Arc-Flash Incident Energy and Boundary (IEEE 1584-2018)
Arcing current, incident energy and arc-flash boundary of a three-phase 208 V to 15 kV equipment by the IEEE Std 1584-2018 empirical model, with the arcing current variation.
Caution
This tool gives engineering estimates by the empirical model of IEEE Std 1584-2018. It is not an arc-flash study and does not replace one. The results must be reviewed by a qualified person before they are used to label equipment, choose PPE or plan work. The tool gives no PPE category or safe-work decision.
Arc-flash incident energy and boundary by IEEE 1584-2018
This calculator estimates the arcing current, the incident energy at the working distance and the arc-flash boundary of three-phase equipment from 208 V to 15 kV, using the empirical model of IEEE Std 1584-2018. It covers the five electrode configurations of the standard (VCB, VCBB, HCB, VOA, HOA), the enclosure size correction, the interpolation between 600 V, 2.7 kV and 14.3 kV, and the arcing current variation: both the average and the reduced arcing current are calculated and the higher result is shown.
How to use it
Enter the system voltage, the bolted fault current, the electrode configuration, the gap, the enclosure size and the working distance. Read the arc duration from the time-current curve of the protective device at the arcing current the tool shows, enter it for both cases, and read the incident energy in J/cm2 and cal/cm2. The diagram shows the worker, the enclosure and the arc-flash boundary to scale.
Limits
The model is valid for the ranges of voltage, fault current, gap, distance and enclosure size given under Validity; outside them the tool warns and the result is an extrapolation. It does not select PPE and does not cover dc or single-phase systems.
Disclaimer
The results are engineering estimates, not an arc-flash study. They depend on the data you enter and must be reviewed by a qualified person before they are used for labelling, PPE or work planning.
How it is calculated
Empirical model of IEEE Std 1584-2018 for three-phase 208 V to 15 kV equipment, 50 or 60 Hz.
Steps
- Intermediate arcing currents, Equation (1), at 600, 2700 and 14300 V:
- Final arcing current. Above 600 V the three values are interpolated, Equations (16)-(18); up to 600 V Equation (25) is used.
- Arcing current variation, Equation (2): , applied to the intermediate currents above 600 V and to the final current up to 600 V.
- Arc duration is read by the user from the time-current curve of the protective device at and at (6.9).
- Enclosure correction factor CF from the equivalent enclosure size, Table 6, Equations (11)-(15) and Table 7 (CF = 1 for open air).
- Incident energy, Equations (3)-(6):
Above 600 V it is evaluated at 600, 2700 and 14300 V and interpolated, Equations (19)-(21). Up to 600 V, Equation (6) takes in the term and the final in the term.
- Arc-flash boundary, Equations (7)-(10): the distance at which the incident energy is 5.0 J/cm2 (1.2 cal/cm2); interpolated like E.
- Both cases (average and reduced arcing current) are calculated; the final E and AFB are the higher of the two (4.5).
Incident energy in cal/cm2 is E in J/cm2 divided by 4.184.
Assumptions
The results depend on the input data, above all on the protective device clearing times and the equipment data, which the user must verify. The model has a stated range and uncertainty, and real events can differ from it. The author and the publisher accept no liability for decisions made on these results.
- The model and all coefficients are taken from IEEE Std 1584-2018 (Tables 1 to 7, Equations (1) to (25)); they were transcribed from the standard, not derived here.
- The arc duration is an input: it comes from the protective device curves and is not calculated here. Use the longest time of a band, the total clearing time of fuses, and add the breaker opening time where the curves do not include it (6.9).
- Voc is taken equal to the system nominal voltage (allowed by 4.2).
- Enclosure sizes above 1244.6 mm are treated as 1244.6 mm; the depth only decides shallow or typical (4.8).
- The result is the incident energy at the working distance for a worker's face and chest; it is not a PPE category. Choosing PPE follows another standard (for example NFPA 70E) and is not part of IEEE 1584.
- Single-phase and dc systems are outside the model; the special models for current-limiting fuses (Annex H) and circuit breakers (Annex I) are not included.
- The diagram is a section through the arc drawn to scale: the arc is taken at the centre of the enclosure, the boundary is a circle around it, and the electrodes are not drawn.
- Not verified here: the protective device times you enter, and the enclosure and electrode data of your equipment.
Where it applies
- Voltage 208 V to 15 000 V, three-phase, 50 or 60 Hz.
- Bolted fault current: 0.5 to 106 kA (208-600 V), 0.2 to 65 kA (601-15 000 V).
- Gap: 6.35 to 76.2 mm (208-600 V), 19.05 to 254 mm (601-15 000 V).
- Working distance 305 mm or more.
- Enclosure: largest side up to 1244.6 mm, opening area up to 1.549 m2, width more than four times the gap.
- Outside these ranges the tool shows a warning and the result is an extrapolation.
- Sustained arcs are possible but unlikely at 240 V or less with a bolted fault current below 2 kA.
References
- IEEE Std 1584-2018, IEEE Guide for Performing Arc-Flash Hazard Calculations: Clause 4 (Equations (1)-(25), Tables 1-7), Clause 6.9 (arc duration), Annex D (sample calculations used as reference cases).
- IEEE Std 1584.1, IEEE Guide for the Specification of Scope and Deliverable Requirements for an Arc-Flash Hazard Calculation Study in Accordance with IEEE Std 1584: data collection, system modes and the choice of the protective device that sets the arc duration (cited for these in IEEE Std 1584-2018, 6.2, 6.3 and 6.9). Use the edition that matches the study.
