# History of Arcing Short Circuit Calculations – 1980’s to Now

One of the main variables used for incident energy and arc flash boundary calculations is the arcing short circuit current. How the arcing current is calculated has gone through an evolution beginning back in the 1980’s up through today.

The arcing current will always be less than the “bolted” short circuit determined by performing a “traditional” short circuit study that is used to evaluate the interrupting rating of protective devices. During an arc flash, the short circuit current flows across an air gap which introduces an arcing impedance. The result is that the arcing short circuit current will always be less than the bolted short circuit current at the same location.

Why would a reduced current from the arc impedance be so important? It seems that more current would be worse. When evaluating interrupting ratings, a larger current is the worst case but an arc flash study is different.

The prospective incident energy from an arc flash is dependent on two main variables – the arcing short circuit current and the arc duration which is defined by how long it takes an upstream protective device to operate. The lower arcing current may cause the protective device to take longer to trip – resulting in a longer duration and greater (and more dangerous) incident energy.

**1980’s – No Arcing Current**

Back in the 1980’s a.k.a. the early days of arc flash calculations, the equations were theoretical and quite primitive by today’s standards – but it was a good beginning! The early equations did not consider the arcing current and were based on the bolted short circuit current. When determining how long a protective device might take to operate, it’s time current characteristic is used. If the bolted short circuit current was used, it could indicate the protective device trips instantaneously. However, the lower (and unknown) arcing current could actually result in the device taking longer to trip – leading to a greater incident energy.

**2000 –Bolted Current and 38 Percent**

Equations from a technical paper published in 2000 are listed in NFPA 70E Annex D.3. These equations are based on actual arc flash testing – a significant improvement from earlier theoretical methods. However, there were still no arcing short circuit equations. As work around, the method references earlier research and states: “For 480-volt systems, the industry accepted minimum level for a sustaining arcing fault is 38 percent of the available bolted fault” That was it – multiply the bolted short circuit current by 38 percent and determine if the reduced current causes the protective device to take longer to operate resulting in a greater incident energy. PROGRESS!

**2002 – Arcing Current and 85 Percent**

When the first edition of IEEE 1584 was published in 2002, one of more significant improvements was the introduction of arcing short circuit current equations. However, since there could be many unknown factors that influence the actual arcing current, it was commonly referred to as “estimate”. As an estimate, what if the actual arcing current was lower? It could again possibly result in the protective device taking longer to operate and lead to a greater incident energy.

The solution? Add an additional step where the estimated arcing current would simply be multiplied by 85 percent and the protective device operating time would be re-evaluated with the slightly lower current. The 100% case and 85% case would be compared and the worst case would be used for the study result. The 85% multiplier was used for all arcing current calculations for systems under 1000 Volts.

**2018 – Arcing Current and VarC _{f}**

Based on almost 2000 new arc flash tests, the 2018 Edition of IEEE 1584 has made further improvements to the arcing current calculations for greater accuracy. However, the new equations are much more complex and include different electrode configurations, ten different coefficients as well as other variables. The process involves several calculation steps including determining the “Intermediate Average Arcing Current” with equations based on 600, 2700 and 14,300 volts. The second step is to use the intermediate current(s) and solve for the final arcing current at the specific system voltage.

Similar to the 2002, edition, a second arc duration is calculated using a reduced arcing current to determine if there is an effect on the protective device operating time. Unlike the fixed value of 85% used in the 2002 edition, the 2018 edition has introduced a new equation for an Arcing Current Variation Correction Factor VarC_{f} which is used for all voltages from 208 to 15,000. The VarC_{f} is heavily voltage dependent and has the greatest impact at voltages between 208 to 600 volts.

**The Evolution Continues**

It has taken several decades, hundreds of people, tens of thousands of manhours and millions of dollars in research to move our understanding of arc flash and related calculations to this level. Some say the cost and time is too much. For electrical worker’s that have survived an arc flash with minimal or no injuries because of this effort, they know it is well worth it.