Informative Annex D Incident Energy and Arc Flash Boundary Calculation Methods
This informative annex is not a part of the requirements of this NFPA document but is included for informational purposes only.
D.1 Introduction.
Annex D summarizes calculation methods available for calculating arc flash boundary and incident energy. It is important to investigate the limitations of any methods to be used. The limitations of methods summarized in Annex D are described in Table D.1. Table D.1 Limitation of Calculation Methods Section Source Limitations/Parameters
D.2, D.3, D.4 Ralph Lee paper Calculates arc flash boundary for arc in open air; conservative over 600 V and becomes more conservative as voltage increases
D.5 Doughty/Neal paper Calculates incident energy for three-phase arc on systems rated 600 V and below; applies to short-circuit currents between 16 kA and 50 kA
D.6 Ralph Lee paper Calculates incident energy for three-phase arc in open air on systems rated above 600 V; becomes more conservative as voltage increases
D.7 IEEE Std. 1584 Calculates incident energy and arc flash boundary for: 208 V to 15 kV; three-phase; 50 Hz to 60 Hz; 700 A to 106,000 A short-circuit current; and 13 mm to 152 mm conductor gaps
D.8 ANSI/IEEE C2 NESC, Section 410, Table 410-1 and Table 410-2 Calculates incident energy for open air phase-to-ground arcs 1 kV to 500 kV for live-line work D.2 Basic Equations for Calculating Arc Flash BoundaryDistances.
The short-circuit symmetrical ampacity, Isc, from a bolted three-phase fault at the transformer terminals is calculated with the following formula: e70e-100_2012.png[D.2(a)] where Isc is in amperes, V is in volts, and %Z is based on the transformer MVA.
A typical value for the maximum power, P (in MW) in a three-phase arc can be calculated using the following formula: e70e-101_2012.png[D.2(b)] e70e-102_2012.png[D.2(c)]
The arc flash boundary distance is calculated in accordance with the following formulae: e70e-103_2012.png[D.2(d)] e70e-104_2012.png[D.2(e)]
where:Dc=distance in feet of person from arc source for a just curable burn (that is, skin temperature remains less than 80°C). MVAbf=bolted fault MVA at point involved.
MVA=MVA rating of transformer. For transformers with MVAratings below 0.75 MVA, multiply the transformer MVA rating by 1.25. t=time of arc exposure in seconds.
The clearing time for a current-limiting fuse is approximately ¼cycle or 0.004 second if the arcing fault current is in the fuse’s current-limiting range. The clearing time of a 5-kV and 15-kV circuit breaker is approximately 0.1 second or 6 cycles if the instantaneous function is installed and operating. This can be broken down as follows: actual breaker time (approximately 2 cycles), plus relay operating time of approximately 1.74 cycles, plus an additional safety margin of 2 cycles, giving a total time of approximately 6 cycles. Additional time must be added if a time delay function is installed and operating.
The formulas used in this explanation are from Ralph Lee,“The Other Electrical Hazard: Electrical Arc Blast Burns,” in IEEE Trans. Industrial Applications. Vol. 1A-18. No. 3, Page 246, May/June 1982. The calculations are based on the worst-case arc impedance. (See Table D.2.) Table D.2 Flash Burn Hazard at Various Levels in a Large Petrochemical Plant (1) (2) (3) (4) (5) (6) (7) Bus Nominal Voltage Levels System (MVA) Transformer (MVA) System or Transformer (% Z) Short-Circuit Symmetrical (A) Clearing Time of Fault (cycles) Arc Flash BoundaryTypical Distance* SI U.S. 230 kV 9000 1.11 23,000 6.0 15 m 49.2 ft 13.8 kV 750 9.4 31,300 6.0 1.16 m 3.8 ft Load side of all 13.8-V fuses 750 9.4 31,300 1.0 184 mm 0.61 ft 4.16 kV 10.0 5.5 25,000 6.0 2.96 m 9.7 ft 4.16 kV 5.0 5.5 12,600 6.0 1.4 m 4.6 ft Line side of incoming 600-V fuse 2.5 5.5 44,000 60.0–120.0 7 m–11 m 23 ft–36 ft 600-V bus 2.5 5.5 44,000 0.25 268 mm 0.9 ft 600-V bus 1.5 5.5 26,000 6.0 1.6 m 5.4 ft 600-V bus 1.0 5.57 17,000 6.0 1.2 m 4 ft
*Distance from an open arc to limit skin damage to a curable second degree skin burn [less than 80°C (176°F) on skin] in free air. D.3 Single-Line Diagram of a Typical Petrochemical Complex. The single-line diagram (see Figure D.3) illustrates the complexity of a distribution system in a typical petrochemical plant. g70e-14_2012.png Figure D.3 Single-Line Diagram of a Typical Petrochemical Complex.
