Written by Steve Hudgik
Published by the Institute of Electrical and Electronics Engineers and titled "Guide to Performing Arc Flash Calculations," IEEE 1584 provides empirical formulas for determining arcing fault current, flash protection boundaries, and incident energy. The formulas are valid for systems ranging from 208 V to 15 kV. Theoretical formulas are provided for conditions outside this range.
IEEE 1584 establishes a ninestep process for gathering information and calculating arc flash hazards. The steps are:

Collecting system data is the most difficult and timeintensive step in performing an arc flash hazard analysis, but accurate information is vital to correctly calculating flash boundaries. A relatively small error at this point can invalidate all further arc flash calculations. An IEEE paper* lists the minimum information that should be gathered, as shown in the table at right.
Information collected should be recorded on a oneline diagram of the facility's electrical system. This diagram should be updated whenever modifications are made to the system.
Many electrical systems, especially in smaller facilities, have only a single mode of operation. In large facilities, however, it is common to find a number of operating modes, possibly including: emergency modes in which only backup generators provide power; multiple utility sources or generators that are switched in or out; and motors or portions of the system that may start or cease operation. All of these different modes cause changes in current at various points in the system, altering incident energy and flash boundaries.
The bolted fault current is the current that would flow through a short circuit consisting of two conductors bolted together. It is the maximum current available to flow through a short circuit. This information is used to calculate the arc fault currents. Bolted fault currents should be determined for each piece of equipment likely to require maintenance or inspection while energized.
The current that flows through an arcing fault is usually significantly less than the bolted fault current, due to greater resistance. Arc fault current calculations are based on voltage, bolted fault current, conductor gap distance, and other factors. IEEE 1584 presents two formulas for calculating arc fault currents, one for use with 0.2081 kV systems, and the other for systems between 1 and 15 kV.
For systems between 0.208 and 1 kV:
lg I_{a} = K + 0.662(lg I_{bf}) + 0.0966(V) + 0.000526(G) + 0.5588(V)(lg I_{bf})  0.00304(G)(lg I_{bf})For systems between 1 and 15 kV:
lg I_{a} = 0.00402 + 0.983(lg I_{bf})where I_{a} = arc fault current in kA; K = 0.153 for openair arcs and 0.097 for enclosed arcs; I_{bf} = 3phase bolted fault current in kA; V = voltage in kV; G = conductor gap in mm
The timecurrent curves of upstream protective devices are the major factor in determining how long an arcfault will last. An effort should be made to determine the actual settings rather than relying on standard values, as these may cause incident energy to vary greatly.
Another consideration when analyzing protective devices is that incident energy depends on both fault current and time. Since protective devices are slower at lower currents, minimum fault currents often pose the worstcase arc flash scenario.

Voltage and equipment class determine what equation should be used to find the flash boundary, as well as the bus gap distances required by the equations. Systems operating at <1 kV use a different equation than those operating between 1 kV and 15 kV. In addition, IEEE 1584 recognizes six equipment classes, as shown in the table at the right. The bus distances used to help determine the arcing fault current.
The working distance is the distance from a potential arc source to a worker's face and chest. It is a critical quantity in determining the flash hazard boundary, as even an increase of a few inches in working distance can cause a significant drop in incident energy. 18 inches is the working distance most commonly assumed in calculations, but efforts should be made to determine actual working distances. Some usual working distances are shown in the table at right.

Incident energy is defined in NFPA 70E as "the amount of energy impressed on a surface, a certain distance from the source, generated during an electrical arc event." In an arc flash hazard study, the "surface" is the worker's body at the assumed working distance. Incident energy is expressed in calories/cm^{2}. IEEE 1584 uses the following formulas:
(1) E = 4.184(C_{f})(E_{n})(t/0.2)(610^{x}/D^{x})where E = incident energy in joules/cm^{2}; C_{f} is a calculation factor (1.0 for voltages above 1 kV, and 1.5 for voltages below 1 kV); E_{n} = normalized incident energy (from equation (2) below); t = arc duration in seconds; D = distance from arc in mm; x = distance exponent (see table below)
Equipment Type  D (Distance Exponent) 

Open air  2.0 
Lowvoltage (.2081 kV) switchgear  1.473 
Highvoltage (115 kV) switchgear  0.973 
Lowvoltage MCCs and panels  1.641 
Cables  2.0 
where E_{n} = energy normalized for distance of 610 mm and arc duration of 0.2 seconds, in joules/cm^{2}; K_{1} = 0.792 for openair arcs and 0.555 for enclosed arcs; K_{2} = 0 for ungrounded/highZ systems and 0.113 for grounded systems; G = arc gap in mm; I_{a} = predicted 3phase arc fault current in kA
The FPB is the distance at which incident energy is 1.2 cal/cm2, which is the amount of heat needed to cause seconddegree burns. The IEEE formula for calculating FPB is
D_{B} = [4.184(C_{f})(E_{n})(t/0.2)(610^{x}/E_{B})]^{1/x}where E_{B} is the desired incident energy at the boundary (usually 1.2 cal/cm^{2}, but occasionally set at a value matching proposed PPE rating), with other variables defined as for the incident energy equations above.
* M. Gibbs, "Arc Flash Boundary Calculations Using Computer Software Tools," presented at IEEE IAS Annual Meeting, Seattle, 2004.
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