Asymmetrical and Peak Fault Current from X/R

a DC offset rides the AC wave, sized by the circuit X/R ratio. I_peak = sqrt(2) x I_sym x (1 + e^(-pi/(X/R))) and the asymmetrical RMS multiplier = sqrt(1 + 2 e^(-2 pi/(X/R))). At 20 kA symmetrical, X/R 15 (a stiff service near a large transformer) the first peak is 51.2 kA (2.56x) and the asymmetrical RMS 30.4 kA (1.52x) -- a bus braced only for 20 kA is badly under-rated; at X/R 5 the DC decays faster, so 43.4 kA peak and 25.1 kA RMS. A device's peak-withstand and bus bracing must survive the asymmetrical first-cycle, not the symmetrical RMS. A design aid; the interrupting-duty rating and coordination study govern.

I_peak = sqrt(2) x I_sym x (1 + e^(-pi/(X/R))); MF_rms = sqrt(1 + 2 e^(-2 pi/(X/R))); I_asym = I_sym x MF_rms.

First-cycle fault-asymmetry model (DC offset from X/R), an IEEE C37 / NEMA AB-4 first-cycle relation, by name; the interrupting-duty rating and coordination study govern the applied duty.

The DC-offset asymmetry factors are a standard first-principles first-cycle model; X/R comes from the utility and transformer impedance data.

Estimate. AHJ and licensed professional govern.

Field names used by the API: isym_ka, x_over_r, i_peak_ka, peak_factor, i_asym_ka

• Peak factor I_peak/I_sym = sqrt(2)(1 + e^(-pi/(X/R))), approaching 2.828 as X/R goes to infinityfirst-cycle DC-offset model
• RMS factor MF = sqrt(1 + 2 e^(-2 pi/(X/R))), approaching sqrt(3) in the stiff limitfirst-cycle DC-offset model
• Worst case assumes the fully offset phase; the applied duty per the interrupting rating governsIEEE C37 / NEMA AB-4