So the following is what I used for an Investigation to determine the Arc Flash Incident Energy w/n a Lithium-Ion Battery Bank for NASA:

Doan Method (Ref: NFPA 70E Informative Annex D), for Calculation Arc Power and Incident Energy:
Where, R1 (RBattery) = 2.67 mΩ; R2 (Rconductor)= 50 uΩ; R3 (Rarc) = TBD; Battery = 53.8 Vdc
Using the “Complete Guide to Arc Flash Hazard Calculation Studies,” by Jim Phillips; Ch.12 – “DC Arc Flash Calculations,” based on Daniel R. Doan’s Technical Paper, “Arc Flash Calculations for Exposures to DC Systems,” the following was determined:
Idc bolted = Vdc/Rdc, where Rdc = RBattery + Rconductor, and Rconductor was determined by the volume of the Cu Buss plate involved in this incident.
= 53.8V/ (2.67 mΩ +50 uΩ) = 53.8V/ (2.72 mΩ)
= 19.781X103 A
Then Idc arc = .5* Idc bolted, so:
Idc arc = .5*19.781X103 A = 9.89 X103 A
Calculating for DC Arc Resistance (Rarc):
1) G*.534, where G = gap in mm. So for a ¼” gap or G=6.35mm
G*6.35mm = 3.391mm
2) Step 1) + 20 = 23.391
3) Idc arc.88 = (9.89 X103).88 = 3,279.3
4) Rarc = Step2) / Step3) = 23.391/3,279.3 = 7.1328 mΩ
Then re-solving for Idc arc:
Idc arc = Vdc /(Rdc + Rarc) = 53.8V/ (2.72 mΩ + 7.1328 mΩ)
= 5.4604 X103 A
Note: Both Rarc & Idc arc, were re-solved for 5 more iterations, until these values did not change significantly from the previous values and converged to the final answers of:
Idc arc = 2.149 X103 A & 27.331 mΩ
Using the calculated Rarc & Idc arc, the Power and Energy in the Arc was determined as follows:
Parc = Idc arc2 * Rarc
= (2.149X103 )2 *(27.331X10-3)
= 126.22KW
Earc = Parc*tarc, again assuming tarc = .1s, then:
= (126.22KW)* (.1) = 12.622KJ
Incident Energy is determined by-
Ei = Earc/(4∏D2)
Ei, whereby D = 1”or 25.4mm, then: 12.622KJ /(4*∏*25.42) = 1.5577 J/mm2
For calories/cm2; take J/mm2*(23.39), then:

As you'll notice, I referenced Chapter 12, of Jim's “Complete Guide to Arc Flash Hazard Calculation Studies.” So, you may want to consider purchasing said doc if you don't have it already. I've realized it's well worth the price vs. beating your head against a wall trying to calculate such, especially w/ DC systems. Yes, I realize the math models (Arc flash S/W packages) are now realizing this arena, But....