# More Than Just One Number: Understanding incident-energy calculations Jim Phillips
Published On
Jan 15, 2021

### Playing with fire

When I was around 10 years old, I learned the “fine art” of playing with fire. I thought it was amazing to wave my finger directly through a candle flame without being burned. I also learned (the hard way) that, if you hold your hand several inches above the flame—although it’s not as hot—you get burned. This is similar to the relationship with incident energy. With different values of short-circuit current and arc duration, the incident energy can vary greatly—and it is even possible to have the exact same incident energy with two widely varying short-circuit currents and arc durations.

To illustrate these concepts, three scenarios were developed using calculation methods from the 2018 edition of IEEE 1584— IEEE Guide for Performing Arc-Flash Hazard Calculations .

The following parameters are used for each scenario: voltage: 480V, enclosure opening: 20 in. by 20 inches, electrode gap: 25 millimeters, electrode configuration: vertical conductors inside a metal box, working distance: 18 in.

### Table 1: Vary short-circuit current

Table 1 shows the effect that the bolted short-circuit current has on incident energy. An arc duration of three electrical cycles or 50 milliseconds (ms) was used for each calculation, and only the bolted short-circuit current was varied using four different values listed in column 1. Column 2 lists the calculated-arcing short-circuit current, and column 3 lists the ratio of the arcing short-circuit current compared to the bolted short-circuit current. Although the bolted short-circuit current is increased by 400% from 20 kiloamps (kA) to 80 kA, the resulting incident energy in column 5 only increases by 275% from 1.81 to 4.98 cal/cm2. This indicates that, although the calculated incident energy increases with short-circuit current, it is not directly proportional.

### Table 2: Vary arc duration

The arc duration is often considered to be the most important variable, since the incident energy is directly proportional to the duration, i.e., the duration has the greatest effect on the incident energy. Table 2 uses 20 kA of short-circuit current for each calculation, with only the arc duration varying. Column 3 illustrates that as the arc duration increases by 1,200% from 50 to 600 milliseconds, the incident energy also increases proportionally by 1,200% from 1.81 to 21.67 cal/cm2, as shown in column 4.

### Table 3: Same incident energy, different current, duration

Table 3 illustrates how the incident energy can be the same for multiple cases, even when the short-circuit current is different. In this scenario, the arc duration was adjusted for each bolted short-circuit current so the total incident energy is 4.98 cal/cm2 for each case. Thinking about the candle flame, this is similar to varying how far you hold your hand above the flame and how long it can be held there to receive the same thermal energy. At the lower bolted short-circuit current of 20 kA, it takes 138 ms to achieve 4.98 cal/cm2, and at 80 kA it only takes 50 ms (three cycles).

Note that to match 4.98 cal/cm2 exactly for each calculation, the arc duration in milliseconds does not always match an even number of electrical cycles, as would normally be the case. Although the total incident energy is the same for each calculation, 4.98 cal/cm2 from 80 kA would be much more intense with the shorter duration of 50 ms. The 20 kA would not be as intense since it takes almost three times as long for the same incident energy.

Although these examples illustrate how the incident energy can vary with short-circuit current and duration as well as how it can remain the same with different short-circuit currents and varying the duration, the best number for incident energy is always zero! Zero incident energy means zero voltage. Place the system into an electrically safe working condition.