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# Three Phase Fault Level

### Formulas

The symmetrical three phase short-circuit current Isc of a power system with no-load line and phase voltages Eline and Ephase and source impedance ZS per-phase star is:

Isc = Ephase / ZS = Eline / Ö3ZS

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

Ssc = 3Isc2ZS = 3EphaseIsc = 3Ephase2 / ZS = Eline2 / ZS

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

Transformers

If a transformer of rating ST (taken as base) and per-unit impedance ZTpu is fed from a source with unlimited fault level (infinite busbars), then the per-unit secondary short-circuit current I2pu and fault level S2pu are:

I2pu = E2pu / ZTpu = 1.0 / ZTpu

S2pu = I2pu = 1.0 / ZTpu

If the source fault level is limited to SS by per-unit source impedance ZSpu (to the same base as ZTpu), then the secondary short-circuit current I2pu and fault level S2pu are reduced to:

I2pu = E2pu / (ZTpu + ZSpu) = 1.0 / (ZTpu + ZSpu)

S2pu = I2pu = 1.0 / (ZTpu + ZSpu)

where ZSpu = ST / SS

 NOTATION The symbol font is used for some notation and formulae. If the Greek symbols for alpha beta delta do not appear here [ a b d ] the symbol font needs to be installed for correct display of notation and formulae. B C E f G h I j L P Q susceptance capacitance voltage source frequency conductance h-operator current j-operator inductance active power reactive power [siemens, S] [farads, F] [volts, V] [hertz, Hz] [siemens, S] [1Ð120°] [amps, A] [1Ð90°] [henrys, H] [watts, W] [VAreactive, VArs] Q R S t V W X Y Z f w quality factor resistance apparent power time voltage drop energy reactance admittance impedance phase angle angular frequency [number] [ohms, W] [volt-amps, VA] [seconds, s] [volts, V] [joules, J] [ohms, W] [siemens, S] [ohms, W] [degrees, °] [rad/sec]