Overcurrent Relay Curve Formulas
Overcurrent relay formulas: the IEC operating time for the standard, very and extremely inverse curves from the current multiple and the time multiplier.
The formulas
| To find | Formula |
|---|---|
| Operating time | t = TMS × k / ((I / Is)^α − 1) |
| Standard inverse (SI) | k = 0.14, α = 0.02 |
| Very inverse (VI) | k = 13.5, α = 1 |
| Extremely inverse (EI) | k = 80, α = 2 |
| Long-time inverse (LTI) | k = 120, α = 1 |
I is the fault current seen by the relay, Is the pick-up setting in the same unit and TMS the time multiplier setting. The constants are those of the IEC 60255 curves. The relay does not operate at a current of Is or less, and the time falls as the multiple I / Is rises. The settings come from a co-ordination study that grades each relay against the next one, with a margin for the breaker time and the errors, and a relay maker may show a different curve shape. The currents and settings here are examples.
Worked example: pick-up 100 A, fault 500 A, TMS 0.2
- I / Is = 500 / 100 = 5
- Standard inverse: t = 0.2 × 0.14 / (5^0.02 − 1) = 0.8559 s
- Very inverse: t = 0.2 × 13.5 / (5 − 1) = 0.675 s
- Extremely inverse: t = 0.2 × 80 / (5² − 1) = 0.6667 s
Operating time for TMS = 1 by current multiple
| I / Is | Standard inverse | Very inverse | Extremely inverse |
|---|---|---|---|
| 2 | 10.03 s | 13.5 s | 26.67 s |
| 5 | 4.28 s | 3.375 s | 3.333 s |
| 10 | 2.971 s | 1.5 s | 0.8081 s |
| 20 | 2.267 s | 0.7105 s | 0.2005 s |
Frequently asked questions
What does the time multiplier do?
It scales the whole curve. A TMS of 0.5 gives half the time of a TMS of 1 at every current.
When is a very or extremely inverse curve chosen?
When the fault current falls off quickly with the distance from the source, so a steep curve separates the relays well. A fuse or a thermal load may also call for a steep one.
What is the grading margin?
The time between the operation of a relay and its back-up, to allow for the breaker time and the errors. The study and the standard give the value.
Is the instantaneous element separate?
Yes. A high set element trips with no delay above its own setting, and the curve covers the lower currents.
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