Network Fault Level

The fault level at the source of a cable due to all the upstream elements is the network fault level (or external fault level).  Network fault level can be specified either as an apparent power, impedance or fault current and power factor.  The relationship between the various quantities is given by:

Three Phase a.c System

$I_k=\frac{VA}{\sqrt{3}{U}_n}$                or        $I_k=\frac{U_n}{\sqrt{3}{Z}_e}$

$VA = \sqrt{3}{I}_k{U}_n$        or        $VA=\frac{{U_n}^2}{Z_e}$

$Z_e=\frac{U_n}{\sqrt{3}{I}_k}$                or        $Z_e=\frac{{U_n}^2}{VA}$

Single Phase a.c. System

$I_k=\frac{\sqrt{3}VA}{U_n}$                or        $I_k=\frac{U_n}{\sqrt{3}{Z}_e}$        or         $I_k=\frac{VA}{U_{LN}}$

$VA = \frac{I_k{U}_n}{\sqrt{3}}$              or        $VA=\frac{{U_n}^2}{3Z_e}$        or        $VA=I_k{U}_{LN}$

$Z_e=\frac{U_n}{\sqrt{3}{I}_k}$                or        $Z_e=\frac{{U_n}^2}{3VA}$        or         $Z_e=\frac{U_{LN}}{I_k}$

d.c. System

$I_k=\frac{VA}{U_n}$                or        $I_k=\frac{U_n}{Z_e}$

$VA = I_k{U}_n$           or        $VA=\frac{{U_n}^2}{Z_e}$

$Z_e=\frac{U_n}{I_k}$                or        $Z_e=\frac{{U_n}^2}{VA}$

Note: for a.c. systems the values are phasor quantities and the use of absolute values will lead to some error.  The easiest way to take this into account phasor relationships is by carrying out the calculations with numbers in complex form (ensuring that both resistance are reactance are considered appropriately).  

Symbols

I_k               - network/external fault current, A
VA             - network/external fault apparent power, VA or MVA (x by 10^-6 to convert to VA)
pf              - power factor of the network/external fault
U_LN           - nominal voltage, line-neutral (single phase circuit), V
U_n             - nominal voltage, line-line (or absolute for d.c.), V
Z_e             - network/external fault impedance, Ω