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IEC 60255-1519 min read

Worked Example: Grading a Three-Relay IDMT Chain at a Single Fault Current

A load-end, mid-feeder and source relay all see the same fault — checking whether each step up the chain has enough time separation from the one below it.

Scenario

Relay 1 (load end)Pickup 1 A, CT 200:1, TMS 0.1, IEC SI
Relay 2 (mid-feeder)Pickup 1.2 A, CT 300:1, TMS 0.2, IEC SI
Relay 3 (source)Pickup 1.5 A, CT 400:1, TMS 0.3, IEC SI
Fault current (seen by all three)5000 A primary
Required grading margin0.4 s at every step

Step-by-step calculation

Step 1: Compute each relay's plug setting multiplier at 5000 A

PSM = (Ifault / CT ratio) / pickup
Relay 1: (5000/200)/1 = 25 Relay 2: (5000/300)/1.2 = 13.9 Relay 3: (5000/400)/1.5 = 8.3
PSM1 = 25, PSM2 = 13.9, PSM3 = 8.3

Step 2: Apply the IEC SI curve with each relay's own TMS

t = TMS x (0.14 / (PSM^0.02 - 1))
t1 = 0.211 s (TMS 0.1) t2 = 0.518 s (TMS 0.2) t3 = 0.970 s (TMS 0.3)
t1 = 0.211 s, t2 = 0.518 s, t3 = 0.970 s

Step 3: Check the grading margin at each step of the chain

StepDownstream timeUpstream timeMarginRequirement
Relay 1 → Relay 20.211 s0.518 s0.308 s0.4 s — FAIL
Relay 2 → Relay 30.518 s0.970 s0.451 s0.4 s — PASS

Result summary

CheckRequirementActualStatus
Relay 1 → Relay 2 margin≥ 0.4 s0.308 s✗ FAIL
Relay 2 → Relay 3 margin≥ 0.4 s0.451 s✓ PASS
The chain fails overall: Relay 2's TMS of 0.2 is too close to Relay 1's 0.1 to hold a 0.4 s margin at 5000 A, even though the next step up (Relay 2 to Relay 3) passes comfortably.

Key insight: A grading chain is only as strong as its weakest step — one under-margined pair anywhere in the chain fails the whole study, regardless of how much margin exists elsewhere. Raising Relay 2's TMS to about 0.24 restores the required 0.4 s at this fault level without touching Relay 1 or Relay 3.

Try it with your own numbers

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Frequently asked questions

Does fixing Relay 2's TMS affect the Relay 2 → Relay 3 step?

Yes — raising Relay 2's TMS increases its own trip time everywhere, which widens the Relay 1 → Relay 2 margin but narrows the Relay 2 → Relay 3 margin. In this case there's enough headroom (0.451 s against a 0.4 s requirement) to absorb the small increase, but it should always be rechecked, not assumed.

Should this be checked at more than one fault current?

Yes — a production grading study checks the full range of currents each relay could see (minimum fault at the far end of the protected zone through to maximum fault close to the source), not just one value, for the same reason the two-relay coordination example on this site shows a single-point check can hide a full-range failure.

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