Protection
Inverse-time relay operating time, IEEE C37.112 curves
- where
- multiple of pickup
- fault current (A)
- pickup current (A)
- operating time (s)
- time dial
- curve constants (MI 0.0515, 0.114, 0.02; VI 19.61, 0.491, 2; EI 28.2, 0.1217, 2)
Explain this equation
Gives the operating time of an inverse-time overcurrent relay on the IEEE moderately, very or extremely inverse curve. Use it when relays are set to North American curves or when grading against such relays.
M is the fault current as a multiple of pickup. A and p shape the inverse part of the curve and B adds a fixed time that sets the floor at very high multiples. TD scales the whole time.
The structure matches the IEC curves but with the extra constant B, chosen so the curves fit traditional electromechanical relays. At very high M the first term vanishes and t tends to TD × B.
Sense check: MI at 10 × pickup and TD 1 gives about 1.21 s; VI 0.69 s.
Watch out: some manufacturers use a different time-dial scale. Check that TD here corresponds to your relay’s setting.
Operating time on the IEEE C37.112 moderately, very and extremely inverse characteristics, used on North American relays and in many multi-standard numerical relays.
Enter your values to see the result.
Good to know
Constants: MI A = 0.0515, B = 0.114, p = 0.02; VI A = 19.61, B = 0.491, p = 2; EI A = 28.2, B = 0.1217, p = 2. Some manufacturers scale the time dial differently (e.g. dial 0.5–15 with the equation divided by a constant); check the relay manual.
Common mistake
Using IEC TMS values on an IEEE curve. The curves have different shapes and the B term adds a fixed time, so the same setting number does not give the same time.
Limits
Ideal curve without relay tolerance or the C37.112 reset characteristic.
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.