D.4 Sample Calculation. Many of the electrical characteristics of the systems and equipment are provided in Table D.2. The sample calculation is made on the 4160-volt bus 4A or 4B. Table D.2 tabulates the results of calculating the arc flash boundary for each part of the system. For this calculation, based on Table D.2, the following results are obtained: (1) Calculation is made on a 4160-volt bus. (2) Transformer MVA (and base MVA) = 10 MVA. (3) Transformer impedance on 10 MVA base = 5.5 percent. (4) Circuit breaker clearing time = 6 cycles. Using Equation D.2(a), calculate the short-circuit current: e70e-105_2012.png Using Equation D.2(b), calculate the power in the arc: e70e-106_2012.png Using Equation D.2(d), calculate the second degree burn distance: e70e-107_2012.png Or, using Equation D.2(e), calculate the second degree burn distance using an alternative method: e70e-108_2012.png
D.5 Calculation of Incident Energy Exposure for an Arc Flash Hazard Analysis. The following equations can be used to predict the incident energy produced by a three-phase arc on systems rated 600 V and below. The results of these equations might not represent the worst case in all situations. It is essential that the equations be used only within the limitations indicated in the definitions of the variables shown under the equations. The equations must be used only under qualified engineering supervision. Informational Note: Experimental testing continues to be performed to validate existing incident energy calculations and to determine new formulas. The parameters required to make the calculations follow.
(1) The maximum bolted fault, three-phase short-circuit current available at the equipment and the minimum fault level at which the arc will self-sustain. (Calculations should be made using the maximum value, and then at lowest fault level at which the arc is self-sustaining. For 480-volt systems, the industry accepted minimum level for a sustaining arcing fault is 38 percent of the available bolted fault, three-phase short-circuit current. The highest incident energy exposure could occur at these lower levels where the overcurrent device could take seconds or minutes to open.)
(2) The total protective device clearing time (upstream of the prospective arc location) at the maximum short-circuit current, and at the minimum fault level at which the arc will sustain itself.
(3) The distance of the worker from the prospective arc for the task to be performed. Typical working distances used for incident energy calculations are as follows:
(1) Low voltage (600 V and below) MCC and panelboards — 455 mm (18 in.) (2) Low voltage (600 V and below) switchgear — 610 mm (24 in.) (3) Medium voltage (above 600 V) switchgear — 910 mm (36 in.)
D.5.1 Arc in Open Air. The estimated incident energy for an arc in open air is as follows: e70e-109_2012.png[D.5.1(a)] where:EMA=maximum open arc incident energy, cal/cm2 DA=distance from arc electrodes, in. (for distances 18 in. and greater) tA=arc duration, sec F=short-circuit current, kA (for the range of 16 kA to 50 kA) Sample Calculation: Using Equation D.5.1(a), calculate the maximum open arc incident energy, cal/cm2, where DA = 18 in., tA= 0.2 second, and F = 20 kA. e70e-110_2012.png[D.5.1(b)]
D.5.2 Arc in a Cubic Box. The estimated incident energy for an arc in a cubic box (20 in. on each side, open on one end) is given in the equation that follows. This equation is applicable to arc flashes emanating from within switchgear, motor control centers, or other electrical equipment enclosures. e70e-111_2012.png[D.5.2(a)] where: EMB=maximum 20 in. cubic box incident energy, cal/cm2 DB=distance from arc electrodes, in. (for distances 18 in. and greater) tA=arc duration, sec F=short-circuit current, kA (for the range of 16 kA to 50 kA) Sample Calculation: Using Equation D.5.2(a), calculate the maximum 20 in. cubic box incident energy, cal/cm2, using the following:
(1) DB = 18 in. (2) tA = 0.2 sec (3) F = 20 kA
e70e-112_2012.png[D.5.2(b)]
D.5.3 Reference. The equations for this section were derived in the IEEE paper by R. L. Doughty, T. E. Neal, and H. L. Floyd, II, “Predicting Incident Energy to Better Manage the Electric Arc Hazard on 600 V Power Distribution Systems,” Record of Conference Papers IEEE IAS 45th Annual Petroleum and Chemical Industry Conference, September 28–30, 1998.
