IEC Curve Calculator: Inverse-Time Relay Curves

An IEC curve calculator estimates an inverse-time overcurrent relay’s operating time from the fault current, pickup setting, and selected curve family. Enter those values to get a calculated trip time; the result is a theoretical curve value, not a substitute for protection-coordination studies or the relay manufacturer’s settings.

Formula

The IEC 60255 inverse-time characteristic is commonly written as t = TMS × k / ((I / Is)^α − 1). Here, t is operating time in seconds, TMS is the time multiplier setting (dimensionless), I is the current being evaluated in amperes, and Is is the relay pickup or setting current in amperes. The ratio I/Is is therefore dimensionless.

The curve selector sets the constants in the calculator:

• Standard inverse: k = 0.14, α = 0.02
• Very inverse: k = 13.5, α = 1
• Extremely inverse: k = 80, α = 2
• Long-time inverse: k = 120, α = 1

These are the commonly used IEC inverse-time equations. Actual relay implementations can include defined tolerances, minimum-time behavior, current measurement details, and other configurable features. Verify the relevant device documentation before applying a calculated value.

Worked Example

Using the calculator’s default values: fault current I = 1,000 A, pickup current Is = 100 A, Standard inverse curve, and TMS = 0.1:

1. Calculate the current multiple: I/Is = 1,000/100 = 10.
2. For Standard inverse, k = 0.14 and α = 0.02. Thus 10^0.02 is approximately 1.04713.
3. Subtract 1: 1.04713 − 1 = 0.04713.
4. Calculate the time: t = 0.1 × 0.14/0.04713 ≈ 0.297 seconds.

Rounded to two decimal places, the calculator gives an operating time of 0.30 s.

What an IEC Curve Calculator Does

Inverse-time overcurrent protection responds faster as the measured current rises above pickup. The current multiple, I/Is, indicates how many times the current exceeds the pickup setting. At a modest multiple, the relay may take longer to operate; at a high multiple, it usually operates more quickly, subject to the curve equation and the relay’s limits.

IEC curve calculations help estimate relay timing at a selected current, compare curve families, and examine how changing a time multiplier affects a theoretical operating time. Engineers use this kind of calculation as one part of coordination work, which also considers the protected equipment, fault levels, upstream and downstream devices, and the relay’s actual characteristics.

Choosing a Curve and Reading the Result

The curve family changes how quickly operating time falls as current increases. Standard inverse is a general inverse-time characteristic. Very inverse and extremely inverse curves become progressively steeper with current, while long-time inverse uses its own IEC constants. A curve name alone does not establish which one is appropriate; selection depends on the protection design and coordination requirements.

• Fault current: Use the current at the relay location for the condition being studied, not an unrelated system rating.
• Pickup current: Enter the setting in the same current units as the fault current. If the relay setting is expressed as a secondary current, account correctly for instrument-transformer ratios before comparing values.
• Time multiplier: Enter the relay’s TMS or equivalent time setting as a dimensionless number. It scales the calculated time.
• Output: Read the answer in seconds for the selected current and settings. It is not necessarily the total time until a circuit breaker has cleared the fault.

For instance, if both currents are expressed in amperes, 1,000 A divided by 100 A gives a current multiple of 10. Expressing one in amperes and the other in kiloamperes without conversion would produce a misleading ratio.

Common Errors and Important Limits

The equation’s denominator approaches zero as I/Is approaches 1 from above, so the calculated operating time grows very large near pickup. At or below pickup, the inverse-time operating equation does not yield a meaningful finite trip time. This calculator’s simple formula does not enforce a cutoff or model an instantaneous element; do not interpret its output as a trip prediction for current at or below pickup.

• Do not confuse pickup current with the measured fault current; they have different roles in the formula.
• Do not mix primary and secondary amperes, or amperes and kiloamperes, without converting to consistent units.
• Do not treat a rounded output as exact. Small input or setting changes can matter, especially near pickup.
• Do not assume the equation includes breaker opening time, relay filtering, reset behavior, tolerances, or other protection elements.

The calculator applies an idealized characteristic at one current value. A coordination assessment generally requires checking a range of fault currents and comparing the time-current curves of related devices. For practical settings, use the applicable relay documentation and qualified protection-engineering review.

Frequently Asked Questions

What does TMS mean in an IEC curve?
TMS means time multiplier setting. In the IEC inverse-time equation it scales the characteristic’s calculated time; increasing TMS increases operating time for a given current multiple.

What is the current multiple?
It is the evaluated current divided by the pickup current, I/Is. A value of 10 means the evaluated current is ten times the pickup setting.

Why does the calculator show a long time near pickup?
The IEC inverse-time equation has a denominator that gets close to zero as current approaches pickup from above. The theoretical time therefore rises sharply.

Does the calculated time include breaker operation?
No. It estimates the relay characteristic’s operating time from the entered values. Circuit-breaker opening and clearing time are separate considerations.

Can I use the result to set a protection relay?
Not by itself. Treat the result as a calculation aid, then verify the device’s implementation and complete the necessary protection-coordination checks before applying settings.

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in I | Fault current | A | 1000 | 0
in p | Pickup current | A | 100 | 0
sel c | IEC curve | Standard inverse=1, Very inverse=2, Extremely inverse=3, Long-time inverse=4
in tms | Time multiplier setting | - | 0.1 | 0
out time | Operating time | s | tms * (k / ((I / p)^a - 1)) | 2