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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
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f
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I
j
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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
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t
V
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X
Y
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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]

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