D.6 Calculation of Incident Energy Exposure Greater Than 600 V for an Arc Flash Hazard Analysis. The equation that follows can be used to predict the incident energy produced by a three-phase arc in open air on systems rated above 600 V. The parameters required to make the calculations follow.
(1) The maximum bolted fault, three-phase short-circuit current available at the equipment.
(2) The total protective device clearing time (upstream of the prospective arc location) at the maximum short-circuit current. If the total protective device clearing time is longer than 2 seconds, consider how long a person is likely to remain in the location of the arc flash. It is likely that a person exposed to an arc flash will move away quickly if it is physically possible, and 2 seconds is a reasonable maximum time for calculations. A person in a bucket truck or a person who has crawled into equipment will need more time to move away. Sound engineering judgment must be used in applying the 2-second maximum clearing time, since there could be circumstances where an employee’s egress is inhibited.
(3) The distance from the arc source.
(4) Rated phase-to-phase voltage of the system.
e70e-113_2012.png where:E=incident energy, cal/cm2 F=bolted fault short-circuit current, kA V=system phase-to-phase voltage, kV tA=arc duration, sec D=distance from the arc source, in.
D.7 Basic Equations for Calculating Incident Energy and Arc Flash Boundary. This section provides excerpts from IEEE 1584 for estimating incident energy and arc flash boundaries based on statistical analysis and curve fitting of available test data. An IEEE working group produced the data from tests it performed to produce models of incident energy. The complete data, including a spreadsheet calculator to solve the equations, can be found in the IEEE 1584, Guide for Performing Arc Flash Hazard Calculations. Users are encouraged to consult the latest version of the complete document to understand the basis, limitation, rationale, and other pertinent information for proper application of the standard. It can be ordered from the Institute of Electrical and Electronics Engineers, Inc., 445 Hoes Lane, P.O. Box 1331, Piscataway, NJ 08855-1331. D.7.1 System Limits. An equation for calculating incident energy can be empirically derived using statistical analysis of raw data along with a curve-fitting algorithm. It can be used for systems with the following limits:
(1) 0.208 kV to 15 kV, three-phase (2) 50 Hz to 60 Hz (3) 700 A to 106,000 A available short-circuit current (4) 13 mm to 152 mm conductor gaps
For three-phase systems in open-air substations, open-air transmission systems, and distribution systems, a theoretically derived model is available. This theoretically derived model is intended for use with applications where faults escalate to three-phase faults. Where such an escalation is not possible or likely, or where single-phase systems are encountered, this equation will likely provide conservative results.
D.7.2 Arcing Current. To determine the operating time for protective devices, find the predicted three-phase arcing current. For applications with a system voltage under 1 kV, solve Equation D.7.2(a) as follows: e70e-114_2012.png[D.7.2(a)] where:
lg=the log10 Ia=arcing current, kA K=−0.153 for open air arcs; −0.097 for arcs-in-a-box Ibf=bolted three-phase available short-circuit current (symmetrical rms), kA V=system voltage, kV G=conductor gap, mm (see Table D.7.2) For systems greater than or equal to 1 kV, use Equation D.7.2(b): e70e-115_2012.png[D.7.2(b)] This higher voltage formula is used for both open-air arcs and for arcs-in-a-box. Convert from lg: e70e-116_2012.png[D.7.2(c)]
Use 0.85Ia to find a second arc duration. This second arc duration accounts for variations in the arcing current and the time for the overcurrent device to open. Calculate the incident energy using both arc durations (Ia and 0.85 Ia), and use the higher incident energy. Table D.7.2 Factors for Equipment and Voltage Classes System Voltage (kV) Type of Equipment Typical Conductor Gap (mm) Distance Exponent Factor X Open air 10–40 2.000 0.208–1 Switchgear 32 1.473 MCCs and panels 25 1.641 Cables 13 2.000 Open air 102 2.000 >1–5 Switchgear 13–102 0.973 Cables 13 2.000 Open air 13–153 2.000 >5–15 Switchgear 153 0.973 Cables 13 2.000
D.7.3 Incident Energy at Working Distance — Empirically Derived Equation. To determine the incident energy using the empirically derived equation, determine the log10 of the normalized incident energy. The following equation is based on data normalized for an arc time of 0.2 second and a distance from the possible arc point to the person of 610 mm: e70e-117_2012.png[D.7.3(a)] where:
En=incident energy, normalized for time and distance, J/cm2 k1=−0.792 for open air arcs; −0.555 for arcs-in-a-box k2=0 for ungrounded and high-resistance grounded systems =−0.113 for grounded systems G=conductor gap, mm (see Table D.7.2) Then,e70e-118_2012.png[D.7.3(b)] Converting from normalized: e70e-119_2012.png[D.7.3(c)] where:E=incident energy, J/cm2.Cf=calculation factor =1.0 for voltages above 1 kV. =1.5 for voltages at or below 1 kV. En=incident energy normalized. t=arcing time, sec. x=distance exponent from Table D.7.2. D=distance, mm, from the arc to the person (working distance). See Table D.7.3 for typical working distances. Table D.7.3 Typical Working Distances Classes of Equipment Typical Working Distance* (mm) 15-kV switchgear 910 5-kV switchgear 910 Low-voltage switchgear 610 Low-voltage MCCs and panelboards 455 Cable 455 Other To be determined in field
* Typical working distance is the sum of the distance between the worker and the front of the equipment and the distance from the front of the equipment to the potential arc source inside the equipment.
