TNT equivalent for energy released in electrical fault 4

[HydroChuck]

Can anyone advise a simple relationship between the energy released in an electrical fault and the equivalent TNT explosive force?
For a specific example: if a 1,500 kVA transformer primary voltage 11 kV, has a fault which is cleared in 1 second, and the worst case fault current is 27. kAmps, what is the relationship between the energy produced (assuming reasonable accurate fault current is known, and voltage does not decrease)?

 

[HydroChuck]

Further to my description:
TNT equivalents have been used in other applications for "relative" comparison purposes. Nuclear bombs is the obvious; and as I recall, the Apollo space program used "TNT equivalent" to have a uniform scale for the explosive potential for all pressurized vessels (small or large) which were flying with the astronauts.

 

[jbartos]

Electrical energy released from the above short (phase-to-phase-to-phase)=3**0.5 x 11000 Volts x 27000 Amps x 1 second = 514.4 MVAsec
The power factor is needed to obtain MWsec
Assume approximately cos(85°)=0.087=Power Factor
1 watts-second = 1 Joule
514.4 MVAses x 0.087 = 44.75 MWsec = 44.75 Mega Joules
This needs to be properly correlated to the TNT energy release.

 

[busbar]

"The equivalent energy for trinitrotoluene is 4680 joules/gram. . ." As noted, 1 joule = 1 watt∙second.

 

[jbartos]

Yes, 1 Joule = 1 Wattsecond
See, various Electrical or Electronic Handbooks

 

[don01]

hi guys
Yeh the theory is correct. Perform the mathematics and thats the equivalent.
As a note where the hell did you dig that number up Busbar? I don't dispute it but we have looked for it for some 20 years and never found it ( not the royal we but the crazy we being collegues -spelling?- and mad physicists).

Just to play devils advocate - consider that TNT is discharged in a compressed form and usually an electrical fault is generally "unrestrained" in terms of being an adiabatic reaction or not. This may alter the answer but who cares its one hell of a bang if your near it.
I post a star to busbar for the number

Regards Don

 

[don01]

back again
and a star to jbartos for reminding me of a fundamental calc which had eluded me
Don

 

[busbar]

Well don01, thanks for the star! Honestly, it started out as kind of a joke, but turned into an effective correlation. I used to work at an explosives test site run by a weapons-development lab. An old timer there mailed me a photocopied page out of one of his handbooks. I'd read the paper by Ralph H Lee (~1982 IEEE/IAS) about electrical fault arc-blast destruction and just wanted to get some perspective on the matter. A hand grenade contains about 2 ounces of TNT equivalent, and that turned out to be about the same damage capability of a moderate low-voltage arcing ground fault.

Hope that answers your question.

 

[stevenal]

Not only is the fault energy unrestrained, it is dissipated all along the resistive path from the source to the fault. The amount of energy released at the fault itself is dependent upon the arc resistance (length), currrent and interupting time. Worst case is when arc resistance is equal to the equivalent source resistance. For a free program that calculates the energy, check out

http://www.cadickcorp.com/program001.htm.

Doesn't do TNT equivalent, though.

 

[busbar]

One other comment--if you have to deal with arc-flash/blast hazards from a personnel-safety standpoint, you might browse

http://www.arcwear.com/id3.htm

 

[BillJ]

Stevenal, thanks for the web address. It's a neat program.
Megaconverter II,

http://www.megaconverter.com/mega2/,

gives (under Energy) 1 Ton of TNT = 4.18*10**9 Joules which is about 4609 Joules/gram. Very close to Busbar's answer.

 

[busbar]

So, using Stevenal’s reference, assuming a 6-inch arc (approximate phase-to-phase/phase-to-ground clearance for 15kV-class switchgear) gives a result of 4,809,375 watts. For the specified 1-second clearing time, that’s 4.8E6 joules, so the TNT equivalent is about 2.3 pounds. That'd blister your knuckles.