Inputs
| Input | Symbol | Unit | Default |
|---|---|---|---|
| Open-circuit (system) voltage, line-to-line Three-phase, 50 or 60 Hz. The model covers 208 V to 15 000 V. | V_oc | kV | 0.48 |
| Bolted three-phase fault current (symmetrical rms) Range of the model: 0.5 to 106 kA for 208 V to 600 V; 0.2 to 65 kA above 600 V. | I_bf | kA | 45 |
| Electrode configuration | ec | VCB - vertical conductors in a box | |
| Gap between conductors (electrodes) Range of the model: 6.35 to 76.2 mm for 208 V to 600 V; 19.05 to 254 mm above 600 V. | G | mm | 32 |
| Enclosure height Larger than 1244.6 mm is treated as 1244.6 mm by the model. | H_enc | mm | 610 |
| Enclosure width Larger than 1244.6 mm is treated as 1244.6 mm by the model. | W_enc | mm | 610 |
| Enclosure depth Used only to tell a shallow enclosure (depth up to 203.2 mm, both sides below 508 mm, Voc below 600 V) from a typical one. | Dp_enc | mm | 254 |
| Working distance Distance from the arc to the worker's face and chest. The model is valid for 305 mm and more. | D_w | mm | 609.6 |
| Arc duration at the arcing current I_arc Clearing time of the protective device read from its time-current curve at the calculated I_arc (shown under the results). | T_arc | ms | 61.3 |
| Arc duration at the reduced arcing current I_arc_min Clearing time at the reduced arcing current I_arc_min (arcing current variation, 4.5). The final result is the higher of the two cases. | T_arc_min | ms | 319 |
Results
With the default inputs above, the calc gives:
| Result | Value |
|---|---|
| Arcing current I_arc (read the arc duration from the protective device at this current) | 28.79 kA |
| Reduced arcing current I_arc_min (read the second arc duration at this current) | 25.24 kA |
| Incident energy (higher of the two cases) | 12.7 cal/cm² |
| Incident energy (higher of the two cases) | 53.16 J/cm² |
| Arc-flash boundary (5.0 J/cm2 = 1.2 cal/cm2) | 2,669 mm |
| Incident energy, average arcing current | 2.77 cal/cm² |
| Incident energy, reduced arcing current | 12.7 cal/cm² |
| Enclosure size correction factor CF | 1.085 |
Checked against sources
Each case below was calculated by this calc and agrees with the value from its source (within the tolerance where one is shown).
IEEE 1584-2018 Annex D.1: 4160 V, VCB, 15 kA
Source: Worked example D.1 of IEEE Std 1584-2018 (Equations D.9, D.17, D.22, D.32, D.42, D.51, D.62, D.72): inputs and printed results as in the standard, arc durations 197 ms and 223 ms from the example's time-current curves. Independent of the formulas of this tool.
Inputs: Open-circuit (system) voltage, line-to-line = 4.16 kV; Bolted three-phase fault current (symmetrical rms) = 15 kA; Gap between conductors (electrodes) = 104 mm; Enclosure height = 1,143 mm; Enclosure width = 762 mm; Enclosure depth = 762 mm; Working distance = 914.4 mm; Arc duration at the arcing current I_arc = 197 ms; Arc duration at the reduced arcing current I_arc_min = 223 ms; the others as above.
| Result | Source | This calc |
|---|---|---|
| Intermediate arcing current at 600 V, Equation (1) | 11.117 kA | 11.117 kA |
| Arcing current I_arc (read the arc duration from the protective device at this current) | 12.979 kA | 12.979 kA |
| Reduced arcing current I_arc_min (read the second arc duration at this current) | 12.675 kA | 12.675 kA |
| Enclosure size correction factor CF | 1.284 | 1.284 |
| Incident energy, average arcing current | 12.152 J/cm² | 12.152 J/cm² |
| Incident energy, reduced arcing current | 13.343 J/cm² | 13.343 J/cm² |
| Arc-flash boundary, average arcing current | 1,606 mm | 1,606 mm |
| Arc-flash boundary, reduced arcing current | 1,704 mm | 1,704 mm |
IEEE 1584-2018 Annex D.2: 480 V, VCB, 45 kA
Source: Worked example D.2 of IEEE Std 1584-2018 (Equations D.82, D.84, D.89, D.91, D.94, D.99, D.102, D.105): inputs and printed results as in the standard, arc durations 61.3 ms and 319 ms from the example's time-current curves. Independent of the formulas of this tool.
Inputs: the default inputs above.
| Result | Source | This calc |
|---|---|---|
| Intermediate arcing current at 600 V, Equation (1) | 32.449 kA | 32.449 kA |
| Arcing current I_arc (read the arc duration from the protective device at this current) | 28.793 kA | 28.793 kA |
| Reduced arcing current I_arc_min (read the second arc duration at this current) | 25.244 kA | 25.244 kA |
| Enclosure size correction factor CF | 1.085 | 1.085 |
| Incident energy, average arcing current | 11.585 J/cm² | 11.585 J/cm² |
| Incident energy, reduced arcing current | 53.156 J/cm² | 53.156 J/cm² |
| Arc-flash boundary, average arcing current | 1,029 mm | 1,029 mm |
| Arc-flash boundary, reduced arcing current | 2,669 mm | 2,669 mm |
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