# IEC 60909 Fault Calculations

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 ${I}_{k2}^{"}=\frac{c{U}_{n}}{{Z}_{1}+{Z}_{2}}=\frac{c{U}_{n}}{2{Z}_{1}}=\frac{\sqrt{3}}{2}{I}_{k}^{"}$ ${I}_{k}^{"}=\frac{c{U}_{n}}{\sqrt{3}2{Z}_{1}}$ ${I}_{k}^{"}=\frac{c{U}_{n}}{2{Z}_{1}}$
Line-to-line-earth short circuit ${I}_{kE2E}^{"}=\frac{\sqrt{3}c{U}_{n}{Z}_{2}}{{Z}_{1}{Z}_{2}+{Z}_{1}{Z}_{0}+{Z}_{2}{Z}_{0}}=\frac{\sqrt{3}c{U}_{n}}{{Z}_{1}+2{Z}_{0}}$ - -
Line-earth short circuit ${I}_{k1}^{"}=\frac{\sqrt{3}c{U}_{n}}{{Z}_{1}+{Z}_{2}+{Z}_{0}}=\frac{\sqrt{3}c{U}_{n}}{2{Z}_{1}+{Z}_{0}}$ ${I}_{k}^{"}=\frac{c{U}_{n}}{\sqrt{3}\left({Z}_{1}+{Z}_{0}\right)}$ ${I}_{k}^{"}=\frac{c{U}_{n}}{{Z}_{1}+{Z}_{0}}$

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:

${I}_{k}^{"}=\frac{c{U}_{n}}{\sqrt{3}\sum _{i}{Z}_{i}}$        - for a.c. circtuis

${I}_{k}^{"}=\frac{c{U}_{n}}{\sum _{i}{Z}_{i}}$        - for d.c. circuits

## Source Impedance

Source impedance Z, 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 cmax or cmin voltage factor as appropriate
2. When calculating external network impedances (Zq), 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.

Voltage Factor, c
Nominal Voltage
Un
Voltage Factor, c
maximum short-circuit currents
cmax
minimum short-circuit currents
cmin
Low Voltage, 100 to 1000 V 1.05 0.95
Medium Voltage, 1 kV to 33 kV 1.10 1.00
High Voltage, > 35 kV 1.10 1.00

## 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
Un             - 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
Zq        - impedance or any external network, Ω