs but ultimately I need to consider both.

 

[pc1966]

The smaller sizes (60A and below) look OK for C-curve MCBs which would be expected anyway. But those would be limited in the UK to typically 6kA domestic or 10kA commercial max PFC.

It would be unusual to be taking smaller cables direct from a crazy-high PFC board anyway, usually a board with ~1kA load and tens of kA PFC would feed ~100A sub-boards for low current end circuits, and by then the PFC is somewhat more sane to wrangle with a MCB.

 

[Cookie]

The smaller sizes (60A and below) look OK for C-curve MCBs which would be expected anyway. But those would be limited in the UK to typically 6kA domestic or 10kA commercial max PFC.

It would be unusual to be taking smaller cables direct from a crazy-high PFC board anyway, usually a board with ~1kA load and tens of kA PFC would feed sub-boards for low current end circuits, and by then the PFC is somewhat more sane to wrangle with a MCB.

Agree.

FWIW in some cases you do have 3.31 and 5.261mm2 wire coming out of a 22ka or 65ka panel board though fortunately its not ultra common.

 

[pc1966]

FWIW in some cases you do have 3.31 and 5.261mm2 wire coming out of a 22ka or 65ka panel board though fortunately its not ultra common.

Wow, that looks scary to me!

I know some MCCB also have HRC fuses to act as ultimate peak fault current limiters, but I suspect those in your picture are just normal therma-magnetic MCCB.

 

[Cookie]

Wow, that looks scary to me!

I know some MCCB also have HRC fuses to act as ultimate peak fault current limiters, but I suspect those in your picture are just normal therma-magnetic MCCB.

Yup, standard thermal mags.

I can't see that small gauge wire surviving. But hey, if the NEC lets you get away with it...

 

[pc1966]

Can you explain what 5E5 and the number in the I2R column mean?

It is just the I2t values scientific notation, sometime in lazy format. So:

500,000 = 5 * 10^5 = 5.0E+05 = 5E5

US breakers do not always trip magnetically either due to the run length or high pickup. Some older breakers did not have a magnetic trip.

No magnetic trip sounds like an utter disaster for any usable protection. The thermal element is simply not fast enough (unlike a fuse, but its heating element is on a one-way trip to vapour).

You make a valid point about high current, I was thinking about low current from long runs but ultimately I need to consider both.

Yes, your worst-case is not always the highest fault.

Usually fuses decrease in I2t as you go from low overload / long disconnect to high current fast faults. There it is the longest time (highest Zs, etc) that is worst.

MCCB & MCB have two regions, the thermal one is quite slow so the 't' in I2t is large, and while the magnetic trip is fast at ~10ms in many cases, it does not get faster or limit the fault current to a great degree as PFC goes up. So typically your worst-case points in the breaker design is either max PFC, or just below the magnetic trip point where 't' is long but 'I' is fairly high.

 

[UKPN]

Thanks but don't think it will as I/we work to standard UK cable sizes and BS 7671.
Typically, a 100A supply would be 25mm and earth size determined by tables /calc from BS 7671 and/or adiabatic equation!

ESQCR/DNO decide earthing conductor sizes. In the case above its 16sqmm. bonding, 10mmsq

 

[Cookie]

It is just the I2t values scientific notation, sometime in lazy format. So:

500,000 = 5 * 10^5 = 5.0E+05 = 5E5



Yes, your worst-case is not always the highest fault.

Usually fuses decrease in I2t as you go from low overload / long disconnect to high current fast faults. There it is the longest time (highest Zs, etc) that is worst.

MCCB & MCB have two regions, the thermal one is quite slow so the 't' in I2t is large, and while the magnetic trip is fast at ~10ms in many cases, it does not get faster or limit the fault current to a great degree as PFC goes up. So typically your worst-case points in the breaker design is either max PFC, or just below the magnetic trip point where 't' is long but 'I' is fairly high.

