Protection
IDMT relay operating time, IEC 60255-151 curves
- where
- multiple of setting
- fault current (A)
- current setting (A)
- operating time (s)
- time multiplier setting
- curve constant (0.14, 13.5, 80 or 120)
- curve exponent (0.02, 1, 2 or 1)
Explain this equation
Gives the operating time of an IDMT overcurrent relay on the IEC standard, very, extremely or long-time inverse curve. Use it to set and check overcurrent and earth-fault protection.
M is how many times the fault current exceeds the setting. k and α define the curve: SI 0.14 and 0.02, VI 13.5 and 1, EI 80 and 2, LTI 120 and 1. TMS scales the whole curve vertically.
The form copies the behaviour of the old induction-disc relay: the time falls steeply just above setting and flattens at high multiples. A small α gives a flat curve suited to systems where fault level varies little along the feeder; α = 2 mimics fuse I²t behaviour.
Sense check: at 10 × setting and TMS 1, SI gives 2.97 s, VI 1.5 s, EI 0.81 s. Halving TMS halves the time.
Watch out: Is and If must be on the same base, both primary or both secondary amps.
Operating time of an inverse definite minimum time (IDMT) overcurrent relay on the four IEC 60255-151 curves (standard, very, extremely and long-time inverse).
Enter your values to see the result.
Good to know
Constants: SI k = 0.14, α = 0.02; VI k = 13.5, α = 1; EI k = 80, α = 2; LTI k = 120, α = 1. At 10 × setting and TMS 1 these give 2.97 s, 1.5 s, 0.81 s and 13.3 s. Use the same base (primary or secondary amps) for Is and If.
Common mistake
Entering the plug setting in percent or per unit of CT rating and the fault current in primary amps. Convert both to the same base first.
Limits
Ideal curve without the relay’s tolerance (typically ±5 % or ±40 ms), reset characteristic or definite-time minimum. Electromechanical relays deviate from the formula, especially at low multiples.
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.