Three Phase Fault Level

Formulas

The symmetrical three phase short-circuit current I_sc of a power system with no-load line and phase voltages E_line and E_phase and source impedance Z_S per-phase star is:

I_sc = E_phase / Z_S = E_line / Ö3Z_S

The three phase fault level S_sc of the power system is:

S_sc = 3I_sc²Z_S = 3E_phaseI_sc = 3E_phase² / Z_S = E_line² / Z_S

Note that if the X / R ratio of the source impedance Z_S (comprising resistance R_S and reactance X_S) is sufficiently large, then Z_S » X_S.

Transformers

If a transformer of rating S_T (taken as base) and per-unit impedance Z_Tpu is fed from a source with unlimited fault level (infinite busbars), then the per-unit secondary short-circuit current I_2pu and fault level S_2pu are:

I_2pu = E_2pu / Z_Tpu = 1.0 / Z_Tpu

S_2pu = I_2pu = 1.0 / Z_Tpu

If the source fault level is limited to S_S by per-unit source impedance Z_Spu (to the same base as Z_Tpu), then the secondary short-circuit current I_2pu and fault level S_2pu are reduced to:

I_2pu = E_2pu / (Z_Tpu + Z_Spu) = 1.0 / (Z_Tpu + Z_Spu)

S_2pu = I_2pu = 1.0 / (Z_Tpu + Z_Spu)

where Z_Spu = S_T / S_S