DC Short Circuit Calculations

[Ahmed Abdelfattah]

Hi,

I'm working on calculating the arc flash for 125VDC system. The first step was to calculate the battery contribution to the short circuit.

Per IEEE 946 (Annex E), it is mentioned that the inductance of the cable between the battery bank and the distribution bus needs to be taken into account. It is understood that this inductance is very small as compared to the cable resistance. Therefore, it doe not have any significant impact on the cable impedance. The reason why this inductance is important is that it affects the short-circuit time constant for the battery contribution which has some impact on the overall short circuit for both the batteries and the charger.

My question is; How to calculate the inductance of a cable under DC short circuit?

Thanks,
Ahmed

 

[Phil Corso]

Ahmed...

If the 125-V battery consists of a number of 2-volt cells in series, say, 3-rows of 20 cells each, then the total resistance is based on the total length of inter-cell connecting cables! But, just as important, depending on configuration the positive and negative leads could end-up being some distance apart... e.g. maybe 2 ft or more! Then, for the conditions noted inductance may be signifiant!

Also, remember inductance does not limit fault-current magnitude, but will impact fault-current rate-of-rise! Thereby, affecting available fault-current at time of interruption!

Regards, Phil Corso

 

[Ahmed Abdelfattah]

for the conditions noted inductance may be significant!

Thanks Phil.
Any idea on how to calculate this inductance?

 

[Phil Corso]

Thanks Phil. Any idea on how to calculate this inductance?

Ahmed…

You probably know how to calculate battery-cell resistance! But, I forgot to tell you about including battery-cell inductance!

My ref for cable is F.W. Grover’s, Inductance Calculations”, but his calculations use metric units! Fortunately, I recall a project I had while working for US Gypsum (ca 1956)! Both Battery and Cable Inductances were calculated in English-units!

Will get back to you when I recover it!

Phil

 

[Besoeker]

Ahmed…

You probably know how to calculate battery-cell resistance! But, I forgot to tell you about including battery-cell inductance!

My ref for cable is F.W. Grover’s, Inductance Calculations”, but his calculations use metric units! Fortunately, I recall a project I had while working for US Gypsum (ca 1956)! Both Battery and Cable Inductances were calculated in English-units!

Will get back to you when I recover it!

Phil

Why not just post it and do the conversions?

 

[Ingenieur]

This should be close for a 2 wire ckt where d>>r

 

[Ahmed Abdelfattah]

Phil,
I agree with Besoeker. If you can send me "F.W. Grover’s, Inductance Calculations" with the metric units. The conversion should be easy.. I think.

Ingenieur,
Can you please send me the reference document which includes the formula that you mentioned?

 

[Besoeker]

This should be close for a 2 wire ckt where d>>r

Care to define what the variable terms are?

 

[Ingenieur]

Care to define what the variable terms are?

r conductor radius
d distance between conductors

text pulled from, I have the book, not a file
https://www.amazon.com/Electrical-Transients-Power-Systems-Greenwood/dp/0471620580

 

[Ahmed Abdelfattah]

r conductor radius
d distance between conductors

text pulled from, I have the book, not a file
https://www.amazon.com/Electrical-Transients-Power-Systems-Greenwood/dp/0471620580

Thanks Ingenieur...
Fortunately I have this book. Never thought of looking into it.

 

[Ingenieur]

Thanks Ingenieur...
Fortunately I have this book. Never thought of looking into it.

it is for a 2 conductor single phase ckt
should be sufficient for a 2 wire dc ckt
as you said the bigger factors are
battery internal R
conductor R
as you see as d and r converge it goes to 0
you can assume a very low x/r for your calcs
makes a difference subtransient but since R>>X dampens quickly

should be similar to an ac faults dc component
I have a text on hvdc transmission but it's at work
if it has anything relevant I'll post it

 

[topgone]

Hi,

I'm working on calculating the arc flash for 125VDC system. The first step was to calculate the battery contribution to the short circuit.

Per IEEE 946 (Annex E), it is mentioned that the inductance of the cable between the battery bank and the distribution bus needs to be taken into account. It is understood that this inductance is very small as compared to the cable resistance. Therefore, it doe not have any significant impact on the cable impedance. The reason why this inductance is important is that it affects the short-circuit time constant for the battery contribution which has some impact on the overall short circuit for both the batteries and the charger.

My question is; How to calculate the inductance of a cable under DC short circuit?

Thanks,
Ahmed

Ahmed,
Please read more from this link.

 

[Ingenieur]

Ahmed,
Please read more from this link.

That is a good link
thnx, will be saved
DC is still used in mining, 250 VDC
We usually ignore L since we are only concerned with the max magnitude

 

[Ahmed Abdelfattah]

Ahmed,
Please read more from this link.

Excellent document. Thanks a lot.

 

[drcampbell]

r conductor radius
d distance between conductors

text pulled from, I have the book, not a file
https://www.amazon.com/Electrical-Transients-Power-Systems-Greenwood/dp/0471620580

Length isn't a factor?

 

[Ingenieur]

Length isn't a factor?

I did not write the text

but it appears it is based on unit analysis
µ₀ = 4π × 10⁻⁷H·m^{−1
or H/m
the other units cancel so the result is H/m
total L = the equations result x length}

but for his use does not matter since all he needs is the time constant
and the lengths cancel
tc = L/R
but it is moot anyways
first the max isc = v/R
all the L does is dampen the rise
but still moot
assume that R is = to L or tc = 1 (unlikey L that large compared to R
at 0.01 sec (0.6 60 Hz cycles) isc is at 99% max

that is why it is typically ignored except for hvdc applications where d>>>r

in the case where d ~ r as when 2 conductors in a conduit
L approaches 0

 

[mivey]

I did not write the text

but it appears it is based on unit analysis

That is correct: per meter. Per mile or per ft formulas tend to have the permeability constant converted into a decimal included with the other factors.

 

[Ingenieur]

Looking at nec tables they give Xl and R for a 3 ph ckt per 1000'
can be converted to single phase but it cancels out for tc

example
eg 1/0 Cu in pvc
Xl 0.044 so L = 0.117 mH per 1000'
R 0.12
note length does matter for tc since it cancels
tc = 0.001 sec
solve for i at 0.1 cycle or 0.0017 sec
i = 99.999% of max
is there a cb or fuse that trips in less than 0.0017 sec / 0.1 cycle?

 

[Ingenieur]

Using the formula I previously posted
assume 1/0 as above

r = 0.372/2 = 0.186"
assume d 3 x r (2 cond r + a gap of 1r center to center)

L = ((4 Pi 10^-7) / Pi) x (ln ((3r - r)/r) + 0.25) = 3.77 x 10^-7 H/m
converted to 1000' = 0.115 mH
Very close to the nec table value of 0.117 mH posted above
a reasonable sanity check

 

[junkhound]

For decades for a 1st cut number have simply used 300 NH per foot or 1 uH per meter. As good as anything for mast cases.

If critical applications, either mock it up and measure or use one of the electromagnetic FEA analysis programs

For aerospace use even the fancy/pricey full FEA programs relay on correct inputs, so nearly always do a mockup and measure, have never trusted models or calculations for critical/complex systems.

Just because you can calculate it does not mean your inputs are correct, as per the 1960 computer sayings, 'garbage in, garbage out".