ajg5542 wrote:

I have worked on projects where we are calculating the incident energy at different areas of a utility's substation. Often, the transformer high-side relay and feeder relays will have a 50 element. Depending on the impedance of the fault, the fault current could be high enough to trip the relay on the 50 element or if the impedance of the fault is very high, the relay could trip on the 51 element. Generally we calculate the incident energy at the fault current the program calculates, and below the instantaneous pickup so that we figure out which is the worst case. Has anyone had experience with similar methods of calculation?

Calculations are done using the ohm's law method for a reason. IEEE 1584 only specifies how to calculate incident energy given the available fault current plus some other factors and does not specify the specific short circuit calculation method. But knowing that with arc flash lower currents tend to result in greater incident energy, the software vendors all use the most accurate short circuit calculation available to generate the lowest available fault current. Methods such as the ANSI simplified method that ignore resistance (as opposed to impedance) and use some other simplifications make the problem tractable back in the slide rule days and produce "conservative" (high) results which is acceptable from an equipment maximum withstand point of view but totally invalid for an arcing fault point of view.

On a 51 element curve with typical settings (standard inverse, very inverse, or extremely inverse) as the available fault current goes down, the incident energy goes up. So obviously there is a tremendous advantage in having it trip within the range of a definite time relay (50 element) over 51 elements. Second for the same reason during laboratory testing IEEE 1584 itself notes a sort of "double lobe" effect in the incident energy and thus arcing current. Most of the time the arc behaves as expected with a fairly low impedance. But every so often it has a much lower impedance which kind of "blows up" the model and produces much higher incident energy. This is accounted for in the calculation by running the calculation once with the given available fault current and again with 85% of this. There is still a long tail distribution of exceptions but this seems to be less critical overall according to the standard.

Second, the incident energy at medium voltage is pretty much unaffected by voltage and the bolted fault current is pretty much the same as the arcing current, implying a nearly zero arc impedance, so the medium voltage equation drops the initial arcing current calculation. The low voltage case includes a calculation of arcing current derived from the available fault current. This value varies between about 40 and 85% of the available (bolted) fault current. The major reason that this occurs is that an arcing fault is not a sine wave. It extinguishes at the current zero then restrikes as the voltage exceeds a minimum value resulting in more of a "square wave" appearance at least at low voltages. This "jump" near zero reduces the time that the arcing current actually flows and is treated mathematically as a reduction in RMS current for modelling purposes. As voltage increases obviously the time in which this "jump" occurs more or less becomes meaningless and so for medium voltage it gets ignored. There are other reasons and explanations behind the arcing vs. available short circuit current but since IEEE 1584 empirical equation is just that...empirical, the actual arc mechanics are not being modelled, just a math equation that matches the test case conditions with the test case results.

So the result for you should be that you should be attempting to predict short circuit current and opening time as accurately as possible and the results are whatever they are, good or bad. The alternative strategy in a substation environment would be to use the equipment-specific table based approach contained in IEEE C2 (NESC), or by consulting the underlying reports from EPRI. Note that in the U.S. at least OSHA has given some guidance about the use of IEEE C2 that accepts results in some cases and substitutes their own in others so before you go that way, make sure you are aware of their stance.