I'm still confused as to what the I2t limit represents. Joules?

No magnetic trip sounds like an utter disaster for any usable protection. The thermal element is simply not fast enough (unlike a fuse, but its heating element is on a one-way trip to vapour).

I will go trip curve hunting- however- I think my eyes were just opened again... you might be right. As in spot on. But I'm still willing to challenge the concept. ?

Ok- here is a commercial/industrial US breaker trip curve:

https://library.industrialsolutions.abb.com/publibrary/checkout/GES6237B?TNR=Time%20Current%20Curves%7CGES6237B%7CPDF&filename=GES6237.pdf

If I'm reading the above time current curves correctly:

0.8 disconnection time on thermal takes about (roughly) 15x the handle rating worse care.

0.4 disconnection time on thermal takes about (roughly) 22x the handle rating worse case.

Assuming a 20 amp breaker-

15 x 20= 300 amps. At 120 volts a loop of 0.4 ohms is required.

22 x 20= 440 amps. At 277 volts a loop of 0.62 ohms is required.


A 500 foot circuit run consisting of 3.31mm2 wire has a R1+R2 of 2 ohms.


3.31mm2 wire has an 60Hz AC Resistance of 0.002 ohms per foot at 75*C.

At 120 volts I am limited to a 100 foot run. (30 meters)

At 277 volts I am limited 50 a 155 foot run. (47 meters)

Not unrealistic for a good chunk of circuits.

Technically I am incorrect to use 120 and 277 volts in that supplies vary below this value, but at the same time a 75*C resistance covers it reasonably well for the discussion at hand IMO.

Am I correct to conclude that it is indeed possible to provide adequate disconnection times with US breakers when the fault current does not trip the breaker magnetically? Or is this just me being overly wishful?


My mind keeps telling me that it is possible to achieve 0.8 and 0.4 with thermal elements. But I am humble in my argument. ?

 

[Cookie]

Here is where I obtained my 2 ohms per 1000 feet for 3.31mm2 wire (12 gauge). NEC chapter 9 table 9:

 

[pc1966]

I'm still confused as to what the I2t limit represents. Joules?

The units are 'Ampere^2 second' and it represents Joules per ohm of resistance.

So if you know the resistance per unit length of your conductor (from material resistivity and cross sectional area) it allows you to compute the resulting fault energy per unit length. Then from the specific heat capacity of the material and its mass per unit length you can compute the change in temperature that fault energy causes.

From knowledge of the starting temperature and the peak short-term survival temperature of the cable (typically decided by the insulation type) you can decide if that fault is going to permanently damage the cable or not (i.e. will the fault delta-temperature exceed your operating margin).

In most cases the material properties (resistivity, specific heat capacity, temperature limits) are combined in to a single constant 'k' that is used in the adiabatic cable equation.

 

[pc1966]

Ok- here is a commercial/industrial US breaker trip curve:

https://library.industrialsolutions.abb.com/publibrary/checkout/GES6237B?TNR=Time%20Current%20Curves%7CGES6237B%7CPDF&filename=GES6237.pdf

If I'm reading the above time current curves correctly:

0.8 disconnection time on thermal takes about (roughly) 15x the handle rating worse care.

0.4 disconnection time on thermal takes about (roughly) 22x the handle rating worse case.

Yes, it looks like that.

It has a magnetic trip as well, but not coming in until very high. It also appears (from my reading of the plot) that the magnetic trip is fixed at about 540-900A (36-60 * 15A) as you see the 30A range is about half of the multiplier.

That sort of fixed-magnetic approach is not uncommon for MCCB over here, but our MCB all have the magnetic trip at a set ratio of the thermal trip (our B/C/D curves). That example USA breaker is above our D-curve (10-20 * In) by a factor of almost 4 at 15A and 2 at 20A.

In UK domestic installations is is rare even to see C-curve being used, and D-curve is usually restricted to very high inrush things like big transformers or motors.

