Arc flash: other methods
Ralph Lee theoretical method (above 15 kV, or outside the empirical models)
- where
- incident energy (J/cm²)
- system voltage (kV)
- bolted three-phase fault current (kA)
- arcing time (s)
- working distance (mm)
- arc flash boundary (mm)
- incident energy at the boundary, 5.0 J/cm²
Explain this equation
Gives incident energy and the arc flash boundary for three-phase systems above 15 kV, such as 33 kV and 132 kV substations, where the empirical models were not tested.
Lee assumed the arc takes the maximum power the source can deliver, which is half the bolted three-phase MVA (when arc resistance equals source impedance). V × Ibf is proportional to that MVA, t is the arc duration and D the distance from a point source radiating equally in all directions.
The 1/D² is inverse-square spreading from a point source. The constant 2.142 × 10⁶ is not simply half the bolted power spread over a sphere (that alone would give a value about three times larger): it is Lee’s curable-burn distance Dc = √(2.65 × MVAbf × t) ft rewritten so that E equals 5.0 J/cm² (1.2 cal/cm²) at Dc, with the conversions that let V in kV, Ibf in kA, t in s and D in mm give J/cm². The boundary is where E falls to EB.
Sense check: 33 kV, 10 kA, 0.5 s at 910 mm gives about 427 J/cm² (102 cal/cm²) and a boundary over 8 m. Halving the time halves E; doubling distance quarters it.
Watch out: usually conservative for open-air HV arcs, but it ignores enclosure focusing.
Lee’s 1982 theoretical model assumes the maximum possible arc power (half the bolted three-phase MVA) radiates as from a point in open air. IEEE 1584 and NFPA 70E point to it for systems above 15 kV.
Enter your values to see the result.
Good to know
Units: V in kV, Ibf in kA, t in s, D in mm gives E in J/cm² (equivalently 5.12 × 10⁵ in cal/cm²). The same model gives the NFPA 70E curable-burn distance Dc = √(2.65 × MVAbf × t) in feet. Because it assumes maximum power transfer and an inverse-square law, it is conservative for open-air arcs at HV, often by a large factor at long working distances, but it does not account for the focusing effect of an enclosure. For 33–132 kV outdoor substation work the arc is in open air and gaps are large; still treat the result as an indication, not a precise value.
Common mistake
Using it below 15 kV where IEEE 1584-2018 applies (it can grossly overstate energy), or using it for an arc in a box at LV, where it can understate the energy at the opening.
Limits
Theoretical, three-phase, open air, maximum power transfer, inverse-square spreading. IEEE 1584-2018 notes the method is likely to be conservative above 15 kV. No account of arc length, electrode configuration or enclosure. 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. H. Lee, The other electrical hazard: electric arc blast burns, IEEE Trans. Industry Applications IA-18(3), 1982, pp. 246–251
- IEEE Std 1584-2002 IEEE Guide for Performing Arc-Flash Hazard Calculations (superseded; empirical model and Lee method)
- 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)
- ABB / Thomas Domitrovich et al.: Arc flash hazard analysis and mitigation (restates IEEE 1584-2002, Lee and Doughty–Neal equations)
- 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.