Protection
Grading margin check between two inverse-time relays
- where
- downstream and upstream operating times (s)
- IEC 60255-151 or IEEE C37.112 curve equation
- curve codes (1–4 IEC SI, VI, EI, LTI; 5–7 IEEE MI, VI, EI)
- fault current (A)
- relay settings (A)
- TMS or time dial
Explain this equation
Checks that an upstream relay waits long enough for the downstream relay and breaker to clear a fault first. Use it when setting or reviewing a protection grading study.
t1 and t2 are the times each relay takes at the same fault current, each from its own curve, setting and time multiplier. The margin is the gap between them, which must cover breaker clearance, overshoot and errors.
Each time comes from the standard curve equation (IEC: TMS·k/(M^α − 1); IEEE: TD·(A/(M^p − 1) + B)). Grading is usually checked at the maximum fault at the downstream relay because that is where inverse curves are closest together.
Sense check: two SI relays at 400 A TMS 0.1 and 800 A TMS 0.2 with 8 kA flowing give about 0.23 s and 0.59 s, a 0.37 s margin, comfortable for numerical relays.
Watch out: curves of different shape can cross at low current. Check the margin over the full range of fault currents, not just one point.
Compares the operating times of a downstream and an upstream IDMT relay at the same fault current and checks the time between them against the required grading margin.
Enter your values to see the result.
Good to know
Both curves are written in the IEEE C37.112 form t = TMS × (k/(M^α − 1) + B); the working shows the constants k, α (a) and B of the selected curves, with B = 0 for the IEC 60255-151 curves. Grade at the maximum fault current at the downstream relay location, where curves are closest. NPAG gives typical fixed margins of 0.4 s for electromechanical relays and 0.25–0.3 s for numerical relays with fast breakers; use the margin calculator to build one from relay and CT errors. Settings and fault current must be on the same base (refer both to primary amps if the CT ratios differ).
Common mistake
Checking the margin only at one current. Curves of different shapes (e.g. EI below SI) can cross at low current, so check across the whole range of fault currents.
Limits
Ideal curves only; no definite-time elements, instantaneous stages or fuse curves. Curve formulas as in the IEC 60255-151 and IEEE C37.112 calculators.
Sources
- GE / Alstom Grid, Network Protection & Automation Guide (NPAG), 2011 edn – chapters 6 (CTs) and 9 (overcurrent protection)
- IEC 60255-151:2009 Measuring relays and protection equipment – Part 151: Functional requirements for over/under current protection
- IEEE C37.112-2018 Standard for inverse-time characteristics equations for overcurrent relays
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.