Assuming a 20 amp breaker-

15 x 20= 300 amps. At 120 volts a loop of 0.4 ohms is required.

22 x 20= 440 amps. At 277 volts a loop of 0.62 ohms is required.

A 500 foot circuit run consisting of 3.31mm2 wire has a R1+R2 of 2 ohms.

3.31mm2 wire has an 60Hz AC Resistance of 0.002 ohms per foot at 75*C.

At 120 volts I am limited to a 100 foot run. (30 meters)

At 277 volts I am limited 50 a 155 foot run. (47 meters)

Not unrealistic for a good chunk of circuits.

Those look right and reasonable, though you have not allowed for the supply impedance (probably quite small for USA with 200A boards and TN-C-S style of connection as common).

Technically I am incorrect to use 120 and 277 volts in that supplies vary below this value, but at the same time a 75*C resistance covers it reasonably well for the discussion at hand IMO.

Yes, voltage range and starting temperature for working resistance would reduce that distance by 20-30% or so.

Am I correct to conclude that it is indeed possible to provide adequate disconnection times with US breakers when the fault current does not trip the breaker magnetically? Or is this just me being overly wishful?

My mind keeps telling me that it is possible to achieve 0.8 and 0.4 with thermal elements. But I am humble in my argument. ?

You are right that they can meet our sort of disconnection times on the thermal part. But are doing so at far higher currents than we would expect to see without the magnetic part tripping.

Much of your example thermal curve is "inverse time" and approximately constant I2t, so a reasonably good match for cable protection. But it is allowing of the order of 45k A2s let-through for a 15A breaker, and we would only expect to see that sort of a fault energy at PFC of around 10kA, or at around 40A when it is quite slow to trip and some of the fault heat is able to escape (so less "adiabatic" in the true sense).

 

[Cookie]

Yes, it looks like that.

It has a magnetic trip as well, but not coming in until very high. It also appears (from my reading of the plot) that the magnetic trip is fixed at about 540-900A (36-60 * 15A) as you see the 30A range is about half of the multiplier.

That sort of fixed-magnetic approach is not uncommon for MCCB over here, but our MCB all have the magnetic trip at a set ratio of the thermal trip (our B/C/D curves). That example USA breaker is above our D-curve (10-20 * In) by a factor of almost 4 at 15A and 2 at 20A.

In UK domestic installations is is rare even to see C-curve being used, and D-curve is usually restricted to very high inrush things like big transformers or motors.

Those look right and reasonable, though you have not allowed for the supply impedance (probably quite small for USA with 200A boards and TN-C-S style of connection as common).

Yes, voltage range and starting temperature for working resistance would reduce that distance by 20-30% or so.

You are right that they can meet our sort of disconnection times on the thermal part. But are doing so at far higher currents than we would expect to see without the magnetic part tripping.

Much of your example thermal curve is "inverse time" and approximately constant I2t, so a reasonably good match for cable protection. But it is allowing of the order of 45k A2s let-through for a 15A breaker, and we would only expect to see that sort of a fault energy at PFC of around 10kA, or at around 40A when it is quite slow to trip and some of the fault heat is able to escape (so less "adiabatic" in the true sense).

Your observation is correct, the magnetic trip pickup values are fixed for a lot of thermal magnetic breakers across the product line meaning 15-30, 40-70, 80-125, ect all have the same magnetic pickup with only the thermal portion of the breaker differing to match the handle rating. Not all breakers, but roughly about 40-50% of the market.

Here is another example of a fixed magnetic pickup:

https://download.schneider-electric...ng&p_File_Name=50-01.pdf&p_Doc_Ref=0050TC0401

From what I've been told the (but can't confirm) is that the magnetic pickup is primarily intended to protect the panel board's busbars and supports from short circuit stress during high current faults.

If I am correct France is big on type C breakers for socket circuits.

