Arc Flash Screening: Method

Arc Flash Screening

An electric arc releases heat in a fraction of a second. The quantity used to plan work near energized parts is the incident energy: the heat received per unit area at the worker's face and chest, in cal/cm² (1 cal/cm² = 4.184 J/cm²). About 1.2 cal/cm² (5 J/cm²) on bare skin is the generally accepted level for the onset of a second-degree burn, and the distance at which the energy falls to that level is the arc flash boundary. This page estimates both with the methods that are public, so that a planner can see the order of magnitude, what drives it and whether a set of arc ratings covers it.

It is a screening estimate and not a substitute for an arc-flash study. The model that industry uses for enclosed equipment from 208 V to 15 kV, IEEE Std 1584, predicts the arcing current and accounts for the electrode arrangement, the gap and the enclosure size; its equations are copyrighted and are not implemented here. Equipment labels, energized-work permits and the selection of protective equipment for a facility need a study by a qualified person with the actual protective-device settings.

Which method for which exposure

Appendix E to 29 CFR 1910.269 lists the methods the Occupational Safety and Health Administration considers reasonable for a single-phase arc in open air, a three-phase arc in open air and a three-phase arc in an enclosure, in three voltage classes (its Table 3, printed in the results with the column of the chosen exposure marked). The page follows that table:

Overhead line, single-phase arc in open air. The look-up Tables 6 and 7 of the appendix give the estimate where they apply (4 to 46 kV for rubber-glove work, 4 to 800 kV for live-line tool work); the Lee equation, which OSHA rates acceptable but conservative for a single-phase arc up to 15 kV, is shown beside it and supplies the boundary. Outside the tables the estimate is by equation.

Three-phase arc in open air. The Lee equation at any voltage (acceptable at 600 V and below, conservative from 601 V to 15 kV; above 15 kV OSHA accepts it only to show that the energy does not exceed 2.0 cal/cm², because its results there are extremely conservative), with the Doughty, Neal and Floyd open-air equation beside it at 600 V and below. The larger of the acceptable values is carried forward.

Three-phase arc in an enclosure, 600 V and below. The Doughty, Neal and Floyd arc-in-a-box equation. OSHA rates the Lee equation not acceptable here because it underestimates an arc whose heat is directed out of a box; the page shows the Lee value for comparison only. Above 600 V no public method covers an enclosed arc and the page refuses the case.

DC system. A maximum-power estimate. OSHA's table does not rate DC methods.

At 15 kV and below OSHA presumes that an arc is three-phase unless only one phase is present or the spacing of the phases prevents a multiphase arc.

Lee maximum-power equation

Lee (1982) took the arc at the point of maximum power transfer from an inductive source and treated it as a source radiating in all directions, so the energy is proportional to the bolted-fault power and the duration and inversely proportional to the square of the distance. In the inch form that OSHA applied (the equation of NFPA 70E Annex D):

E = 793 F V t / D²

with E in cal/cm², F the bolted three-phase fault current in kA, V the phase-to-phase voltage in kV, t the arc duration in seconds and D the distance in inches. Solving for the distance at 1.2 cal/cm² gives Lee's boundary D_c = √(2.65 MVA_bf t) in feet, with MVA_bf = √3 V F the bolted-fault power; for a transformer of 5 percent impedance on an infinite bus this is √(53 MVA t) with the transformer rating. The constant is confirmed by a value OSHA printed: for 15 kV, 5 kA and 34.5 cycles at 15 in the preamble of the 2014 rule gives 152 cal/cm² (79 FR 20465, Table 11), and 793 × 5 × 15 × 0.575 / 15² = 152.0. That case is the default of the page; the same preamble sets it beside the 5.0 cal/cm² of the table OSHA had proposed (the final Table 6 gives 4 cal/cm² or less for the case) and explains why the equation is so conservative on a medium-voltage line.

The equation has no arcing current, no gap and no enclosure in it. It grows in proportion to the voltage, which is why it overstates the energy more and more as the voltage rises.

Doughty, Neal and Floyd equations

Doughty, Neal and Floyd fitted the highest incident energy measured in three-phase arc tests on a 600 V system with electrodes 1.25 in (32 mm) apart, in open air and in a 20 in cubic box open on one side, for bolted fault currents of 16 to 50 kA and distances of 18 in and more:

open air: E = 5271 D^−1.9593 t (0.0016 F² − 0.0076 F + 0.8938)

in a box: E = 1038.7 D^−1.4738 t (0.0093 F² − 0.3453 F + 5.9675)

with D in inches, t in seconds, F in kA and E in cal/cm². OSHA finds them reliable for the 600 V systems they represent and conservative for lower voltages and single-phase systems, and not reasonable above 600 V. The box equation falls more slowly with distance than the inverse square because the enclosure directs the heat. Outside 16 to 50 kA or inside 18 in the page prints the value with a caution: it is then an extrapolation of a curve fit. The coefficients are those of the published equations as they are commonly reprinted; no government document that prints them was found, so the test script checks them against what OSHA reports of the paper (the open-air boundary coincides almost exactly with Lee's at 600 V, the box boundary is much larger and the difference grows with the fault current).

