Protection
Required grading margin from relay and CT errors (NPAG)
- where
- required grading margin (s)
- relay timing error (%)
- CT ratio error allowance (%)
- nominal operating time of the downstream relay (s)
- downstream breaker interrupting time (s)
- upstream relay overshoot (s)
- safety margin (s)
Explain this equation
Builds the grading margin needed between two time-graded relays from the actual error sources instead of a fixed rule of thumb. Use it to justify a tighter margin on numerical schemes or a wider one where times are long.
Er is the relay timing tolerance and Ect the CT error; they act as a percentage of the downstream operating time t. tcb is the time for the downstream breaker to clear, to the time the upstream relay keeps going after the current stops, and ts a safety allowance.
Er is doubled because the downstream relay may be slow while the upstream one is fast. Fixed times simply add because they happen in sequence before the upstream relay must reset.
Sense check: numerical relays with 5 % error, 10 % CT allowance, a 0.5 s downstream time and an 80 ms breaker give about 0.23 s. Electromechanical relays with slower breakers come out nearer 0.4–0.5 s.
Watch out: the percentage term grows with t, so longer times at low fault currents need a bigger margin.
Builds the grading margin needed between two time-graded relays from relay timing errors, CT errors, breaker clearance time, relay overshoot and a safety allowance, following the Network Protection & Automation Guide.
Enter your values to see the result.
Good to know
Er is counted twice because both relays may err in opposite directions. Typical values: Er 5 % (numerical) to 7.5 % (electromechanical); Ect up to 10 % for protection CTs near their accuracy limit; tcb 0.05–0.1 s for vacuum and SF₆ breakers at HV; overshoot about 0.02 s numerical, 0.05 s electromechanical; ts about 0.03–0.1 s. Because the error term scales with t, the margin is larger at low fault currents.
Common mistake
Using a single fixed 0.4 s everywhere. It is wasteful on numerical schemes and can be inadequate where the downstream relay is slow at low fault currents.
Limits
Simplified NPAG error budget; assumes the errors add linearly (worst case). Does not cover fuse–relay grading, which uses fuse pre-arcing and total clearance curves.
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.