I did leave out Ze in those equations which would change the values by 5% having run the numbers. Typically the transformer is close to the building with over sized service conductors so Ze tends to be negligible in comparison.

Its good/comforting to know that US breakers can meet disconnection times on thermal pick-up alone. However as I've said before the NEC does not restrict circuit length so it is legally possible to exceed 0.4 or 0.8 seconds.

My biggest concern however which had me start this thread are the size of the CPCs mandated under the NEC. While I am fairly confident that high short circuit levels will prevent the CPC from over heating longer circuit runs and slow thermal trip could push the CPC over 150*C (the recommended temperature limit) during a short circuit.

For example, 2000 amps on a 13.3mm2 CPC (200 amp breaker) for 5 seconds would heat the conductor substantially.

 

[Cookie]

The units are 'Ampere^2 second' and it represents Joules per ohm of resistance.

So if you know the resistance per unit length of your conductor (from material resistivity and cross sectional area) it allows you to compute the resulting fault energy per unit length. Then from the specific heat capacity of the material and its mass per unit length you can compute the change in temperature that fault energy causes.

From knowledge of the starting temperature and the peak short-term survival temperature of the cable (typically decided by the insulation type) you can decide if that fault is going to permanently damage the cable or not (i.e. will the fault delta-temperature exceed your operating margin).

In most cases the material properties (resistivity, specific heat capacity, temperature limits) are combined in to a single constant 'k' that is used in the adiabatic cable equation.

Any idea of the k factor for my wires above?

 

[pc1966]

Any idea of the k factor for my wires above?

A quick search pulls this up with a lot of details:

myCableEngineering.com > The adiabatic equation

Electrical cable sizing software. Current capacity to BS 7671, ERA 69-30 and IEC 60502. Impedance and voltage drop to IEC 60909 and CENELEC CLC/TR 50480. Cloud based - any device, anywhere.

mycableengineering.com

For copper wire and 70C PVC (common case) then k=115

 

[pc1966]

Your observation is correct, the magnetic trip pickup values are fixed for a lot of thermal magnetic breakers across the product line meaning 15-30, 40-70, 80-125, ect all have the same magnetic pickup with only the thermal portion of the breaker differing to match the handle rating. Not all breakers, but roughly about 40-50% of the market.

OK, that makes sense from a production cost point of view. Probably similar argument for MCCB, but there the use of a very high magnetic trip point can help with selectivity (depending on down-stream fault impedances)

If I am correct France is big on type C breakers for socket circuits.

Possibly. But commonly they use 16A/20A for a few radials, where as we tend to have 32A B-curve on a lot of sockets with individual HRC fuses in the 3-13A range.

I did leave out Ze in those equations which would change the values by 5% having run the numbers. Typically the transformer is close to the building with over sized service conductors so Ze tends to be negligible in comparison.

Its good/comforting to know that US breakers can meet disconnection times on thermal pick-up alone. However as I've said before the NEC does not restrict circuit length so it is legally possible to exceed 0.4 or 0.8 seconds.

To me that the the main issue - that proper design to meet shock and overload safety is not always applied. Then fancy electronics is added to try and fix the results of that...

My biggest concern however which had me start this thread are the size of the CPCs mandated under the NEC. While I am fairly confident that high short circuit levels will prevent the CPC from over heating longer circuit runs and slow thermal trip could push the CPC over 150*C (the recommended temperature limit) during a short circuit.

For example, 2000 amps on a 13.3mm2 CPC (200 amp breaker) for 5 seconds would heat the conductor substantially.

Yes, the CPC table you started with looks awfully small for the larger breaker sizes (100A and above).

They are usable, but only just when the disconnection let-through is carefully controlled. To me that is not good enough for "rule of thumb" as that ought to be safe for all common combinations, and going to smaller CPC ought to be part of detailed analysis to justify it.

 

[Cookie]

To me that the the main issue - that proper design to meet shock and overload safety is not always applied. Then fancy electronics is added to try and fix the results of that...

