Arc flash: other methods
DC arc flash: maximum power method (Ammerman et al. / NFPA 70E Annex D)
- where
- arcing current (kA)
- d.c. bolted fault current (kA)
- maximum arc power (kW)
- d.c. system voltage (V)
- working distance (cm)
- working distance (mm)
- incident energy (cal/cm²)
- arc duration (s)
- multiplying factor: 1 open air, 3 in a box
- arc flash boundary (mm)
Explain this equation
Gives a quick, conservative incident energy for d.c. systems such as battery rooms, UPS and substation d.c. supplies.
For a source with internal resistance, the arc takes the most power when its voltage is half the system voltage and the current is half the bolted current, so Parc = Vsys × Ibf / 4. Tarc is the arc duration, Dcm the distance in centimetres, and Mf allows for an enclosure.
The arc energy Pmax × Tarc is spread over a sphere of area 4πD². With the arc voltage at half Vsys, combining that factor of a half, 1/4π and the joule-to-calorie conversion (1/4.184) gives 0.0095, rounded to 0.01, for Iarc in amperes (hence × 10³ from kA) and D in centimetres. The 10 in front of the root turns the boundary from cm into mm.
Sense check: 250 V, 20 kA, 0.5 s at 455 mm gives about 6 cal/cm² in open air; Mf = 3 for a box triples it.
Watch out: this is an upper bound for arc power; the actual arcing current is usually different, which affects protection timing.
A conservative screening method for d.c. systems (batteries, PV, traction, substation d.c.): the arc is assumed to take the maximum possible power, which occurs when the arc voltage is half the system voltage.
Enter your values to see the result.
Good to know
Units: Vsys in V, Iarc in A, Tarc in s, D in cm gives E in cal/cm² (Iarc is shown in kA, hence the 10^3 in the working). The 0.01 comes from the arc voltage being half the system voltage (× 0.5), spreading the arc energy over a sphere (1/4π) and converting joules to calories (1/4.184): 0.5/(4π × 4.184) = 0.0095, rounded to 0.01. NFPA 70E suggests a multiplying factor of 3 for an arc in a box or enclosure (Doan 2010); Wilkins’ box factors are an alternative. For battery systems Ibf is set by the internal resistance (often quoted by the manufacturer as a short-circuit current); remember the battery does not stop feeding the fault by itself, so arc duration may be set by a fuse or by the arc self-extinguishing.
Common mistake
Taking 2 s as the arc duration for a battery with no protective device between it and the work position, or forgetting that the half-voltage assumption is the worst case only, not the expected current for reading a fuse curve.
Limits
Theoretical upper bound; no published consensus d.c. model is validated by testing across the range. Below about 100 V d.c. sustained arcs are unlikely (NFPA 70E). Box factor 3 is a judgement-based value. UK duty: under the Electricity at Work Regulations 1989 work on or near live conductors is allowed only where reg 14 is met (unreasonable to make dead, reasonable to work live, suitable precautions); regs 12 and 13 require isolation and precautions for dead working, and reg 4(4) requires suitable protective equipment. HSE HSG85 and your DNO or company safety rules (ENA-based distribution safety rules) take precedence. Apply the hierarchy of controls: de-energise first, then engineering controls (faster protection, maintenance switches, remote racking/operation, arc-resistant switchgear), then distance and procedures; arc-rated PPE is the last line of defence.
Sources
- R. F. Ammerman, T. Gammon, P. K. Sen, J. P. Nelson, DC-arc models and incident-energy calculations, IEEE Trans. Industry Applications 46(5), 2010
- D. R. Doan, Arc flash calculations for exposures to DC systems, IEEE Trans. Industry Applications 46(6), 2010
- NFPA 70E-2024 Standard for Electrical Safety in the Workplace: Informative Annex D (incident energy and arc flash boundary methods) and Table 130.7(C)(15)(c)
- Battcon 2014: Arc in a box – DC arc flash calculations using a simplified approach (NFPA 70E maximum power method and box factors)
- The Electricity at Work Regulations 1989 (SI 1989/635), regulations 4, 12, 13 and 14
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.