Asymmetry and duration
Peak short-circuit current ip = κ√2·I″k
- where
- peak factor
- reactance to resistance ratio at the fault
- peak short-circuit current (kA)
- initial symmetrical short-circuit current (kA)
Explain this equation
Gives the highest instantaneous current in the first half-cycle of a fault. Compare it with switchgear rated making and peak withstand current, and use it for busbar and support forces.
I″k is the r.m.s. symmetrical current; √2 converts it to the a.c. peak. κ is the extra factor caused by the d.c. offset when the fault starts at the worst point on the wave. X/R is the ratio of reactance to resistance seen from the fault.
In a series R–L circuit the d.c. offset decays with time constant L/R. The first peak arrives about half a cycle in, so the more inductive the circuit, the less the offset has decayed. The IEC 60909 expression 1.02 + 0.98·e^(−3/(X/R)) fits this behaviour, running from 1.02 for a resistive circuit to 2 for a purely inductive one.
Sense check: X/R = 10 gives κ ≈ 1.75; X/R = 14 (a 45 ms time constant at 50 Hz) gives about 1.81. Standard switchgear has a peak rating of 2.5 times its breaking current, which covers κ up to about 1.77.
Watch out: in meshed networks a single branch X/R is not enough; IEC 60909 method B or C applies.
The highest instantaneous current in the first half-cycle, for checking switchgear making capacity and busbar mechanical withstand.
Enter your values to see the result.
Good to know
κ ranges from 1.02 (purely resistive) to 2.0 (purely reactive). X/R = 10 gives κ ≈ 1.75, X/R = 14 (the 45 ms time constant at 50 Hz) gives κ ≈ 1.81. Compare ip with the switchgear rated peak withstand / making current (2.5 × rated breaking current at 50 Hz for 45 ms switchgear).
Common mistake
Using X/R of one branch in a meshed network. IEC 60909 method B multiplies κ by 1.15 (capped at 2.0 for HV), or use method C with an equivalent frequency.
Limits
κ formula is IEC 60909 eq. (55) for a series R-X circuit. For meshed networks apply method B (1.15·κb) or C; near generators other factors apply.
Sources
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.