Asymmetry and duration
DC component and asymmetrical current at time t
- where
- maximum d.c. component (kA)
- initial symmetrical short-circuit current (kA)
- system frequency (Hz)
- time after fault inception (s)
- reactance to resistance ratio at the fault
- d.c. component as a percentage of the a.c. peak (%)
- asymmetrical r.m.s. current (kA)
- d.c. time constant (ms)
Explain this equation
Shows how much d.c. offset remains in a fault current at a given time, and the resulting asymmetrical r.m.s. current. Use it with the minimum contact-parting time to check a circuit-breaker's asymmetrical breaking duty.
I″k is the symmetrical r.m.s. current and √2·I″k its peak, which is also the largest possible initial d.c. offset. f is the system frequency, t the time since the fault started, and X/R sets how fast the offset dies away. p expresses what is left as a percentage of the a.c. peak.
The d.c. term decays exponentially with time constant τ = L/R = (X/R)/(2πf); the 1000 shows τ in milliseconds. Because the a.c. and d.c. parts are independent, their r.m.s. values combine as the square root of the sum of squares, giving Iasym.
Sense check: X/R = 14 at 50 Hz gives τ ≈ 45 ms, the standard value for IEC 62271-100 breakers. At t = τ about 37% remains; after three time constants only 5% is left.
Watch out: this assumes a constant a.c. component. Close to generators the a.c. part also decays, and the d.c. part can be larger than the a.c. peak, which needs a different check.
Decaying d.c. offset of a fault current at a given time, and the resulting asymmetrical r.m.s. current a circuit-breaker must interrupt.
Enter your values to see the result.
Good to know
For breaker checks, t is the minimum contact-parting time (relay time plus breaker opening time). IEC 62271-100 standard breakers are tested with τ = 45 ms; if the system X/R gives a longer τ, check the breaker’s d.c. capability. The asymmetrical r.m.s. is Iac·√(1 + 2p²) with p the d.c. fraction.
Common mistake
Comparing the d.c. percentage with the breaker rating at the full clearing time instead of at contact parting, which understates the d.c. duty.
Limits
Assumes worst-case point-on-wave (maximum offset) and a constant a.c. component (far from generators). Near generators the a.c. component also decays; use IEC 60909 Ib with μ.
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.