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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
15-kV MCC	36×36×36	152
5-kV switchgear	36×36×36	104
5-kV switchgear	45×30×30	104
5-kV MCC	26×26×26	104
Low voltage switchgear	20×20×20	32
Shallow low voltage MCCs and panel boards	14×12×≤8	25
Deep voltage MCCs and panel boards	14×12×>8	25
Cable junction box	14×12×≤8 or14×12×>8	13

(1.10)

where:

 Ia = arcing current in kA

 G = conductor gap in mm, typical conductor gaps are specified in [9] (see Table 1.5)

 K = −0.153 for open air arcs, −0.097 for arc in a box

 V = system voltage in kV

 Ibf = bolted three-phase fault current kA, rms symmetrical.

For systems of 1 kV and higher, the following equation is solved:

(1.11)

This expression is valid for arcs both in open air and in a box. Use 0.85 I_a 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 incident energy using both 0.85 I_a and I_a and use the higher value.

Equation (1.11) is a statistical fit to the test data and is derived using a least square method; see Appendix A for a brief explanation of least square method.

Incident energy at working distance, an empirically derived equation, is given by:

(1.12)

The equation is based upon data normalized for an arc time of 0.2 seconds, Where:

 En = Incident energy (J/cm2) normalized for time and distance

 K1 = −0.792 for open air and −0.555 for arcs in a box

 K2 = 0 for ungrounded and high resistance grounded systems and −0.113 for grounded systems. Low resistance grounded, high resistance grounded, and ungrounded systems are all considered ungrounded for the purpose of calculation of incident energy.

 G = conductor gap in mm (Table 1.5).

Conversion from normalized values gives the equation:

(1.13)

where:

 E = incident energy in J/cm2

 Cf = calculation factor = 1.0 for voltages above 1 kV and 1.5 for voltages at or below 1 kV

 t = arcing time in seconds

 D = distance from the arc to the person, working distance (Table 1.6)

 x = distance exponent as given in Reference [9] and reproduced in Table 1.7.

A theoretically derived equation can be applied for voltages above 15 kV or when the gap is outside the range in Table 1.5 (from Reference [9]).

(1.14)

TABLE 1.6. Classes of Equipment and Typical Working Distances

Source: IEEE 1584-2018 Guide [9]. © 2002 IEEE. Also see Chapter 3.

Classes of Equipment	Working Distance
15-kV switchgear	36
15-kV MCC	36
5-kV switchgear	36
5-kV switchgear	36
5-kV MCC	36
Low voltage switchgear	24
Shallow low voltage MCCs and panel boards	18
Deep voltage MCCs and panel boards	18
Cable junction box	18

TABLE 1.7. Factors for Equipment and Voltage Classes

Source: IEEE 1584 Guide [9]. © 2002 IEEE.

System Voltage, kV	Equipment Type	Typical Gap between Conductors	Distance × Factor
0.208–1	Open air	10–40	2.000
	Switchgear	32	1.473
	MCC and panels	25	1.641
	Cable	13	2.000
>1–5	Open air	102	2.000
	Switchgear	13–102	0.973
	Cable	13	2.000
>5–15	Open air	153	2.000
	Switchgear	13–153	0.973
	Cable	13	2.000

For the arc flash protection boundary, defined further, the empirically derived equation is:

(1.15)

where E_B is the incident energy in J/cm² at the distance of arc flash protection boundary.

For Lee’s method:

(1.16)

Due to complexity of IEEE equations, the arc flash analysis is conducted on digital computers. It is obvious that the incident energy release and the consequent hazard depend upon:

 The available three-phase rms symmetrical short-circuit currents in the system. The actual bolted three-phase symmetrical fault current should be available at the point where the arc flash hazard is to be calculated. In low voltage systems, the arc flash current will be 50–60% of the bolted three-phase current, due to arc voltage drop. In medium and high voltage systems, it will be only slightly lower than the bolted three-phase current. The short-circuit currents are accompanied by a DC component, whether it is the short circuit of a generator, a motor, or a utility source. However, for arc flash hazard calculations, the DC component is ignored. Also, any unsymmetrical fault currents, such as line-to-ground fault currents, need not be calculated. As evident from the cited equations, only three-phase symmetrical bolted fault current need be calculated.

 The time duration for which the event lasts. This is obviously the sum of protective-relay (or any other protection device) operating time plus the opening time of the switching device. For example, if the relay operating time is 20 cycles, and the interrupting time of the circuit breaker is 5 cycles, then the arc flash time or arcing time is 25 cycles.

 The type of equipment, that is, switchgear or MCC, or panel and the operating voltage

 The system grounding. This is deleted in 2018 edition, see Chapter 3

We can add to this list:

1 Electrical electrodes and potential arc lengths; spacing between phases, spacing between phases and ground, orientation-vertical or horizontal, insulated versus non-insulated buses.

2 Atmospheric conditions like ambient temperature, barometric pressure, and humidity.

3 Dissipation of energy in the form of heat, light, sound, and pressure waves.

4 Arc conditions like, randomness of arc, its interruption, arc plasma characteristics, size, and shape of enclosure.

For using the IEEE equations, the factors listed above need not be considered. As an example, there are many discussions about the gap distances specified in IEEE 1584 Guide and their effects on the incident energy release. While critique of IEEE equations and methodology does add to the technical aspects and paves the way for further revisions, this book limits the calculations according to current IEEE methodology. See also Chapter 3.

IEEE Standard 1584 Guide also provided equations for class L and RK1 fuses, not reproduced here.