# Incident-Energy Calculations This article is the third in a series that provides a step-by-step approach for performing arc flash hazard calculations. Parts 1 and 2 appeared in the January and March 2016 issues of ELECTRICAL CONTRACTOR, respectively.

When performing an arc flash hazard risk assessment, how do you determine the arc rating of protective clothing and personal protective equipment? Arc ratings are expressed in calories per square centimeter (cal/cm2), and, in general, the greater the hazard, the higher the rating needs to be. Is a rating of 8 cal/cm2 sufficient? Perhaps a higher rating of 12 cal/cm2 or even the 40 cal/cm2 “moon suit” is necessary. How do you know what to use?

### Arcing current and time

Incident-energy calculations are at the heart of arc flash risk assessments. Most perform these calculations with an arc flash computer program, but what do the actual calculations look like? The IEEE 1584 2002—IEEE Guide for Performing Arc Flash Hazard Calculations (IEEE 1584) provides the equations most commonly used for arc flash studies. The results include the prospective incident energy in cal/cm2 at a specific working distance for each piece of electrical equipment that is part of the study. This information can be used to select protective equipment and clothing.

Although many variables need to be considered when performing incident-energy calculations, two important ones include the arcing short-circuit current (discussed in part 2 of this series) and the arcing time, which defines the duration of the arc flash. For the arcing time, the typical practice is to use the clearing time of a protective device located upstream in a separate piece of equipment or enclosure. However, based on individual interpretations, there may be variations depending on equipment design and type.

The clearing time is determined by evaluating the device’s time-current curve (TCC). Each device has a unique TCC, which is a graphical representation indicating how long it will take to clear a fault for a given magnitude of current. In the case of an incident-energy calculation, the current is the arcing short-circuit current.

IEEE 1584 Amendment A includes an 85 percent multiplier that can be used to reduce the arcing current as a what-if scenario in case the actual arcing current is lower than the calculated value. Using the reduced arcing current, the protective device’s TCC defining the arcing time can be re-evaluated to see if it would take longer to operate with the lower current. This can happen if the arcing current falls below a protective device’s instantaneous tripping threshold and operates in the time delay region. If this occurs, the lower current and longer arcing time could result in a greater total incident energy, and that value would be used instead.

### Incident-energy calculations—IEEE 1584

IEEE 1584 provides three equations for determining the incident energy at a specific working distance. The first two equations are used to calculate the incident energy normalized to a 24-inch (610 mm) working distance and an arcing time of 0.2 seconds. The third equation is used to adjust the normalized value to the actual working distance and arcing time for specific conditions.

Equation 1—Calculation of the logarithm of the normalized incident energy:

log Ein = K1 + K2 + 1.081 × log Ia + 0.0011G

Equation 2—Normalized incident energy in cal/cm2:

Ein = 10logEin

There are many terms and variables in the above equations, including:

log Ein = Logarithm of the normalized incident energy. Logarithm functions are common on most scientific calculators and are often shown as a LOG button.

K1 = Accounts for the difference in incident energy reaching the worker based on whether the arc flash occurs in open air (no enclosure) or is focused out of the open end of a box (enclosed equipment). Use –0.792 for arcs in open air and –0.555 for arcs in a box/enclosure

K2 = Grounded vs. ungrounded factor—there is a minor difference in the incident energy depending on whether the system is effectively grounded. To account for this, K2 = 0 for ungrounded and high resistance grounded systems and –0.113 is used for grounded system

G = The air gap in millimeters between the conductors that the arc jumps across (Table 1)

Ein = Incident energy (cal/cm2) normalized to a 2-foot (610 mm) working distance and 0.2 second arcing time

Equation 3—Adjustment from normalized conditions to a specific working distance and arcing time:

Ei = Cf Ein [t / 0.2] [610 / D]x

Note: IEEE 1584 includes a constant of 4.184 in equation 3 that is used to convert the result from cal/cm2 to J/cm2. Because the arc rating of protective clothing and equipment is cal/cm2, this conversion constant is omitted here, and the results will be in cal/cm2.

The terms and variables for equation three include the following:

Ei = Incident energy in cal/cm2

Cf = Calculation factor—a Cf of 1.5 is used for systems with a voltage up through 1 kV. No Cf is used above 1 kV.

Ein = Normalized incident energy determined from equation 1

t = Arcing time in seconds

0.2 = Normalized arcing time in seconds

X = Distance exponent—the exponent from Table 1 used to define how the incident energy varies with distance.

D = Working distance—the distance from the point of the perspective arc flash to the person in mm (Table 2)

610 = The normalized working distance of 24 inches expressed in mm

### Example—incident energy calculations

As an example, Figure 1 illustrates a one-line diagram with a 480-volt (V) panel PP-1. An available arcing short-circuit current of 16,761 amperes (A) was previously calculated in part 2 of this series. The arcing time is given as 0.05 seconds (3 cycles), which is defined by the TCC (not shown in this example) of the upstream 225A circuit breaker.

A 25-mm gap distance and 1.641 distance exponent factor were selected from Table 1 because the panel falls into the MCC and panelboard category. An 18-inch (457-mm) working distance was selected from Table 2. The transformer connection shown on the one-line drawing indicates the system is grounded.

To aid in the calculation process, two worksheets were developed. Worksheet A (Figure 2) is used for calculating the normalized incident energy, and worksheet B (Figure 3) is used to calculated the incident energy adjusted for the specific working distance and arcing time.

### Worksheet A—normalized incident energy

Step 1: Using the arcing current Ia of 16.761 kA from part 2 of this series, multiply the logarithm of 16.761 by the constant 1.0811.

Step 2: Select the gap distance of 25 mm from Table 1 since the equipment is a 480V panelboard. Multiply it by 0.0011.

Step 3: Since a panel behaves like a box, select the value of K1 as -0.555 for the arc in a box factor.

Step 4: The transformer symbol on the one-line diagram indicates the 480V system is grounded. Therefore, select the K2 value based on whether the power system is effectively grounded.

Step 5: Add the values from steps 1 through 4 to determine the logarithm of the normalized incident energy Ein.

Step 6: Raise the number 10 to the value found in step 5. This is the incident energy normalized to a working distance of 24 inches and a duration of 0.2 seconds (12 cycles).

### Worksheet B—incident energy

Incident-energy worksheet B is used to convert the normalized value to an incident energy at a specific working distance and arcing time used in the study.

Step 1: This step is used to adjust the incident energy from the normalized 24-inch (610 mm) working distance to the actual working distance (D) used for the equipment under study.

Step 2: Incident energy is directly proportional to the arc duration. This step scales the incident energy by the ratio of the actual arcing time in seconds to the 0.2-second normalized value. The arcing time was given as 0.05 seconds (3 cycles).

Step 3: Since the voltage is 480V, a calculation factor of 1.5 is used.

Step 4: This requires multiplying the values of steps 1 through 3 together, resulting in the total incident energy in cal/cm2 at the specific working distance and arcing time.

The resulting incident energy is 2.9 cal/cm2, which can be factored into the arc flash risk assessment. The arc rating of the protective clothing and equipment that should be used at this location when an arc flash hazard exists can be selected to have a rating sufficient for this value.

Part 4 in this series will address the arc flash boundary calculations.