Asymmetrical and Peak Fault Current from X/R
The first-cycle fault current the symmetrical value hides: 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.
Formula and source
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.
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