### Formulas

The symmetrical three phase short-circuit current **I _{sc}** of a power system with no-load line and phase voltages

**E**and

_{line}**E**and source impedance

_{phase}**Z**per-phase star is:

_{S}**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_{sc}^{2}Z_{S} = 3E_{phase}I_{sc} = 3E_{phase}^{2} / Z_{S} = E_{line}^{2} / Z_{S}**

Note that if the **X / R** ratio of the source impedance **Z _{S}** (comprising resistance

**R**and reactance

_{S}**X**) is sufficiently large, then

_{S}**Z**.

_{S}» X_{S}*Transformers*

If a transformer of rating **S _{T}** (taken as base) and per-unit impedance

**Z**is fed from a source with unlimited fault level (infinite busbars), then the per-unit secondary short-circuit current

_{Tpu}**I**and fault level

_{2pu}**S**are:

_{2pu}**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**(to the same base as

_{Spu}**Z**), then the secondary short-circuit current

_{Tpu}**I**and fault level

_{2pu}**S**are reduced to:

_{2pu}**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}**

NOTATION |
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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] |
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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] |