Hello,
I am wondering if anyone has ever run across this before.
For some background, my office has been debating the two second "rule" for quite some time now. I think it has been somewhat concluded that this "rule" is not actually stated as an actual standard but is just mentioned that a two second clearing time can be implemented if it is apparent that personnel can get out of the way within that time frame. It is not meant to be a function of arc sustainability or anything else, from my understanding.
During this debate, I had used the argument that if you take the partial derivative of the IEEE 1584 equation with respect to working distance, there is a speed at which the person moving away from the arcing event can limit (or even halt) the further accumulated energy at their skin's surface. Therefore, one can use the two second rule with a greater level of confidence since most people will at least start moving away from the arc within those two seconds.
Hopefully my attachment shows up, but this shows a multivariable plot of the equation w.r. to working distance and arcing time.
My question is regarding the validity of this argument. Considering that the formulas are empirically derived using linear regression, can I use a simple partial derivative on it to arrive at my argument?


I apologize for the convoluted nature of this question.

Thank you

I didn't see the attachment (that might be something on this end).

I believe the overall concept is valid. I have simply stated to a few in the past that using the 2 second cut off, the incident energy exposure would likely be less since the increasing working distance (as a function of panic) would be in a persons favor. However, I have never attempted to quantify this. Since there isn't any supporting data that I know of, I'm not sure how you could validate what you have. That is something your company/organization will have to mull over. However, great thinking!

There is also the argument that one could be propelled out of the way.

It is almost impossible to validate anything about injuries. IEEE 1584 shows that numerically there is a 5% chance of failure to protect based on the long tail distribution of arcing currents using Monte Carlo analysis. However, that means we need to wait for 1 in 20 arc flashes to occur where the incident energy is virtually equal to the PPE ATPV. Looking at Kinetrics reports on FR material tests, below about 0.5 cal, there are zero PPE failures so the delta is very narrow. Based on these tight limits, it might be decades before a PPE failure occurs that can validate/fail IEEE 1584.

So it might be a very long time before we can quantify the error spread.

Thanks for the responses.

PaulEngr, could you briefly just expand on how the 1584 equations have a 5% chance of failure? Is it due to the fact that the derivations are based on a 95% confidence interval of arcing current?


Thanks

Yes/no. Reading the IEEE 1584 standard is the best way to understand it.

Monte Carlo analysis is a computer-oriented method of calculating probability even if the inputs are highly nonlinear. The method is very simple. Essentially we randomly run an "experiment" and calculate or look up the result picked from a test bank. We calculate "pass/fail" and then accumulate statistics based on the synthetic "experiments". This method works best when the test data is highly nonlinear in nature.

In the case of IEEE 1584, the numerical test data is the actual laboratory experiements. The method is to select a test case at random, calculate the incident energy using the IEEE 1584 empirical formula, calculate "pass/fail" based on an ASTM 1959 ATPV PPE rated at the exact same incident energy level (PPE is curve fitted to a sigmoidal curve reprsenting pass/fail), and then determine from the actual experimental result whether or not the PPE would have successfully protected against an arc flash injury.

The result is that the IEEE 1584 equation "works" numerically 95% of the time based on the IEEE 1584 test bank of data. Knowing that especially the relationship with current is highly nonlinear, we can't really go much further and try to look at confidence intervals or standard deviations without Monte-Carlo methods which copmute the result directly rather than rely on statistics that assume a gaussian distribution.

Taking the partial derivative approach assumes that the underlying data is linear in nature, that the distribution of error is gaussian, etc. Even though as described previously it's not linear, we are talking about timing which is a different matter. Time is clearly linearly related to incident energy. The rate that an arc forms or extinguishes is generally at a rate of nanoseconds to picoseconds so for all intents and purposes it is instantaneous. So I see no problems with your math, even if the underlying model is mostly nonlinear.

Currently IEEE 1584 makes no reference to performing the analysis as a time-series or even suggesting that it could be done as a piece-wise linear solution. SKM and ETAP at least (the two I'm familiar with) definitely make some accomodation for time-series analysis by calculating a piecewise solution to arc flash while computing different currents over time to account for the transient and subtransient currents. This makes for a more accurate result than if only the symmetrical fault current was taken into consideration. The next edition is supposed to use a software library that calculates arc flash much more accurately using a true time domain analysis similar to a paper by Wilkins posted on Mersen's web site.

