Knowing how long an arc flash could last is the most important piece of information in predicting its severity. The duration is usually dependent on how fast an upstream protective device will trip. The longer it takes, the greater the incident energy and resulting hazard.

**Time current curves**

How can you predict how long it takes a device to trip? The best method is to use time current curves (TCC), as shown in the figure. Every overcurrent-protective device, such as circuit breakers, fuses and relays, have their own unique TCC that defines specifically how fast they will operate for given levels of current.

The horizontal axis of the graph represents current in amperes (A). Although this axis begins on the left at 0.5A, a “scaling factor” is often used, such as “ 100,” as shown at the bottom. In this case, each value of current is multiplied by 100, so 0.5 becomes 0.5 100 or 50A, 1 is multiplied by 100 and is now 100A, and so on.

The vertical axis on the left of the graph represents time plotted in seconds. The graph uses a logarithmic scale, which simply means current and time increase by orders of magnitude (i.e., 1, 10, 100, 1,000 instead of 1, 2, 3, 4).

To determine the arc flash duration using the upstream device’s time current curve, the arcing current must first be identified on the bottom of the graph. This current is normally calculated using equations found in IEEE 1584—IEEE Guide for Performing Arc Flash Hazard Calculations. Next, a vertical line is drawn from the current until it intersects the top of the TCC. The time value associated with this intersection is the time that is used for the arc flash duration. It is very important to recognize that this time value assumes the device is in good condition and performs as the TCC indicates.

**Example 1—1,600A circuit breaker, 32,000A arcing current**

An arc flash calculation study has predicted the arcing short-circuit current is 32,000A. This current is plotted on the TCC as shown in the figure. Locate 32,000A at the bottom of the graph and draw a vertical line until it intersects the top of the 1,600A breaker’s TCC. This intersection occurs at 0.083 seconds (five cycles), which means that is how long it should take the breaker to trip and clear the arc flash. The current in this example falls in the band at the lower far-right end of the curve, which is referred to as the instantaneous function. Based on IEEE 1584 incident-energy calculations, using 32,000A and 0.083 seconds, the equivalent incident energy for this example is 5.1 calories per centimeter2 (cal/cm2).

**Example 2—When less is more, 16,000A arcing current**

Surprising as it may be, it is possible that a lower short-circuit current could result in a greater incident energy. What if a switching change occurs either at the facility or electric utility that reduces the available short-circuit current to 16,000A—half of what it was in Example 1. Conventional wisdom would dictate that the greater the short-circuit current, the greater the incident energy, and as a result, the greater the arc flash hazard. However, this is not always the case.

In Example 2, the lower current of 16,000A results in an increase of the circuit breaker clearing time to 0.5 seconds (30 cycles) as shown above. This is a six-fold increase in arc flash duration, which would result in an increase in incident energy to 16.2 cal/cm2. Although the current is now only 50 percent of the original value, the incident energy increases to more than 300 percent of its original value.

Worst case? Not always as it appears

When performing an arc flash calculation study, the maximum short-circuit current is not always going to result in the maximum incident energy. As part of any arc flash calculation study, alternate scenarios of lower short-circuit current should be evaluated as they could result in a greater, worst case incident energy.

**PHILLIPS**, founder of www.brainfiller.com and www.ArcFlashForum.com, is an internationally known educator on electrical power systems. His experience includes industrial, commercial and utility systems, and he is a member of the IEEE 1584 Arc Flash Working Group. Reach him at jphillips@brainfiller.com.