(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:
This expression is valid for arcs both in open air and in a box. Use 0.85 Ia 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 Ia and Ia 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:
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:
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 |