If the arcing time, t, in Equation D.7.3(c) is longer than 2 seconds, consider how long a person is likely to remain in the location of the arc flash. It is likely that a person exposed to an arc flash will move away quickly if it is physically possible, and 2 seconds is a reasonable maximum time for calculations. Sound engineering judgment should be used in applying the 2-second maximum clearing time, because there could be circumstances where an employee’s egress is inhibited. For example, a person in a bucket truck or a person who has crawled into equipment will need more time to move away.
D.7.4 Incident Energy at Working Distance — Theoretical Equation. The following theoretically derived equation can be applied in cases where the voltage is over 15 kV or the gap is outside the range:e70e-120_2012.png[D.7.4] where:E=incident energy, J/cm2 V=system voltage, kV Ibf=available three-phase bolted fault current t=arcing time, sec D=distance (mm) from the arc to the person (working distance) For voltages over 15 kV, arcing fault current and bolted fault current are considered equal. D.7.5 Arc Flash Boundary. The arc flash boundary is the distance at which a person is likely to receive a second degree burn. The onset of a second degree burn is assumed to be when the skin receives 5.0 J/cm2 of incident energy. For the empirically derived equation, e70e-121_2012.png[D.7.5(a)] For the theoretically derived equation, e70e-122_2012.png[D.7.5(b)] where:DB=distance (mm) of the arc flash boundary from the arcing point Cf=calculation factor =1.0 for voltages above 1 kV =1.5 for voltages at or below 1 kV En=incident energy normalized t=time, sec X=distance exponent from Table D.7.2 EB=incident energy in J/cm2 at the distance of the arc flash boundary V=system voltage, kV Ibf=bolted three-phase available short-circuit current
Informational Note: These equations could be used to determine whether selected personal protective equipment is adequate to prevent thermal injury at a specified distance in the event of an arc flash.
D.7.6 Current-Limiting Fuses. The formulas in this section were developed for calculating arc flash energies for use with current-limiting Class L and Class RK1 fuses. The testing was done at 600 V and at a distance of 455 mm, using commercially available fuses from one manufacturer. The following variables are noted: Ibf = available three-phase bolted fault current (symmetrical rms), kA E = incident energy, J/cm2
(A) Class L Fuses 1601 A through 2000 A. Where Ibf <22.6 kA, calculate the arcing current using Equation D.7.2(a), and use time-current curves to determine the incident energy using Equations D.7.3(a), D.7.3(b), and D.7.3(c). Where 22.6 kA ≤Ibf ≤65.9 kA, e70e-123_2012.png[D.7.6(a)] Where 65.9 kA < Ibf ≤106 kA, e70e-124_2012.png[D.7.6(b)] Where Ibf >106 kA, contact the manufacturer
(B) Class L Fuses 1201 A through 1600 A. Where Ibf <15.7 kA, calculate the arcing current using Equation D.7.2(a), and use time-current curves to determine the incident energy using Equations D.7.3(a), D.7.3(b), and D.7.3(c).
Where 15.7 kA ≤Ibf ≤31.8 kA,
e70e-125_2012.png[D.7.6(c)]
Where 44.1 kA ≤Ibf ≤65.9 kA,
e70e-127_2012.png[D.7.6(e)]
Where 65.9 kA Where Ibf >106 kA, contact the manufacturer.
(C) Class L Fuses 801 A through 1200 A. Where Ibf <15.7 kA, calculate the arcing current using Equation D.7.2(a), and use time-current curves to determine the incident energy per Equations D.7.3(a), D.7.3(b), and D.7.3(c).
