Annex D introduces five sets of equations to calculate the arc flash boundary and/or the incident energy level. It also provides formulas for calculating arc flash energies and boundaries to be used with current-limiting Class L and Class RK1 fuses as well as with circuit breakers. This Annex also includes numerical examples that demonstrate the calculation procedure.

The equations in this Annex can be used for low-voltage and medium-voltage systems, but each has its own limitations. Thus, the reader must use the set of equations that best suits his/her application. The limitations are in terms of voltage, short circuit current range, open air space, or inside a cubical (applicable to arc flashes emanating from within switchgear, motor control centers, or other electrical equipment enclosures).

For typical low-voltage applications (<600V), these equations seem to best fit.

The following equation is used to estimate the incident energy in a cubic box (20 in. on each side):

EMB = 1038.7 DB-1.4738  tA [ 0.0093F2 - 0.3453 F + 5.9675 ]

Where:

EMB : is the maximum 20-inch cubic box incident energy in cal/cm2.

DB: is the distance from arc electrodes in inches. DB is the working distance and it is 18 in. for low-voltage application the origin of this value is in NFPA 70 Table 110.26(A)(1) Working Space (Low Voltage).

F: is the short circuit current, kA (for range of 16kA to 50kA), for the circuit under consideration.

tA: is the arc duration in seconds. To calculate tA, first calculate the arc fault current (IA) from the following equation:

log(IA) = K + 0.662log(Ibf)+0.0966V+0.000526(G) + 0.5588(V)log(Ibf)-0.00304(G)log(Ibf)

Where:

IA: is the arc fault current.

Ibf: is the bolted short circuit current (3-phase symmetrical rms kA).

G: is the gap between conductors or buses. Obtain the value of G from Table D.7.2 Factors for Equipment and Voltage Classes.

K: -0.153 for open air or -0.097 for “In Box.”

V: is the system voltage (0.208kV to 15kV).

Then, calculate IA = 10 lg IA

Time is the most controllable factor in the amount of incident energy and can be controlled by the settings of the upstream circuit breaker during the time current characteristics TCC coordination study. The time can be directly obtained from protective device time current characteristics TCC curve. The maximum value for the time to be used in calculations is 2 sec.

For 480V systems, the industry accepted minimum level for a sustaining arcing fault is 38% of the available bolted fault, 3-phase short circuit current. The highest incident energy exposure could occur at these lower levels where the overcurrent device could take seconds or minutes to open.

Notice that you can 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 the incident energy using both arc durations (Ia and 0.85 × IA), and use the these two values to obtain from the TCC of the upstream protective devices two values for tA. Then calculate the incident energy and use the largest amount.

Another set of data you will find useful when performing arc flash calculations is the 480V portion of Table D.7.7, “Incident Energy and Arc Flash Protection Boundary by Circuit Breaker Type and Rating 480V and Lower”:

Rating
(Amp)

Breaker
(Type)

Trip Unit
(Type)

Incident Energy
(J/cm2)

Arc Flash
[ Boundary (mm) ]

100 to 400

MCCB

TM or M

0.189 Ibf + 0.548

9.16 Ibf+ 194

600 to 1,200

MCCB

TM or M

0.223 Ibf + 1.590

8.45 Ibf + 364

600 to 1,200

MCCB

E, LI

0.377 Ibf + 1.360

12.50 Ibf + 428

In this table, MCCB stands for molded-case circuit breaker, TM is a thermal-magnetic trip unit, M is a magnetic (instantaneous only) trip unit, and E is an electronic trip unit that has three characteristics, which may be used separately or in combination — long time, short time, and instantaneous. The equations in the Table have one unknown: Ibf. When the incident energy is known, the HRC can be determined from the information in Table 2.

Notes:

Ibf is based on a working distance of 455 mm (18 in.).

Ibf is between 700A and 106,000A.

TCC curves are not necessary when Ibf is in the range above.

The equations above can be used for checking calculations or in lieu of detailed calculations.

The incident energy is in joule/cm2 and needs to be converted to cal/cm2 as follows:

1 J/cm2 = 0.238902957619 cal/cm2