I am new to this forum and relatively new to arc flash calculations.

I found some earlier threads that touched on this topic, but for clarity want to ask again.

How does one calcuate the total incident energy for multiple sources to a fault that clear at different times?

IEEE 1584 does not seem to cover this scenario. Obviously the conservative way to do this is to assume that the combined current from all sources remains until the last source has cleared. However, I think there is cases where this will lead to overly conservative results and a much higher level of PPE than might actually be required - especially when a strong source trips quickly and a weaker source persists for an extended period of time.

Intuitively, I am assuming that the way to do this calculation would be to do iterative steps as outlined below. This theory seems to be substantiated by some of the comments I have read from older threads. However, I am hoping to find some kind of paper or document to back up my methodology. Any comments or suggestions are welcomed.

Theory of Iterative Calculation Steps for Two Sources with Different Clearing Times
1) Sum the bolted fault current from both sources.
2) Calculate resultant arcing current.
3) Calculate incident energy from the time of fault inception to the time of first source being removed by protection tripping.
4) Calculate bolted fault current from remaining source (recognizing that it might be different from the current from that source found in step 1 - likely higher).
5) Calculate the resultant arcing current from the remaining source.
6) Calculate the incident energy using the time period from when the first source tripped to the fault cleared by protection tripping of second source.
7) Sum the incident energies found in 3) and 6) to get a total incident energy for the event.
8) Repeat all of above for 85% of bolted fault level c/w resulting clearing times at these lower fault leves. Use the highest incident energy level found between step 7) and 8)
9) If more than two sources, use same approach for additional windows of time between each protection device operation and summate all.

IEEE 1584 as currently written only mentions time and current as single, constant variables. It does not consider assymetric fault current or multiple sources with multiple overcurrent protection. This is understandable. The laboratory data uses a power source with a constant voltage and impedance. Arc voltage can and does vary significantly, especially at low currents/voltages but the input conditions are held constant in order to be able to get repeatable experimental data. Thus the voltage, current, and time are all constants in the current model.

Most of the major power system analysis software packages (I'm familiar with ETAP and SKM at least) definitely do tke this into consideration and perform essentially a piece-wise estimate of incident energy. Further, a paper published by Wilkins which I believe may be one of the early publications detailing what will be the basis for the model in the next edition models arc flash as an entirely time-series event and has much more accurate prediction capability than the current arc flash model. Wilkins falls short in that there are a number of adjustments and factors in it that are not published so don't bother tracking it down if your intent is to use it. But it points out the fact that treating incident energy in a piece-wise approach is not only valid but very accurate.

In addition there is information from a study on DC arcing (where arcing is more stable in general) from the EFCOG group which gives arc formation/extinction data. Arcs form and/or extinguish in microseconds. From an arc flash modelling point of view thus the piecewise approach is validated since there is no time delay.

Technically, the proposed approach makes sense but it implies that fuses and breakers protecting each individual source start melting and tripping due to arcing fault way down the line. If system is properly designed and selectively co-ordinated, than only the first upstream protection device should clear the fault prior to other protection devices (including devices protecting the sources) starting melting, tripping and clearing the fault.

The incident energy is a product of heat flux and time. I would recommend doing the incident energy flux calculations based on maximum available short circuit current (all short-circuit current sources running and contributing to the fault). This will lead to worst case heat flux intensity.

I would also determine arc duration based on the first upstream protection device time-current characteristics and minimum available short circuit current through the device (such as short circuit current coming from service entrance only while other short circuit current sources such as gens and motors are turned off and are not contributing to the fault). This will lead to the longest arc duration.

The product of the the highest heat flux intensity and the longest arc duration leads to the worst case incident energy. The result varies depending on number of sources and consequently the difference between maximum and minimum available short circuit current.

You may consider using {link deleted} ARCAD's Short Circuit Analytic software program to determine both minimum and maximum available short circuit currents for arc flash analysis. You may also considered using {link deleted} ARCAD's Arc Flash Analytic software program taking into account both available 3-ph short circuit current and part of the available short circuit current through protection device in arc flash assessment.

I agree with the iterative approach, and I believe you will find this is exactly how the software packages treat multiple sources.

Arcad,

Properly designed and coordinated radial systems behave as you state. The question is specifically about multiple source (non-radial) systems. For example a grid tied generator. Source 1 is the grid, source 2 is the generator. Consider an arcing fault at the tie point where "upstream" is in two directions with two interrupting devices with two different fault current contributions and two different clearing times.

Is there ever a case where one source or the other is not present? I would then only take the worse case of one source and assume each bus has worse case dependent which source is available. Otherwise you iterative approach appears correct.

Thankyou all for your input.

The situation I am studying is a medium voltage switchgear lineup at a utility distribution station. There are a couple of local sources from the power tranformers at the station. They are normally run with the tie breaker between the transformers open, but on occasion the tie may be closed so I am studying both situations. There is also a number of feeders leaving the station that are normally networked to other distribution stations in the area - so if there was an arc flash event in the switchgear, these networked feeders would also contribute fault current. So there is actually several sources each with different fault contributions and clearing times.

Unfortunately the arc flash calculator I am using does not seem to handle more than one clearing time for different sources. It seems based on the comments provided that the iterative approach I am using is probably correct - but unless I can validate it - I may need to use one of the other programs mentioned.

I know that EasyPower has an Integrated function that can be used for multiple sources and accounts for various tripping times from those sources. I would suspect that this is a common feature in the higher end programs.