A Siemens SIVACON ( Un = 690V ) switchboard has been tested - to DIN EN 60439 - and certified to withstand an internal arcing fault of 50 kA for 0.30 sec.
Can the I²t value of 50 kA^2 * 0.3 be used as a constant to determine the switchboard's permissible withstand arcing time for other arcing currents ?
eg. 20 kA^2 * 1.875 sec = 50 kA^2 * 0.3 sec

NEMA Publication PB 2.2-2004 Annex A - Arc Damage Levels

NEMA Publication PB 2.2-2004 Annex A - Arcing Fault Damage Levels
Tests at 277V have been used to arrive at a formula for :
“Material Burnt Away� = k * I^1.5 * t Equi. 1
where :
k = constant for different materials; 1.52 * 10^-6, 0.72 * 10^-6, 0.66 * 10^-6 for Al, Cu, steel resp.
I = single phase to earth arcing fault current in amps
t = arc duration in sec
It is assumed that the switchboard is designed so that the maximum damage – or material burnt away – by a single phase to earth arcing fault current is defined as :
I^1.5 * t <= 250 * Ir Equi. 2
where :
Ir = LTPU setting of protection device

Using above equations, and assuming Ir = 4000 A, a 50,000A arcing current :
Cu burnt away = 0.72 inches^3, 11.80 cm^3
Arcing time = 0.089 sec
Using the switchboards rated internal arcing current withstand rating of 50,000A for 0.3 sec :
Cu burnt away = 2.42 inches^3, 39.6 cm^3

Questions :
During 50 kA for 0.3 sec test for internal arcing fault withstand, does 2.42 in^3 of Cu get vaporized ?
Can the constant ( 50,000^1.5 ) * 0.3 be used to calculate the internal arcing fault withstand for other times ? eg. 35,500A for 0.5 sec

Comments:
In the above NEMA formulas, the “material burnt away� is proportional to the arcing current^1.5
In the IEEE 1584 and the Lee equations, incident energy is proportional to the arcing current.
The IEEE 1584 incident energy equation assumes a three phase fault.

I see your location is Western Australia. I just returned from Victoria and NSW, Australia last week. A very long trip but always worth it. A great place. I even finally learned to drive on the left side of the road this time. A bit of a challenge when the first traffic I hit is downtown Sydney. Everyone survived.

Back when I worked at Square D Company in the very early 1980’s the Chief Electrical Engineer was instrumental in the 277 V Arcing Fault Damage tests. (Harry Stanback). It was to assist in developing ground fault protection requirements. It has all progressed a great deal since those days.

I’m not as familiar with this publication as many others but I’ll give my 2 cents. Perhaps others can join in.

For your first question about 2.42 in^3 of copper being vaporized in 0.3 seconds. Based on the calculations you seem to have the correct number. In the lab, copper vaporizes at an amazing rate under fault conditions so I would not be surprised if this value is close to what happens.

This issue is also addressed in the Australian / New Zealand AS/NZS Standard 3000 Wiring Rules for internal arcing faults and uses the following equation to calculate the damage limit:

Clearing Time t = (Ke x Ir) / (If^1.5)

If = 30% of prospective fault current
Ke = 250 constant (same as you have)
Ir = current rating of switchboard
T = clearing time in seconds.

It looks like the AS Standard follows a similar logic to NEMA (or vice-versa). However, they don’t seem to take into account the difference between copper and aluminum.

As far as your comments:

I^2*t is typically thought of as the thermal energy and damage characteristics. Interesting to see 1.5 being used for both.

I’m not sure I would say incident energy is proportional to arcing current. There are logarithms and exponents involved in the calculations (non-linear). Many factors come into play.

You are correct - IEEE 1584 is only for 3 phase. It assumes Line-Ground (Line-Earth) can escalate to 3 Phase.

MCC internal arc-flash current withstand

Thanks Jim for your posting. Driving in Sydney - you are braver than me, when in Sydney I take the bus or walk.
An MCC has been certified to withstand an internal arcing fault current of 50 kA for 0.3 sec ( at 690V ).
The calculated arcing current at the main bus is 15 kA. This arcing current will cause the Incomer ACB to clear the fault in 0.16 sec, this is well within the switchboards withstand rating.
However the Incomer ACB short-time-pickup ( STPU ) setting of 10 kA and would allow an arcing fault current below 10kA to persist for approximately 20 sec.
Can the the 50kA, 0.3 sec withstand rating be used to determine the permissible internal arcing current at diffent times ?


In the attached spreadsheet, incident energy calculated to Lee's equation varies linearly with arcing current and time.
The 50kA for 0.3 sec has been used as a reference and shows that the incident energy to IEEE 1584 also varies linearly with current and time.