If the arc is enclosed, then factors are selected in accordance with the following table from the Wilkins paper.

 Optimal Values of a and k Enclosure Type a (mm) k LV Switchgear 400 0.312 MV Switchgear 950 0.416 Panelboard 100 0.127

Table 18

The enclosed (box) incident energy is found by:

Ei box =
 Earc x k x 23.9 a2 x d2
cal/cm2

Figure 14.16 shows the dashboard from the DC incident energy calculator. An enclosure type or open air is selected form the drop-down field and this will require values for the internal resistance of the source, the conductor resistance and the arc gap. The Arcing Current Idc arc is then shown which can be used to determine the disconnection time from the TCC and entered into the disconnection time t. If this is not available or there is not a device in circuit, a value can be entered which is an estimate of reaction time. (note, the IEEE 1584 Guide uses a figure of two seconds if there is no restriction of access). Finally, a working distance d is entered which is measured to the source of the arc.

The calculated incident energy, which is shown, depends upon the type of enclosure (or air) distance and disconnection time given the electrical system parameters.

The entry and output field are listed as follows:

Enclosure Type
Choose from a dropdown menu as described in Table 14.18 previously.

System Voltage (volts)
Enter DC open circuit volts.

Conductor Resistance (Ω)
Enter the total conductor resistance from the source to the equipment in ohms.

System Internal Resistance (Ω)
Enter the internal resistance of the system or source in ohms.

Conductor Gap Distance (mm)
Enter the gap between conductors in mm.

Working Distance (mm)
The distance between the potential arc source (not just the front of the panel) and the face and chest of the worker.

DC Arcing Current Iarc (kA)
The calculated dc arcing current.

Disconnection Time (seconds)
This is the time to clear the dc arcing current Iarc and is obtained from the time current curve of the upstream protective device.

Incident Energy (cal/cm2)
The calculated dc incident energy at the working distance.

References

1. Complete Guide to Arc Flash Hazard Calculation Studies by Jim Phillips P.E – Brainfiller Inc. 2010
2. DC Arc Flash Calculations by Jim Phillips – Posted on Brainfiller.com, November 20, 2019
3. Arc Flash Calculations for Exposures to DC Systems by D.R. Doan – IEEE Transactions on Industry Applications, Vol.46 No 5
4. DC Arc Models and Incident Energy Calculations by R.F. Ammerman, T. Gammon, P.K. Sen and J.P. Nelson – IEEE Transactions on Industry Applications, Vol.46 No 6
5. Electric Arcs in open Air by A.D.Stokes and W.T.Oppenlander – Journal of Physics D: Applied Physics 1991
6. Simple Improved Equations for Arc Flash Analysis by R. Wilkins – IEEE Electrical Safety Forum, August 30, 2004