Inverse Time Over Current (TOC/IDMT) relay trip time calculator.

The Inverse Time Over Current (TOC/IDMT) relay trip time calculator calculates the protection trip time according to IEC 60255 and IEEE C37.112-1996 protection curves.

Parameters

• Trip curve. Select from the standard set of IEC and IEEE curves.
• Relay pickup current (A). The electrical current pickup set point Is in the relay.
• Fault current (A). The expected short circuit fault current I.
• TMS (IEC) or TD (IEEE) setting.
• IEC Time Multiplier Setting (TMS).
• IEEE Time Dial (TD). In some relays a Time Dial Multiplier (TDM) is specified instead of a Time Dial (TD). See conversion here.

How to convert from Time Dial Multiplier (TDM) to a Time Dial (TD)?

For IEEE curves, convert from a Time Dial Multiplier (TDM) to Time Dial (TD) as follows:

$$TD = 7 \cdot TDM$$

What is Inverse Time Overcurrent (TOC)?

Inverse Time Over Current (TOC), also referred to as Time Over Current (TOC), or Inverse Definite Minimum Time (IDMT), means that the trip time is inversely proportional to the fault current.

What is IDMT?

Inverse Definite Minimum Time (IDMT), also referred to as Inverse Time Over Current (TOC), or Time Over Current (TOC), means that the trip time is inversely proportional to the fault current.

IEC 60255 IDMT (TOC) Trip Curves

The IDMT curve formula to calculate the trip time is:

$$t(I)= TMS \displaystyle \left( \frac {k}{\displaystyle \left(\frac{I}{Is}\right)^\alpha-1}\right)$$

Where:

• Is is the current setting.
• I is the actual current.
• k and α are the curve type constants. See table below.

IEC 60255 equation constants

Curve type k α
IEC standard inverse curve 0.140 0.020
IEC very inverse curve 13.5 1
IEC extremely inverse curve 80 2
IEC long time standard inverse curve 120 1

IEEE C37.112-1996 IDMT (TOC) Trip Curves

The IDMT curve formula to calculate the trip time is:

$$t(I)= TD \displaystyle \left( \frac {A}{\displaystyle \left(\frac{I}{Is}\right)^p-1}+B\right)$$

Where:

• Is is the current setting.
• I is the actual current.
• k and α are the curve type constants. See table below.

As mentioned in parameters, a Time Dial Multiplier (TDM) is sometimes specified by the relay manufacturer instead of a Time Dial (TD). See conversion here.

Curve type A B p
IEEE moderately inverse curve 0.0515 0.114 0.02
IEEE very inverse curve 19.61 0.491 2
IEEE extremely inverse curve 28.2 0.1217 2.0