To calculate system faults, we can use the guidance given in IEC 609096 "Short-circuit currents in three-phase a.c. systems. For faults far from the generator faults in three phase systems, each type of fault the symmetrical short-circuit current I"_k is given by:

The Formulae

	Three-Phase System	Single-Phase System	D.C. System
Three phase short circuit	$I_k^{"}=\frac{c{U}_n}{\sqrt{3}{Z}_1}$	-	-
Line-to-line short circuit	$I_{k2}^{"}=\frac{c{U}_n}{Z_1+Z_2}=\frac{c{U}_n}{2Z_1}=\frac{\sqrt{3}}{2}{I}_k^{"}$	$I_k^{"}=\frac{c{U}_n}{\sqrt{3}2Z_1}$	$I_k^{"}=\frac{c{U}_n}{2Z_1}$
Line-to-line-earth short circuit	$I_{kE2E}^{"}=\frac{\sqrt{3}c{U}_n{Z}_2}{Z_1{Z}_2+Z_1{Z}_0+Z_2{Z}_0}=\frac{\sqrt{3}c{U}_n}{Z_1+2Z_0}$	-	-
Line-earth short circuit	$I_{k1}^{"}=\frac{\sqrt{3}c{U}_n}{Z_1+Z_2+Z_0}=\frac{\sqrt{3}c{U}_n}{2Z_1+Z_0}$	$I_k^{"}=\frac{c{U}_n}{\sqrt{3}\left(Z_1+Z_0\right)}$	$I_k^{"}=\frac{c{U}_n}{Z_1+Z_0}$

Note:

1. Z₁, Z₂ and Z₀ are the symmetrical components
2. for most components (except synchronous machines), we can take Z₂ as equal to Z₁.
3. for single-phase line to line is equivalent to line-neutral, and for d.c. positive to negative

For several series circuits in the fault loop, the final fault current is given by:

$I_k^{"}=\frac{c{U}_n}{\sqrt{3}{\displaystyle \sum _i}{Z}_i}$        - for a.c. circtuis

$I_k^{"}=\frac{c{U}_n}{\sum _i{Z}_i}$        - for d.c. circuits

Source Impedance

Source impedance Z_Q , is given by:

$Z_Q=\frac{c{U}_n}{\sqrt{3}{I}_k^{"}}$        - three phase and single phase systems

$Z_Q=\frac{c{U}_n}{I_k^{"}}$        - d.c. systems

 

Maximum & Minimum Fault Levels

Typically both a maximum fault level (used for rating equipment), and minimum level (used for protections settings) are calculated.  When evaluating the maximum and minimum, the following condtions are taken into account:

1. Use the c_max or c_min voltage factor as appropriate
2. When calculating external network impedances (Z_q), use the maximum or minimum value of short circuit current as appropriate

Note: IEC 60909 recommends resistance calculated at 20 °C for the maximum short circuit, and at the end of short circuit temperature for the minimum short circuit level.  Presently, in myCableEngineering we use the conductor operating temperature as the reference for both maximum and minimum fault levels. User specified (input) fault levels are taken as being those with the voltage factor c = 1.

Symbols

c                   - voltage factor
I"_k                  - initial symmetrical three phase short-circuit current (r.m.s.), A
                        - I"_k1        line-to-earth
                        - I"_k2        line-to-line
                        - I"_kE2E     line-to-line-earth
U_n             - nominal system voltage, line-to-line (r.m.s.), V
                        - positive-negative voltage for d.c. systems
Z₁             - positive sequence short -circuit impedance, Ω
Z₂             - negative sequence short circuit impedance, Ω
Z₀             - zero sequence short circuit impedance, Ω
Z_q        - impedance or any external network, Ω