IEC 60909 Fault Calculations: Short-Circuit Current Formulae

IEC 60909 gives a method for calculating short-circuit currents in three-phase a.c. systems. It is commonly used to estimate maximum and minimum fault levels for switchgear rating, protection settings and cable withstand checks.

This article summarises the formulae used for faults far from generators. It sits under the wider Fault Current Calculations topic and links to Earth Fault Loop Impedance where IEC 60909 sequence values are used in cable calculations.

Short-circuit current formulae

For most components other than synchronous machines, the negative sequence impedance Z₂ can often be taken as equal to the positive sequence impedance Z₁.

Fault type	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	$I_{k 2}^{″} = \frac{c U_{n}}{Z_{1} + Z_{2}} = \frac{c U_{n}}{2 Z_{1}} = \frac{\sqrt{3}}{2} I_{k}^{″}$	$I_{k}^{″} = \frac{c U_{n}}{\sqrt{3} \times 2 Z_{1}}$	$I_{k}^{″} = \frac{c U_{n}}{2 Z_{1}}$
Line-to-line-earth short circuit	$I_{kE 2 E}^{″} = \frac{\sqrt{3} c U_{n} Z_{2}}{Z_{1} Z_{2} + Z_{1} Z_{0} + Z_{2} Z_{0}} = \frac{\sqrt{3} c U_{n}}{Z_{1} + 2 Z_{0}}$	–	–
Line-earth short circuit	$I_{k 1}^{″} = \frac{\sqrt{3} c U_{n}}{Z_{1} + Z_{2} + Z_{0}} = \frac{\sqrt{3} c U_{n}}{2 Z_{1} + Z_{0}}$	$I_{k}^{″} = \frac{c U_{n}}{\sqrt{3} (Z_{1} + Z_{0})}$	$I_{k}^{″} = \frac{c U_{n}}{Z_{1} + Z_{0}}$

For a single-phase system, a line-to-line fault is equivalent to a line-neutral fault. For a d.c. system, it is equivalent to a positive-to-negative fault.

For several series circuits in the fault loop, the final fault current can be calculated from the sum of the series impedances:

I_{k}^{″} = \frac{c U_{n}}{\sqrt{3} \sum_{i} Z_{i}}

For d.c. circuits:

I_{k}^{″} = \frac{c U_{n}}{\sum_{i} Z_{i}}

Source impedance

The source or external network impedance Z_Q can be calculated from the short-circuit current. For three-phase and single-phase systems:

Z_{Q} = \frac{c U_{n}}{\sqrt{3} I_{k}^{″}}

For d.c. systems:

Z_{Q} = \frac{c U_{n}}{I_{k}^{″}}

Maximum and minimum fault levels

Both maximum and minimum fault levels are normally required. Maximum fault current is used for equipment short-circuit ratings. Minimum fault current is used to confirm that protective devices operate correctly under the least favourable fault condition.

Use c_max or c_min as appropriate.
When calculating external network impedance Z_Q, use the maximum or minimum short-circuit current as appropriate.
IEC 60909 recommends resistance at 20 °C for maximum short-circuit current, and resistance at end-of-short-circuit temperature for minimum short-circuit current.
User-entered fault levels are commonly treated as values with voltage factor c = 1.

In myCableEngineering, conductor operating temperature is used as the reference for both maximum and minimum fault levels.

Voltage factor

Nominal voltage U_n	c_max for maximum short-circuit current	c_min for minimum short-circuit current
Low voltage, 100 to 1000 V	1.05	0.95
Medium voltage, 1 kV to 33 kV	1.10	1.00
High voltage, above 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 short-circuit current, A
I_k2″	Line-to-line short-circuit current, A
I_kE2E″	Line-to-line-earth short-circuit current, A
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, ohm
Z₂	Negative-sequence short-circuit impedance, ohm
Z₀	Zero-sequence short-circuit impedance, ohm
Z_Q	Impedance of an external network, ohm

For converting upstream fault level data into source impedance, see Network Fault Level.

For estimating a transformer secondary source fault level before IEC 60909 network calculations, see Transformer Secondary Fault Level.

For the cable sequence impedance inputs used by IEC 60909, see Cable Impedance.

IEC 60909 Fault Calculations: Short-Circuit Current Formulae

Short-circuit current formulae

Source impedance

Maximum and minimum fault levels

Voltage factor

Symbols

Related Articles

Cable Impedance: Positive and Zero Sequence Calculations

Cable Inductance: Self, Mutual and BICC Handbook Formulae

Cable Sizing: Current Capacity, Voltage Drop and Fault Withstand