Where 15.7 kA ≤Ibf ≤22.6 kA,
e70e-129_2012.png[D.7.6(g)]
Where 22.6 kA (D) Class L Fuses 601 A through 800 A. Where Ibf <15.7 kA, calculate the arcing current using Equation D.7.2(a), and use time-current curves to determine the incident energy using Equations D.7.3(a), D.7.3(b), and D.7.3(c).
Where 15.7 kA ≤Ibf ≤44.1 kA,
e70e-132_2012.png[D.7.6(j)]
Where 44.1 kA < Ibf ≤106 kA,
e70e-133_2012.png[D.7.6(k)]
Where Ibf > 106 kA, contact the manufacturer. (E) Class RK1 Fuses 401 A through 600 A. Where Ibf <8.5 kA, calculate the arcing current using Equation D.7.2(a), and use time-current curves to determine the incident energy using Equations D.7.3(a), D.7.3(b), and D.7.3(c).
Where 8.5 kA ≤Ibf ≤14 kA,
e70e-134_2012.png[D.7.6(l)]
Where 14 kA < Ibf ≤15.7 kA,
e70e-135_2012.png[D.7.6(m)]
Where 15.7 kA < Ibf ≤22.6 kA,
e70e-136_2012.png[D.7.6(n)]
Where 22.6 kA < Ibf ≤106 kA,
e70e-137_2012.png[D.7.6(o)]
Where Ibf >106 kA, contact the manufacturer. (F) Class RK1 Fuses 201 A through 400 A. Where Ibf <3.16 kA, calculate the arcing current using Equation D.7.2(a), and use time-current curves to determine the incident energy using Equations D.7.3(a), D.7.3(b), and D.7.3(c).
Where 3.16 kA ≤Ibf ≤5.04 kA,
e70e-138_2012.png[D.7.6(p)]
Where 5.04 kA < Ibf ≤ 22.6 kA,
e70e-139_2012.png[D.7.6(q)]
Where 22.6 kA (G) Class RK1 Fuses 101 A through 200 A. Where Ibf <1.16 kA, calculate the arcing current using Equation D.7.2(a), and use time-current curves to determine the incident energy using Equations D.7.3(a), D.7.3(b), and D.7.3(c).
Where 1.16 kA ≤Ibf ≤1.6 kA,
e70e-141_2012.png[D.7.6(s)]
Where 1.6 kA < Ibf ≤3.16 kA,
e70e-142_2012.png[D.7.6(t)]
Where 3.16 kA (H) Class RK1 Fuses 1 A through 100 A. Where Ibf <0.65 kA, calculate the arcing current using Equation D.7.2(a), and use time-current curves to determine the incident energy using Equations D.7.3(a), D.7.3(b), and D.7.3(c).
Where 0.65 kA ≤Ibf ≤1.16 kA,
e70e-144_2012.png[D.7.6(v)]
Where 1.16 kA < Ibf ≤1.4 kA,
e70e-145_2012.png[D.7.6(w)]
Where 1.4 kA < Ibf ≤106 kA,
e70e-146_2012.png[D.7.6(x)]
Where Ibf > 106 kA, contact the manufacturer. D.7.7 Low-Voltage Circuit Breakers. The equations in Table D.7.7can be used for systems with low-voltage circuit breakers. The results of the equations will determine the incident energy and arc flash boundary when Ibf is within the range as described. Time-current curves for the circuit breaker are not necessary within the appropriate range.