OSHA look-up tables for overhead lines

Tables 6 and 7 of Appendix E list, for phase-to-ground arcs in open air, the longest clearing time in cycles that keeps the heat energy at 4, 5, 8 and 12 cal/cm² for each voltage range and fault current. OSHA calculated them with the ARCPRO program. Table 6 is for rubber insulating glove work with the worker 15 in (380 mm) from the arc; Table 7 is for live-line tool work with the worker at the minimum approach distance less twice the arc length, and above 72.5 kV may be used only when the minimum approach distance is at least the value in the table's note. The appendix says to read the row of the next higher listed fault current and the first column whose clearing time is at or above the actual one; the result is a level, "4 cal/cm² or less", and not a computed energy. A clearing time beyond the last column means more than 12 cal/cm², and the page then falls back on the equation.

DC maximum-power estimate

A DC source with open-circuit voltage V and bolted current I_bf delivers the most power to an arc when the arc voltage is V / 2 and the arc current is I_arc = I_bf / 2, that is P = V I_bf / 4. Radiated uniformly from a point, the energy at the distance D after the time t is V I_arc t / (8 π D²) in J/cm², or 0.00951 V I_arc t / D² in cal/cm² with D in centimetres. The published form of the method (Doan 2010; NFPA 70E Annex D) rounds the constant to 0.01, and the page uses 0.01 and prints the unrounded value beside it. For an arc in an enclosure the open-air value is multiplied by an entered factor; 3 is the value commonly quoted. The estimate assumes that the arc holds the maximum-power point for the whole duration, which is conservative for most sources and is not a prediction for batteries or photovoltaic arrays, whose current and voltage do not follow a fixed source resistance.

Fault current and clearing time

The bolted fault current is entered, or taken at the secondary terminals of a transformer on an infinite primary bus: I_FL = kVA / (√3 V) and I_bf = I_FL / (Z / 100). That is the largest current the transformer can deliver; conductor impedance lowers it and motors add to it, and the Voltage Drop and Short Circuit tool gives the current at the end of a feeder.

The clearing time is the time the protective device takes to open the circuit. It is entered in seconds or in cycles, or read from two points of the device's total-clearing curve: on log-log paper the curve between the points is taken as a straight line, t = t₁ (I / I₁)^k with k = ln(t₂ / t₁) / ln(I₂ / I₁). Two points describe one region of a real curve; enter points on either side of the current of interest and read instantaneous or definite-time regions from the curve itself.

Reduced fault current case

Every method on the page is proportional to the duration, and an overcurrent device takes longer to clear a smaller current. The largest fault current is therefore not always the worst case: a fault at the end of a long circuit, a weaker source, or an arc that limits the current can fall in the slow part of the device curve, where the clearing time grows faster than the current falls. The page runs a second case at an entered percentage of the fault current with its own clearing time (entered, or read from the two curve points) and carries forward the larger result. The percentage is the user's choice; the DOE handbook notes that an arcing fault on a low-voltage system can sit in the long-time band of a breaker instead of the instantaneous region, 30 s instead of 0.015 s in its example.

Protective equipment

The estimate is compared with entered arc ratings. The default list, 4, 8, 25 and 40 cal/cm², is the set of minimum ratings of the NFPA 70E hazard/risk categories 1 to 4 as OSHA quotes them. An arc rating equal to the incident energy corresponds to about an even chance of the onset of a second-degree burn under the fabric, so the comparison is a floor and not a margin. For work covered by 29 CFR 1910.269, arc-rated protection is not required at 2.0 cal/cm² or less, and the head and face protection follows the table of Appendix E: for a single-phase arc in open air none up to 8 cal/cm², an arc-rated faceshield of at least 8 cal/cm² from 9 to 12, a hood or faceshield with balaclava from 13; for three-phase exposures none up to 4, faceshield from 5 to 8, hood from 9. Above 40 cal/cm² NFPA 70E recommends against energized work under any circumstances.

For 200 to 600 V facility systems the page also reports the simple criterion of DOE-HDBK-1092-2013 (a 4 ft boundary without calculation when the fault current does not exceed 50 kA and the clearing time 2 cycles, or when their product does not exceed 100 kA-cycles).

Working distances

Table 4 of the OSHA appendix lists reasonable distances from the worker to the arc: 455 mm (18 in) for cable and for low-voltage motor control centers and panelboards, 610 mm (24 in) for low-voltage switchgear, 910 mm (36 in) for 5 kV and 15 kV switchgear, and 380 mm (15 in) for rubber-glove work on single conductors in air.

What is not included

The IEEE 1584 model (arcing current, electrode configuration, enclosure size, gap); ARCPRO; arc blast pressure, sound, molten metal and shrapnel; motor contribution and source impedance in the fault current; protective-device libraries; equipment labels. The enclosure factor for DC and the reduced-current percentage are entered values.