I'm considering a new idea for calculating DC Incident Energy PPE requirements at solar sites and I'd like to hear your feedback. Even at low fault current values and while using a more detailed calculation method (Ammerman) I regularly see Combiner Boxes exceed HRC 2 or 3 due to long clearing times.

No method for calculating PV array arcing current gives me any degree of confidence in fuse clearing during an arcing fault. The iterative I_arcing calculations have to either treat PV sources as batteries or as voltage-controlled current sources which requires iterations through the V-I curves. And in the end, neither method can predict system pre-fault conditions and produce an arcing current calculation that can confidentially be plotted on a fuse time-current. The event could occur early in the morning, in the winter or on cloudy day and small deviations in arcing current can cause major shifts on the steep section of a fuse curve. The fuse was typically ignored to be on the safe side and FCT was set at 2 seconds.

Instead, I'm not going to calculate what arcing current will be during a fault.

I'm doing this in a spreadsheet that automates the calculation. Here are the steps:

1. Consider an entire a range of currents from 0 to maximum short circuit current.

2. At 10A increments, calculate resultant Heat Flux using Stokes-Oppenlander for V_arcing (gap, working distance and multiplying factor fixed).

5. If Heat Flux is less than 6 cal/cm².s, a 2 second clearing time is assumed. The area under the flux/time curve is stil less than 12cal/cm². (The significance of 12cal/cm² is that it's the minimum arc rated PPE on site)

6. At some current value down the line, the Heat Flux will exceed 6 cal/cm².s. That is the only current value I care about. It's a fixed value unaffected by operating conditions as long as Zg, WD and MF are constant.

7. Only then do I check the fuse curve to see if that current is high enough to burn the fuse in less than 2 seconds. If it is, that point becomes the crest on the flux/time curve. Currents above that value burn the fuse faster and currents below can't accumulate enough IE to exceed minimum PPE. I take into account what portion of that current value would be back-fed through the fuse before checking the TCC.

This should give me a secure way to bring the fuse back into the equation. I don't know what arcing current will be during a fault but it has to be on the left or right side of that crest. This can also help evaluate different fuse models during the design phase. I've seen PV rated fuses with the same continuous rating but extremely different clearing times. The spreadsheet is only equipped with 3 fuse curves for now created using Digitizer4.1.

If fuse clearing time is still greater than 2 seconds at the 6 cal/cm².s mark, then FCT stays fixed at 2 seconds and IE area exceeds 12 cal/cm². I think this should also help with concerns about solar irradiance multipliers, cumulus clouds or NEC multipliers (if you use these).

I attached a few example plots below. One with a fixed FCT = 2 seconds curve. One with a good fuse and one with a slow fuse. All on the same system. The spreadsheet only needs the cells in red to create plot.

Normally the problem I see with some "short cut" methods is that they predict a fault current that is too high. Yours is the other way around.

To look at it another way we basically have 4 "regions" in terms of incident energy.

There is a low current region below which an arc is not sustained (self-extinguishes). Unfortunately to date we really don't have a good way to predict this one yet and even if it does self-extinguish (more of a problem for AC than DC), it might still exceed the concern of 1.2-2 cal/cm^2 (depending on if we are in distribution or industrial equipment).

Second there is a low current region that is so low that the fuse (or circuit breaker) never trips or at least that the trip time exceeds 2 seconds. In this case we are time limited at 2 seconds and incident energy increases with current as we would expect to happen.

Third the fuse (or circuit breaker) curve begins to kick in but this is where something interesting happens. As current increases, the trip speed increases at a rate that is faster than the increase in current. Thus in this region the incident energy actually decreases with increasing current. This isn't a function of current limiting but of the inverse-time relationship.

Fourth we hit a region where we get an "instantaneous" trip where the device is essentially fixed speed. At this point again we are time limited so incident energy increases with current as we'd expect, even if current limiting from a fuse is occurring.

Your proposed method works effectively the same kind of way by eschewing any reasonably knowledge of arcing current and going straight for maximum incident energy irrespective of current (well at least ignoring region 4). This can definitely work but may overpredict the resulting incident energy by a wide margin, but I'd also tend to agree that for PV arrays the system impedance is essentially an unknown variable where at best we may know the minimum only.