My response to your overall concern is this. Look, the "2 second rule" is not a true "rule". It is not set out as a mandatory condition in IEEE 1584. Similarly the "125 kVA rule" is not truly a rule either but merely a suggestion. Both are simply ideas that seem to work well in practice and more or less were mentioned off handed within the IEEE 1584 text. Since most engineers use those suggestions they have been instilled in the "popular arc flash culture" as actual rules when in fact they never were that explicit.

Excellent explanation.

That is another thing I was wondering about, whether piece-wise analysis can even be done with a function like this (not LTI).
I was under the assumption that DC components and transient decay were not taken into account in the software packages (however, induction and synchronous machine contributions are added in like a step function, where the current is just the higher value for the first five cycles).

Is this incorrect?

Currently the standard itself is just a single calculation. It is lumped parameter and based purely on 3 phase data so it can't simulate assymetrical fault currents directly. It is however highly amenable to piecewise analysis so some software uses transient and subyransient values as "step" functions as you describe it. The next edition is purported to use a time domain analysis so it can accommodate DC components.

If you are feeding your circuit from generators only, then the lack of dynamics in the calculation can lead to very high results or longer then anticipated tripping times.

The current used in the arc flash calculation is calculated using the comprehensive method because this is more accurate than for example the IEC-61363 because it makes less assumptions. However because off the lack of decrement in the current I think it is easier and more accurate to use the IEC-61363 current. At least that current takes dynamics into account. This is not only important to calculate the energy but it is also VERY IMPORTANT to get a realistic trip time.

I have a few situations where SKM tells me the incident energy is X kA and it protection device trips in Y seconds. However if I take the decrement into account, the trip time increases from 0,632 seconds to over 2 seconds.

Don’t understand me wrong I am not saying this is the method you should use. I am just saying that what they have right now (the IEEE-1584) are a bunch of formulas that do not make sense to use in all conditions. Same goes for the ‘rules’ like the 2 second rule.

We use the IEC-61363 current as a check on the trip time. For our customers we do have to make the calculation using the IEEE-1584, this is a requirement set by the classification societies. Luckily we are not mandated to do mitigation. Try doing mitigation based on a number that rolls out off an equation you know that does not fit your installation.

I think I speak for a lot of people when I say I can’t wait for the IEEE to take dynamics into account and change from a hazard assessment to a full risk assessment.

While you are contemplating 2 seconds, also think about the impact of X/R. 120 times per second as the current passes through zero, the arc extinguishes. As the voltage (not current) reaches a threshold, the arc restrikes.The restrained voltage depends on gap and indirectly on available fault current. It depends directly on the conductivity of the air at the arc gap which is a function of the arcing current. As X/R decreases, arcing time and air temperature decrease, which becomes more important at low voltages and currents. Right now, X/R is not really a factor. This is over and above the other concern of high X/R, assymetrical fault current But that rabbit hole has the side effect that arc flash becomes dependent on starting phase angle. The downside being that phase angle is random (except starting voltage) and can introduce up to a 200% increase in incident energy depending on phase angle and decay rate. On the other hand it may explain some randomness in the lab tests.

While you are contemplating 2 seconds, also think about the impact of X/R. 120 times per second as the current passes through zero, the arc extinguishes. As the voltage (not current) reaches a threshold, the arc restrikes.The restrained voltage depends on gap and indirectly on available fault current. It depends directly on the conductivity of the air at the arc gap which is a function of the arcing current. As X/R decreases, arcing time and air temperature decrease, which becomes more important at low voltages and currents. Right now, X/R is not really a factor. This is over and above the other concern of high X/R, assymetrical fault current But that rabbit hole has the side effect that arc flash becomes dependent on starting phase angle. The downside being that phase angle is random (except starting voltage) and can introduce up to a 200% increase in incident energy depending on phase angle and decay rate. On the other hand it may explain some randomness in the lab tests.