Arc flash: IEEE 1584

IEEE 1584-2018 arcing current, incident energy and arc flash boundary (600 V–15 kV, end to end)

I_{arc, V} = 10^{k_{1} + k_{2} \lg I_{bf} + k_{3} \lg G} (k_{4} {I_{bf}}^{6} + k_{5} {I_{bf}}^{5} + \dots + k_{9} I_{bf} + k_{10})

I_{arc} = f (I_{arc,600}, I_{arc,2700}, I_{arc,14300}; V_{oc}) (≤ 600 V: equation 25)

I_{min} = I_{arc} (1 - 0.5 {VarC}_{f})

E_{V} = \frac{12.552}{50} T \cdot 10^{k_{1} + k_{2} \lg G + \frac{k_{3} I_{arc, V}}{k_{4} {I_{bf}}^{7} + \dots + k_{10} I_{bf}} + k_{11} \lg I_{bf} + k_{13} \lg I_{arc, V} + \lg (\frac{1}{CF}) + k_{12} \lg D}

E, AFB = interpolated from 600, 2700 and 14 300 V values to V_{oc}

AFB : E = 1.2 cal/cm²

where
$I_{arc,V}$: intermediate arcing current at V = 600, 2700 or 14 300 V (kA)
$I_{arc,V (≤ 600 V)}$: at or below 600 V only the 600 V set is used: the k3 term takes I_arc,600 and the k13 term the final (or reduced) arcing current
$k1…k13$: published model coefficients for the electrode configuration and voltage (IEEE 1584-2018 Tables 1, 3–5)
$I_{bf}$: three-phase bolted fault current (kA)
$G$: gap between conductors (mm)
$I_{arc}$: final arcing current interpolated to V_oc (kA)
$V_{oc}$: open-circuit system voltage (kV)
$I_{min}$: reduced arcing current (kA)
$VarCf$: arcing current variation factor (Table 2)
$E_{V}$: intermediate incident energy (J/cm²)
$T$: arc duration (ms)
$CF$: enclosure size correction factor
$D$: working distance (mm)
$AFB$: arc flash boundary (mm)

Explain this equation

Gives incident energy and arc flash boundary for three-phase equipment from 208 V to 15 kV, for both the full and the reduced arcing current, so a label or permit can use the worse case.

The arc is a plasma whose power is roughly arc voltage × arcing current. Heat reaches the worker by radiation and by hot gas and plasma blown out of the opening, so energy depends on current, gap G, duration T, distance D and how the box directs the plume. The k values are regression constants from about 1800 tests; CF corrects for box size and VarCf for scatter in arcing current.

Energy is linear in T because arc power is roughly constant. The distance exponent k12 (about −1.5 to −2) is shallower than inverse-square in boxes, which focus energy out of the front. Above 600 V the model is run at 600, 2700 and 14 300 V and interpolated.

Sense check: 11 kV switchgear at 12.5 kA, VCB, 914 mm and 100 ms gives about 1.4 cal/cm²; Annex D.1 (4.16 kV, 15 kA, about 0.2 s) about 3 cal/cm².

Watch out: read each clearing time at its own arcing current, never at the bolted current.

Full IEEE 1584-2018 empirical model for three-phase equipment from 208 V to 15 kV: arcing current, reduced arcing current, enclosure correction, incident energy and arc flash boundary, for both current cases.

Enter the two clearing times read from the protection curve at the full and the reduced arcing current (use the arcing current calculator first).

Enter your values to see the result.

Good to know

The working shows the governing case (full or reduced arcing current, whichever gives the higher incident energy) with the Table 1–5 constants for the chosen electrode configuration written in; CF is from the enclosure size calculator. Electrode configurations: VCB vertical conductors in a box; VCBB vertical conductors terminated in an insulating barrier in a box; HCB horizontal conductors in a box (e.g. busbars pointing at the worker, the most onerous); VOA and HOA the open-air equivalents (enclosure size ignored, CF = 1). Typical gaps and working distances (Table 8/10): 15 kV switchgear 152 mm and 914 mm; 5 kV switchgear 104 mm and 914 mm; LV switchgear 32 mm and 610 mm; LV MCC and panelboards 25 mm and 457 mm. Above 600 V the model calculates at 600, 2700 and 14300 V and interpolates; at or below 600 V it uses equation 25 and Table 3 directly. The notice gives both cases in J/cm² and cal/cm². Results must be recorded on the equipment label with the study date, nominal voltage, arc flash boundary, incident energy at the stated working distance (or the PPE requirement) and the limited/restricted approach information your rules require. Clearing time must be read from the upstream protection characteristic at the arcing current that actually flows through that device (scale the arcing current by the ratio of device current to total fault current where several sources feed). Run the study twice: full arcing current with its clearing time, and reduced arcing current with its (often much longer) clearing time; take the higher energy. IEEE 1584 Annex B suggests 2 s may be used as a reasonable maximum where clearing is slower and the person can move away; do not rely on it where escape is restricted (confined space, ladder, inside a cubicle, elevated platform).

Common mistake

Using the full arcing current to read the clearing time only. On an inverse-time or fuse characteristic the slightly lower reduced arcing current can land on the slow part of the curve and give several times the energy. Another common error is using the bolted fault current to read the clearing time.

Limits

IEEE 1584-2018 model range: three-phase a.c., 50 or 60 Hz; Voc 208 V–15 kV; Ibf 500 A–106 kA at 208–600 V and 200 A–65 kA at 601 V–15 kV; gap 6.35–76.2 mm (≤600 V) and 19.05–254 mm (>600 V); working distance at least 305 mm; enclosure height or width up to 1244.6 mm and opening area up to 1.549 m², width greater than four times the gap; no limit on arcing time. Single-phase, d.c. and systems above 15 kV are outside the model. Coefficients are entered exactly as published in IEEE 1584-2018 Tables 1–5 and 7 and reproduce the Annex D.1 and D.2 worked examples. The calculator assumes a single clearing time per case; for changing currents (e.g. motor contribution decaying, one source tripping first) sum the energy of each time step. The arc flash boundary is calculated from the energy at 1.2 cal/cm² using the distance exponent k12 for each intermediate voltage, which is equivalent to equations 7–10. 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

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.

IEEE 1584-2018 arcing current, incident energy and arc flash boundary (600 V–15 kV, end to end)

Good to know

Common mistake

Limits

Sources

IEEE 1584-2018 arcing current, incident energy and arc flash boundary (600 V–15 kV, end to end)

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