When the bolted fault current is below the range indicated, calculate the arcing current using Equation D.7.2(a), and use time-current curves to determine the incident energy using Equations D.7.3(a), D.7.3(b), and D.7.3(c). Table D.7.7 Incident Energy and Arc Flash Protection Boundary by Circuit Breaker Type and Rating 480 V and Lower 575 V–600 V Rating (A) Breaker Type Trip Unit Type Incident Energy (J/cm2)a Arc Flash Boundary
(mm)a Incident Energy (J/cm2)a Arc Flash Boundary (mm)a
100–400 MCCB TM or M 0.189 Ibf+ 0.548 9.16 Ibf + 194 0.271 Ibf+ 0.180 11.8 Ibf + 196
600–1200 MCCB TM or M 0.223 Ibf+ 1.590 8.45 Ibf + 364 0.335 Ibf+ 0.380 11.4 Ibf + 369
600–1200 MCCB E, LI 0.377 Ibf+ 1.360 12.50 Ibf+ 428 0.468 Ibf+ 4.600 14.3 Ibf + 568
1600–6000 MCCB or ICCB TM or E, LI 0.448 Ibf+ 3.000 11.10 Ibf+ 696 0.686 Ibf+ 0.165 16.7 Ibf + 606
800–6300 LVPCB E, LI 0.636 Ibf+ 3.670 14.50 Ibf+ 786 0.958 Ibf+ 0.292 19.1 Ibf + 864
800–6300 LVPCB E, LSb 4.560 Ibf+ 27.230 47.20 Ibf+ 2660 6.860 Ibf+ 2.170 62.4 Ibf + 2930 MCCB: Molded-case circuit breaker. TM: Thermal-magnetic trip units. M: Magnetic (instantaneous only) trip units. E: Electronic trip units have three characteristics that may be used separately or in combination: L: Long time, S: Short time, I: Instantaneous. ICCB: Insulated-case circuit breaker. LVPCB: Low-voltage power circuit breaker. a Ibf is in kA; working distance is 455 mm (18 in.). b Short-time delay is assumed to be set at maximum. The range of available three-phase bolted fault currents is from 700 A to 106,000 A. Each equation is applicable for the following range:
e70e-147_2012.png where: I1=minimum available three-phase, bolted, short-circuit current at which this method can be applied. I1 is the lowest available three-phase, bolted, short-circuit current level that causes enough arcing current for instantaneous tripping to occur, or, for circuit breakers with no instantaneous trip, that causes short-time tripping to occur.
I2=interrupting rating of the circuit breaker at the voltage of interest. To find I1, the instantaneous trip (It) of the circuit breaker must be found. It can be determined from the time-current curve, or it can be assumed to be 10 times the rating of the circuit breaker for circuit breakers rated above 100 amperes. For circuit breakers rated 100 amperes and below, a value of It = 1300 A can be used. When short-time delay is utilized, It is the short-time pickup current. The corresponding bolted fault current, Ibf, is found by solving the equation for arc current for box configurations by substituting It for arcing current. The 1.3 factor in Equation D.7.7(b) adjusts current to the top of the tripping band.
e70e-148_2012.png[D.7.7(a)]
At 600 V,
e70e-149_2012.png[D.7.7(b)]
At 480 V and lower,
e70e-150_2012.png[D.7.7(c)]
e70e-151_2012.png[D.7.7(d)] D.7.8 References. The complete data, including a spreadsheet calculator to solve the equations, can be found in IEEE 1584, Guide for Performing Arc Flash Hazard Calculations. IEEE publications are available from the Institute of Electrical and Electronics Engineers, 445 Hoes Lane, P.O. Box 1331, Piscataway, NJ 08855-1331, USA (http://standards.ieee.org/). D.8 Direct-Current Incident Energy Calculations. D.8.1 Direct-Current Arc Flash Calculations. D.8.1.1 Maximum Power Method. The method of estimating dc arc flash incident energy that follows was presented at the 2007 IEEE Electrical Safety Workshop (see reference 2, which follows). This method is based on the concept that the maximum power possible in a dc arc will occur when the arcing voltage is one-half of the system voltage. Testing completed for Bruce Power (see reference 3, which follows) has shown that this calculation is conservatively high in estimating the arc flash value. This method applies to dc systems rated up to 1000 Vdc.e70e-152_2012.png where:Iarc=arcing current, amperes
Ibf=system bolted fault current, amperes
IEm=estimated dc arc flash incident energy at the maximum power point, cal/cm2
Vsys=system voltage, volts
Tarc=arcing time, sec
D=working distance, cm For exposures where the arc is in a box or enclosure, it would be prudent to use a multiplying factor of 3 for the resulting incident energy value. D.8.1.2 Detailed Arcing Current and Energy Calculations Method. A thorough theoretical review of dc arcing current and energy was presented at the 2009 IEEE PCIC Conference. Readers are advised to refer to that paper (see reference 1) for those detailed calculations.
References: 1. “DC arc models and incident energy calculations,” Ammerman, R.F.; Gammon, T.; Sen, P.K.; Nelson, J.P.; Petroleum and Chemical Industry Conference, 2009, Record of Conference Papers,14–16 September 2009. 2. “Arc Flash Calculations for Exposures to DC Systems,” Doan, D.R., IEEE IAS Electrical Safety Workshop, 2007, Record of Conference Papers, March 2007. 3. DC Arc Hazard Assessment Phase II Copyright Material Kinectrics Inc. Report No. K-012623-RA-0002-R00.