DC arcs

[retcec]

Does anyone have a formula for calculating incident energy on a DC system? NFPA has one in appendix D, but it requires bolted fault current (my previous post), and transformer rating and impedance are part of calculating bolted fault in an AC system, but not DC. Any information on DC arcs would be great.

 

[templdl]

What is your DC source?

 

[Carultch]

Does anyone have a formula for calculating incident energy on a DC system? NFPA has one in appendix D, but it requires bolted fault current (my previous post), and transformer rating and impedance are part of calculating bolted fault in an AC system, but not DC. Any information on DC arcs would be great.

It depends on the nature of your DC source. It is the same concept as short circuit current. You will find that most DC sources are unable to provide nearly as much short circuit current or bolted fault current, as AC sources.

Think about it this way. Suppose you make a connection between the opposite polarities of zero resistance. How much effective resistance is there in the path of the circuit, that would limit the charges from accelerating indefinitely to infinite fault currents? That amount of resistance can be treated as the exclusive load of the voltage source.

DC sources are more interesting than their typical AC counterparts. This isn't a situation where the current follows the voltage no matter how high the voltage goes. The DC sources often have their own internal resistances, which limit fault current. Batteries have significant internal resistance, and photovoltaics have a current limitation based on the available sunlight.

Transformer-based rectifier DC power supplies can be modeled in a similar manner as transformers in AC. There still is a KVA rating of the device.

 

[ggunn]

Batteries have significant internal resistance, and photovoltaics have a current limitation based on the available sunlight.

Actually, many batteries (especially big ones) have a pretty low internal resistance and operate very close to a constant voltage source for a good portion of their IR curve, i.e. the current has a linear inverse relationship with the load resistance. I=V/R with V held constant.

PV cells are very different animals; they behave as current sources for most of their IV curve. Their current is indeed determined by the incident sunlight but is virtually independent of load resistance until it gets very high.

 

[retcec]

What is your DC source?

Converted ac.

 

[steve66]

Converted ac.

That gets complicated quick. Its probably different for a transformer/rectifier type power supply than it is for a switching mode power supply. And the filtering will have an effect also. Large caps and inductors can store enough energy to increase the bolted fault current, although the stored energy would probably dissipate pretty quickly.

But as a rough guess, I would use the input voltage times the input short circuit current and divide by the output voltage. In other words, take the input short circuit current and scale it up by the input/output voltage ratio.

You could include resistances and energy stored for rectifiers and caps and inductors and make the calculation much more complicated, but that is probably overkill depending on what you are doing.

 

[iceworm]

Does anyone have a formula for calculating incident energy on a DC system? NFPA has one in appendix D, but it requires bolted fault current (my previous post), and transformer rating and impedance are part of calculating bolted fault in an AC system, but not DC. Any information on DC arcs would be great.

As you noted, IEEE 1584 does not address DC arc flash. And NFPA 70E Appendix D5 leaves a lot to be desired. Actually, it really sucks - i don't know why they published it. As you noted, there is no guidance on estimating fault currents. There is no MH cheat sheet nor Internet calculator. This is definitely non-trivial and YOU get to be the "engineer of record".

All is not lost. There are a few papers that can help:
DC Arc Models and Incident Energy Calculations - RF Ammerman (2009)
Electric Arcs in Open Air - AD Stokes (1991)

One current reference incorporating these papers is:
Complete Guide to Arc Flash Hazard Calculation Studies - Jim Philips (2011). I'm sure there are others, I just happen to have read his.

Here is a start:
Consider a DC series circuit: Source Voltage, Source Internal Resistance, Conductor Resistance, Arc Gap Resistance.

Stokes came up with the Arcing Current equations:

Iarc = VDC/Rtot, where​

Iarc = the short cirduit current
VDC = source Voltage
Rtot = Source Internal Resistance + Conductor Resistance + Arc Gap Resistance
(No sweat, that's just Ohm's Law)​

And Stokes trickey part #1:
Rarc = [20 + (.534 x G)] / (Iarc^.88)​

G = the arcing gap (you get to choose that)​

In order to calculate the Iarc, one must know the Rarc. And to calculate the Rarc one must know the Iarc. (almost fubared)

Just use an iteration. Start with Iarc = .5 x I(bolted fault), calculate Rarc, Add in R(source) and R(conductor) to get Rtot. Divide Rtot into VDC to get a new Iarc. Put the new Iarc back into Stokes equation to get a new Rarc. Iterate. Do this a few times and the value Iarc will converge.
​

Now you just need to know the Source Resistance. The following paper is one of the simpler ones for estimating transformer/rectifier impedance:

RailCorp Engineering Standard Electrical, EP 03 00 00 01 TI, Rectifier Transformer & Rectifier Characteristics - Neal Hook (2001)
here is a link:
http://www.asa.transport.nsw.gov.au.../disciplines/electrical/ep-03-00-00-01-ti.pdf
Look at pages 10, 11, 12.

Once you get the Iarc and Rarc, then determine the trip time (CB/fuse curve). With that you calculate Power and Energy (normal formulas)

Now decide if the arc is in open air or in enclosed. The arc flash equations are given by the Ammerman paper.

If you got this far without having to bleach your eyeballs from reading this - we can discuss it some more.

Good luck - let us know how it comes out.

ice

 

[iceworm]

Does anyone have a formula for calculating incident energy on a DC system? ... Any information on DC arcs would be great.

You didn't ask, and I'm pretty sure you already know:

If your systems meet the requirements, 2014 NFPA 70E, Table 130.7(C)(15)(B) Arc-Flash Hazard PPE Categories for Direct Current (dc) Systems, give an Arc flash PPE catagory, and an Arc-Flash Boundary for DC systems.

ice