AC arc flash modeling implemented in ARCMASTER V1.0 software program

Votage drop Varc across the equivalent arc resistance which is introduced by the arc plasma in typical AC circuit depicted on Figure 1 can be expressed as:

Varc = -I * Rs + (Vs2 - I2*Xs2)1/2
Equation 1

where I is current in Amps, Vs stands for an open source voltage in Volts, Rs and Xs are system resistance and reactance respectively, including source and feeders.


Figure 1. Single & three phase AC arc flash equivalent circuit.

It was demonstrated that there is a minimum voltage needed to maintain an arc. That minimum depends on the current magnitude, gap width, and orientation of the electrodes. This transitional point can be calculated by [1]:

It = 10 + 0.2 * G
Equation 2

G - conductor gap distance in millimeters
It - the transitional point current measured in amperes

Above that minimum, the arc V-I characteristic can be expressed as [1]:

Varc = (20 + 0.534 * G) * Iarc0.12
Equation 3

or alternatively as:

Iarc = [Varc / (20 + 0.534 * G)]8.33
Equation 4

Varc - arcing voltage in Volts
Iarc - arcing current in Amps Iarc - dc arcing current in amperes

Equations (1) through (3) can be solved for the maximum conductor gap where the arc can likely be sustained under the specified system voltage, the equivalent source X/R ratio and available short circuit fault current.

To find the point where the arc V-I characteristic crosses the circuit load line, solve equations (1) and (4) using the iterative method. As the first approximation, assume Iarc is equal to half of the available short circuit fault current. Then, follow the steps below:

  1. determine Varc from equation (1)
  2. substitute Varc into equation (4) to determine new Iarc

Cycle through the steps 1 and 2 above until the answers for Varc converge.

Table 1 shows arcing current values measured by two laboratories[2] along with accompanying system parameters, and the current values calculated solving equations 1 through 4 using the same parameters. Calculated arcing current values nearly match the actual test data. The calculations have been performed using ARCMASTER V1.0 software program.

Test Line Voltage, V Bolted Fault Current, A Fault P.F., % Gap, in. Measured Arcing Current, A Calculated Arcing Current, A Variation, %
TI-4 276 996 7.9 1 900 940 4%
TI-7 277 980 Low 1/2 900 900 0%
TI-8a 120 940 Low 1/2 750 750 0%
TI-9 146 1150 Low 1/2 1000 990 1%
TI-12 278 650 41.8 1/2 600 590 2%
TII-6 263 2910 44 1 2570 2390 7%
TII-8 263 7400 44 1 6000 5830 3%
TII-9 263 10580 40 1 8450 8360 1%
TII-15 263 25000 22 2-1/4 16600 16590 0%
TII-19 263 41600 22 3-1/4 20640 19530 5%
Table 1 - A comparison between actual arcing current data and the output of ArcMaster software.

Power and energy in the arc

The energy released during an arc flash event is roughly proportional to the arc duration. The upstream protective device operation controls the arc flash duration. A fuse or properly maintained over-current protection device has a predictable time to open the circuit with a specific arc current value. Hence, arcing current impacts the released energy directly through the current itself and through interaction with the protection device.

The power in the arc can be calculated by:

Parc = Iarc * Varc
Equation 7

where the Parc is measured in watts.

The energy in the arc is a function of power and time:

Earc = Parc * tarc
Equation 8

where the Earc is measured in Joules.

Incident energy exposure for an open-air arc where the heat transfer depends on the spherical energy density is then expressed as:

Eiair = Earc/(4 * π * D2)
Equation 9

Eiair - incident energy from an open air arc at distance D in Joules/cm2
D - distance from the arc in centimeters

This formula assumes the radiant heat transfer. Not all of the arc energy will be transferred as radiant heat as a portion of the energy is transformed into pressure rise and in heat conducted to the electrode material. Therefore, the equation (9) will produce a conservative but safe estimate of incident energy exposure.

For the arc in a box, the enclosure has a focusing effect on the incident energy. For the selected enclosure type and test distance, the incident energy from an arc flash in a box can be calculated by [3]:

Eibox = K * Earc / (A2 + D2)
Equation 10

Eibox - the incident energy from an arc flash in a box in Joules/cm2
D - distance from the arc in centimeters

A and K are obtained from optimal values listed in table below:

Enclosure Type A, cm K
Panelboard 10 0.127
LV Switchgear 40 0.312
MV Switchgear 95 0.416

Arc flash boundary

Equation (9) written in terms of arc flash boundary, becomes:

AFB = [Earc / (4 * π * Et)]0.5
Equation 11

AFB - arc flash boundary measured in centimeters
Et - threshold incident energy to second degree burn in J/cm2 calculated by [4]:

Et = 5 * t0.3
Equation 12

where t stands fo exposure time in seconds.

Likewise, equation (10) written in terms of arc flash boundary, becomes:

AFB = [K * Earc / Et - A2]0.5
Equation 13

The above procedure may also be applied for calculating of the released arc energy and arc flash protection boundary in three-phase system. Please keep in mind that in such a case the equivalent circuit impedance values in equation (1) should be calculated based on the available three-phase short circuit fault current values and line-to-line voltage. Also, the arcing energy in equation (8) need be multiplied by 31/2 before the 3-phase fault incident energy and arc flash boundary values can be determined from equations (10) and (11) respectively.


  1. A.D. Stokes and W.T. Oppenlander, "Electric arcs in open air", Journal of Physics D: Applied Physics, 1991, pp. 26-35
  2. L. Fisher, "Resistance of Low-Voltage AC Arcs", IEEE Transactions on Industry and General Applications, vol. IGA-6, No.6, Nov/Dec 1970
  3. R. Wilkins, "Simple improved equations for arc flash hazard analysis", IEEE Electrical Safety Forum, August 2004
  4. M. Furtak and L. Silecky, "Evaluation of onset to second degree burn energy in arc flash hazard analysis", IAEI News, July-August 2012