The thermal energy in a fault is proportional to I^2 t. But the IE result for any arc flash study always shows7 that the IE is proportional to I. I am very curious why is there such an anomaly.

There are many factors that come into play regarding incident energy. First let’s define the term incident energy. According to 2018 IEEE 1584, Incident Energy is defined as:

“The amount of thermal energy impressed on a surface, a certain distance from the source, generated during an electric arc event.�

This means that the incident energy is not the total energy at the arc flash based sole on the current and time as in I^2. It is the energy that travels from the event towards a surface (worker) which means a few things such as.

-Not all of the thermal energy from the arc flash reaches the worker
-The energy dramatically decreases with distance from the arc flash
-The rate of decrease depends on the enclosure, opening size, voltage, electrode orientation and many other factors.

I hope this helps your understanding. Feel free to check back in if you have any other questions. Lots’ of people here ready to help.