Doan adapted Lee method to DC. This is what is in D.8 of 70E-2012. Ammerman refined it significantly by looking at a number of studies that looked at arc voltage vs. current and arc gap. The conclusion overall is that the results that have been reported, stretching all the way back to Ayrton in the early 1900's, have very similar results. The other major conclusion is that below a threshold, DC voltage (conversely, arc resistance) increases significantly. Above that threshold, arc voltage increases only slowly as arc resistance decreases. See for instance slide 12 of the report below:

http://projects-web.engr.colostate.edu/ ... n_Rev3.pdfIntuitively this makes some sense. However with all that being said, Ammerman's much more sophisticated model, though producing lower values, is within about 10% of Doan's model over the voltage/gap/current regions generally of interest. The basic equation is also very similar to the arc voltage equation used by Wilkins in developing a time domain arcing model for AC arcs, and is what I believe is probably in the model being considered by the IEEE 1584 standards committee for the next edition. So...this is the best that theory alone can offer.

Note one important result here as well. Predicting where the "knee" occurs is important. Below the "knee", there is not even enough energy to worry about an arc flash and the arc is in any case unlikely to be sustained. I have long held that this needs to be part of the consideration for DC because it fully explains why for instance arc flashes are totally nonexistant under any circumstances under 20-30 V, and are highly unlikely barring extremely high currents below around 50-100 V. This point is USED in the theoretical models but the focus is on calculating arcing voltages and currents in the constant arc voltage region and beyond, not in the low current region where arcs are weak or impossible. See the following review which is one of the presentations leading up to Ammerman's paper:

http://www.efcog.org/wg/esh_es/events/D ... rkshop.pdfHowever when comparing theory to actual measurements, we have a different story. Radiated energy is much less than predicted. Experimental data has been published but you need to read it carefully and denormalize the data.

http://www.doble.com/content/show/bosto ... Cantor.pdfThe data is normalized to 2 seconds and 12" distance. Within the report it states that for the 20 kA, 130 V, 1/2" gap case, the arc was only sustained for 0.8 seconds. Thus even if the normalized data is at 2 seconds, the arc won't even sustain that long so the result is nonsensical. Also increasing working distance to 18" as per the standard ANSI distances will decrease the value. Doing so, we get 1.3 cal/cm^2 for a 20 kA, 130 V, 1/2" gap arc flash at 0.8 seconds. If the gap increases, the arc cannot be formed. If the gap decreases, the current decreases, or the voltage decreases, the result will be less than this. Thus this appears to be the highest incident energy possible for a 125 V substation battery and even getting to 1.3 cal/cm^2 is a stretch. At the same conditions, Doan's formula predicts a value 273% higher and Ammerman's formula predicts a value 239% higher. Interestingly though the delta drops to only 26% higher at the lower 5 kA current but at this point we are well below 1.2 cal/cm^2 so it's a semantic difference.

At 260 V (in the same report), the difference between the theoretical models and actual measured values appears to be in the range of 100-200% higher so the theoretical models are less error prone for higher voltages such as if UPS systems are running at higher voltages. Thus even though again the theoretical models are wildly off, they appear to be less wildly off at higher voltages where UPS batteries and some DC motors operate.

After evaluating a lot of 125 V substation battery systems, the pattern I noticed is that at the batteries themselves, the gaps are quite large if for no other reason than the post design of the batteries themselves, but the ones I looked at are all flooded lead acid cells, not VRLA or gel cells or NiCd's. The closest gaps were at the battery charger itself and due to the large, heavy design of the leads, gap spacing was closer to the 20-30 mm spacing that is most commonly used for 480 V. I was unable to find any equipment with spacings under 1/2". This is probably in keeping with commonly available terminal strips that are intended for a 600 VAC rating. The only place I found gaps under 1/2" (12.5 mm) is for the connectors to the NiCd and NiMH batteries used in my youngest daughter's battery powered cars and scooters where the voltages are all either 12, 24, or 28 VDC.

So overall...

1. Forget about looking at arc flash for battery systems below 50 VDC, especially below 28 VDC.

2. I'm extremely dubious about substation battery systems at 125 VDC. We are right on the cusp of where empirical data shows that a significant (>1.2 cal/cm^2) arc flash MIGHT be possible under laboratory conditions but check your actual site conditions carefully. Chances are it can't happen when compared to the lab data that does exist. This is backed up by years of actual practice (has anyone reported an arc flash injury from a substation battery?) You can of course predict an arc flash exceeding 40 cal/cm^2 by simply using theoretical equations without understanding them based on theoretical assumptions such as 100% energy conversion, but garbage in = garbage out.

3. Higher voltage UPS systems might have the potential for a serious arc flash. Here we are probably limited to theory right now. Again, garbage in = garbage out.

4. What is missing is enough empirical data to predict how efficiently the energy in an arc converts to radiated heat. I believe that the Duke and Kinetrics models are based on this concept but without complete published equations, it's hard to apply them.