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IEC and IEEE inverse-time curves

Calculate the operating time of a 51 element with the standard curves, see it on a log-log plot and compare it with the backup relay to check the coordination margin over the whole current range.

IEC 60255-151dependent-time characteristicIEEE C37.112inverse curves and reset

Example cases
IEC and IEEE inverse-time curves
E1Fault and criterion
A
s

Use the same side of the CT for everything: primary amperes, or secondary amperes of the same ratio.

E2Relay A, downstream
A
E3Relay B, upstream backup
A

Use a decimal point. The calculation runs in your browser and updates as you type.

Relay A time

— s

Relay B time

— s

Margin B − A

— s

Relay A multiple I/Is

—

Relay B multiple I/Is

—

Relay A reset

— s

Time-current curves
  • Relay A
  • Relay B
  • Maximum fault and margin
Time (s) against current (A), both on logarithmic scales. Each curve starts at 1.1 times its pickup. The dots mark each relay's time at the maximum fault and the yellow dimension, the margin between them.
Margin over the whole range
  • Margin B − A
  • Required margin and maximum fault
Time difference from 1.1 times the higher pickup up to the maximum fault, with current on a logarithmic scale. Below the horizontal yellow line the margin is not met; below zero, the backup operates first. Close to pickup the margin grows sharply and the trace leaves the scale.

Step-by-step calculation

What it means for coordination

    What it is for

    The 51 overcurrent element operates with a time that drops as current rises. For the relay closest to the fault to clear first, the backup curve has to stay above it with enough margin over the whole current range both relays see. Use this tool to check existing settings, prepare the points of a secondary injection test or verify by hand a result from coordination software.

    How it is calculated

    IEC 60255-151dependent-time characteristic

    t = TMS · (k / ((I / Is)α − 1) + c)

    For IEC curves, c = 0. I is the measured current, Is the pickup setting and TMS the time multiplier setting.

    IEEE C37.112inverse curves and reset

    t = TD · (A / (Mp − 1) + B) · tr = TD · tr / (1 − M²) for M < 1

    M = I / Is and TD is the time dial. The second equation is the reset, which emulates the return of the electromechanical disk and matters for intermittent faults: with M = 0 it equals TD · tr. IEC curves have no standard reset; each relay makes it instantaneous or definite-time.

    CurveStandardConstants
    IEC standard inverse (SI)IEC 60255-151k = 0.14; α = 0.02
    IEC very inverse (VI)IEC 60255-151k = 13.5; α = 1
    IEC extremely inverse (EI)IEC 60255-151k = 80; α = 2
    IEC long-time inverse (LTI)IEC 60255-151k = 120; α = 1
    IEEE moderately inverse (MI)IEEE C37.112A = 0.0515; B = 0.114; p = 0.02; tr = 4.85
    IEEE very inverse (VI)IEEE C37.112A = 19.61; B = 0.491; p = 2; tr = 21.6
    IEEE extremely inverse (EI)IEEE C37.112A = 28.2; B = 0.1217; p = 2; tr = 29.1

    Coordination margin

    Δt(I) = tB(I) − tA(I) ≥ required margin

    It is checked at the maximum fault both relays see and also over the whole range from pickup, because two curves of different shape can come close at low currents. The indicator is green if Δt meets the margin, yellow if the backup operates later but without the margin, and red if it operates first.

    Limits of the calculation

    • IEC 60255-151 sets the accuracy of the characteristic between 2 and 20 times pickup. Outside that range the tool warns: above 20 times many relays limit the curve, and near 1 times the actual pickup (around 1.05 to 1.1 times Is) makes the time undefined or very long.
    • It assumes constant current during the fault, no minimum time, no instantaneous element and no CT saturation.
    • Some manufacturers scale the dial differently or add a fixed time to the curve: always confirm with the relay manual before setting.
    • The required margin is set by the coordination study according to the breaker, the relay type and the measurement errors; the preloaded value is only an example.

    Frequently asked questions

    How is the operating time of an IEC standard inverse curve calculated?

    With the IEC 60255-151 equation (IEEE C37.112 uses its own form): t = TMS · 0.14 / ((I/Is)^0.02 − 1). For example, with a current of 10 times pickup and TMS = 0.1, the relay operates in 0.1 · 0.14 / (10^0.02 − 1) = 0.297 s. The other IEC curves change only the constants k and α.

    What coordination time interval is used between two overcurrent relays?

    The interval between the backup relay and the one closest to the fault must cover the breaker interrupting time, relay overtravel and the CT and relay errors. Common references use 0.2 to 0.4 s depending on the technology; the value for each case is set by the protection coordination study, checked over the whole current range both relays see.

    What is the difference between IEC and IEEE curves?

    Both are inverse-time characteristics, but with different equations: IEEE C37.112 adds a constant B and defines a reset that emulates the electromechanical disk, t = TD · tr / (1 − M²). Also, the IEC TMS and the IEEE TD are not on the same scale, so the same dial number does not give the same time.

    We do your protection coordination study

    We model the system, calculate the short circuit and set the curves of every relay so the one closest to the fault clears first. Then we load the settings into the relays, remotely as well.

    See the coordination studySee remote relay configuration

    Related guides

    Overcurrent 50/51 and 50N/51N (PTOC, PIOC): How It WorksPhase overcurrent 50/51 and ground overcurrent 50N/51N: IEC and IEEE inverse curves, setting criteria, why it trips falsely and how it is tested.51V Protection (PVOC): Voltage Restrained OvercurrentWhat 51V protection is, voltage controlled versus voltage restrained overcurrent, how it is set, why it trips and how it is tested on a generator.

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