I'm elated to know that you can see it. Not everyone can. AFCIs and GFCIs are being applied to fix a problem that the NFPA will not admit to. I'd be banned for saying it on a US forum, but the NFPA should not be writing electrical codes. 60 years of ignorance regarding basic electrical theory has been on perpetual display every code cycle.

Yes, the CPC table you started with looks awfully small for the larger breaker sizes (100A and above).

They are usable, but only just when the disconnection let-through is carefully controlled. To me that is not good enough for "rule of thumb" as that ought to be safe for all common combinations, and going to smaller CPC ought to be part of detailed analysis to justify it.

I think the same. But I'd like to prove it. I'm convinced that some NEC installations are a fire hazard despite being code compliant.

 

[Cookie]

A quick search pulls this up with a lot of details:

myCableEngineering.com > The adiabatic equation

Electrical cable sizing software. Current capacity to BS 7671, ERA 69-30 and IEC 60502. Impedance and voltage drop to IEC 60909 and CENELEC CLC/TR 50480. Cloud based - any device, anywhere.

mycableengineering.com

For copper wire and 70C PVC (common case) then k=115

Seems to easy vs the NEC's equation. I'm still confused though, where are they getting 143 as K?

 

[pc1966]

Seems to easy vs the NEC's equation. I'm still confused though, where are they getting 143 as K?

That k=143 is for "Thermosetting, 90°C (XLPE, EDR)" cable
The k=115 is for "Thermoplastic 70°C (PVC)" (and also CSA below 300mm)

 

[pc1966]

The k value is a combination of the material (same copper in both cases) but also the insulation temperature limits (max working and max survival) which differs by cable type and use.

 

[Cookie]

The k value is a combination of the material (same copper in both cases) but also the insulation temperature limits (max working and max survival) which differs by cable type and use.

Right, but how do you turn these variables into a number?

 

[pc1966]

Right, but how do you turn these variables into a number?

Covered here:

myCableEngineering.com > Knowledge Base

Electrical cable sizing software. Current capacity to BS 7671, ERA 69-30 and IEC 60502. Impedance and voltage drop to IEC 60909 and CENELEC CLC/TR 50480. Cloud based - any device, anywhere.

mycableengineering.com

The temperature effect is not quite as simple/linear as described earlier due to the conductor resistance increasing with heating (so a positive feedback situation here), hence the formulae including 'beta' for that coefficient and its non-linear solution with logs and square root.

But equally that is why fuses go so quickly when you get past a certain point and limit energy so effectively!

 

[Cookie]

Covered here:

myCableEngineering.com > Knowledge Base

Electrical cable sizing software. Current capacity to BS 7671, ERA 69-30 and IEC 60502. Impedance and voltage drop to IEC 60909 and CENELEC CLC/TR 50480. Cloud based - any device, anywhere.

mycableengineering.com

The temperature effect is not quite as simple/linear as described earlier due to the conductor resistance increasing with heating (so a positive feedback situation here), hence the formulae including 'beta' for that coefficient and its non-linear solution with logs and square root.

But equally that is why fuses go so quickly when you get past a certain point and limit energy so effectively!

That is unless anyone knows the 150*C impedance of the circuit?

Is using a k of 226 realistic for 90*C PVC insulation?

 

[pc1966]

k is not 226, it is 226 times a factor based on start/stop temperatures.

So if you plug in some values for your cable it ought to give to something closer to the k=100-150 range normally seen.

 

[pc1966]

Here is a simple spread sheet co compute the k values for copper, aluminium and iron based on that web page. Gives numbers very close to tabulated.

OK, so I can't upload a spreadsheet!

 

[Cookie]

k is not 226, it is 226 times a factor based on start/stop temperatures.

So if you plug in some values for your cable it ought to give to something closer to the k=100-150 range normally seen.

Ok, now I'm confused.