It is recognized that to construct an accurate mathematical model of the arcing phenomena is rather impractical. This is because of the spasmodic nature of the fault caused by arc elongation blowout effects, physical flexing of cables and bus bars under short circuits, possible arc reignition, turbulent flow of plasma, and high temperature gradients (the temperature at the core being of the order of 25,000 K, while at the arc boundary, of the order of 300–2000 K).
IEEE 1584 Guide equations are empirical equations based upon laboratory test results, though the standard includes some of Lee’s equations also.
TABLE 1.4. Limitations of ARC Flash Hazard Calculation Methods
Source: NFPA 70E-2018. © 2018 National Fire Protection Association.
| Source | Limitations/Parameters |
| Ralph Lee [11] | Calculates arc flash boundary for arc in open air; conservative over 600 V and becomes more conservative as voltage rises |
| Doughty and Neal [14] | Calculated incident energy for three-phase arc on systems rated 600 V and below, applies to short-circuit currents between 16 and 50 kA |
| Ralph Lee [11] | Calculated incident energy for three-phase arc in open air on systems rated above 600 V, becomes more conservative as voltage rises |
| IEEE Standard 1584 [9] | Calculates incident energy and arc flash boundary for 208 V to 15 kV, three-phase 50–60 Hz; 700–106,000 A short-circuit currents and 13–152 mm conductor gaps.a |
| ANSI/IEEE C2, tables 410-1, 410-2 [32] | Calculates incident energy for open-air phase-to-ground arcs 1 kV to 500 kV for live line work. |
| Doan | Arc flash calculations for exposure to DC systems. Calculates incident energy for DC systems up to 1000 V DC. |
a Equations for higher voltages are included.
If the equipment is maintained under deenergized condition, there is no arc flash hazard. NFPA 70E [17] states that energized electrical conductors and circuit parts that operate at less than 50 V to ground should not be required to be de-energized. Again, it is qualified that the capacity of the source and any overcurrent protection between the source and the worker should be determined and there should be no increased exposure to electrical burns or explosion due to electrical arcs. The IEEE 1584 Guide states that equipment below 240 V need not be analyzed for arc flash unless it involves at least one 125 kVA or larger low impedance transformer in its immediate power supply. The “low impedance” is not defined. Sometimes, the arc flash hazard can be high even in systems of 240 V. When incident energy exceeds 40 cal/cm2, the equipment should only be maintained in the de-energized condition. There is no PPE (personal protective equipment) outfits specified for incident energy release >40 cal/cm2; see Section 1.9 for definitions and discussions of PPE.
That an arc flash analysis shall not be required where all the following conditions exist has been deleted in NFPA 70E 2012:
The circuit is rated 240 V or less.
The circuit is supplied by one transformer.
The transformer supplying the circuit is rated less than 125 kVA.
This qualification has now been removed in 1584, 2018 edition.
The user is referred to IEEE Guide 1584 for three-phase systems rated less than 240 V.
1.8.1 Ralph Lee’s and NFPA Equations
Ralph Lee equations from Reference [11] are as follows:
Maximum power in a three-phase arc is:
(1.5)
where MVAbf is bolted fault mega-volt-ampere (MVA).
The distance in feet of a person from an arc source for a just curable burn, that is, skin temperature remains less than 80°C, is:
where t is the time of exposure in seconds.
The equation for the incident energy produced by a three-phase arc in open air on systems rated above 600 V is given by:
where:
D = distance from the arc source in inches
F = bolted fault short-circuit current, kA
V = system phase-to-phase voltage, kV
tA = arc duration in seconds.
For the low voltage systems of 600 V or below and for an arc in the open air, the estimated incident energy is:
(1.8)
where EMA is the maximum open air incident energy in cal/cm2, F is short-circuit current in kA, range 16–50 kA, and DA is distance from arc electrodes, in inches (for distances 18 in and greater).
The estimated energy for an arc in a cubic box of 20 in, open on one side is given by:
where EMB is the incident energy and DB is the distance from arc electrodes, inches (for distances 18 in and greater).
1.8.2 IEEE 1584 Guide Equations
This is based on IEEE 2002 Guide. Included here for reference and completeness.
The IEEE equations are applicable for the electrical systems operating at 0.208 to 15 kV, three-phase, 50 or 60 Hz, available short-circuit current range 700–106,000 A, and conductor gap = 13–152 mm. For three-phase systems in open air substations, open-air transmission systems, a theoretically derived model is available. For system voltage below 1 kV, the following equation is solved:
TABLE 1.5. Classes of Equipment and Typical Bus Gaps
Source: IEEE 1584-2018 Guide [9]. © 2002 IEEE. Also see Chapter 3.
| Classes of Equipment | Enclosure Size (in) | Typical Bus Gaps (mm) |
| 15-kV switchgear | 45×30×30 |
152
|