# 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.

## Calculator Parameters

Inverse Time Over Current is also referred to as Time Over Current (TOC),  or Inverse Definite Minimum Time (IDMT). It means that the trip time is inversely proportional to the fault current. The trip time is calculated from the following 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 or TD setting.
• IEC time multiplier setting (TMS).
• IEEE time dial (TD). In some relays and literature, a TDM (Time Dial Multiplier) is used, instead of a TD (Time Dial). The relationship is as follows: $$TDM = \displaystyle \frac {TD}{7}$$

## IEC 60255 Trip Curves

Equation for trip time:

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

Where,

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

Equation constants:

Curve type k α
Standard inverse 0.140 0.020
Very inverse 13.5 1
Extremely inverse 80 2
Long time standard inverse 120 1

## IEEE C37.112-1996 Trip Curves

Equation for trip time:

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

Where,

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

As mentioned, a TDM (Time Dial Multiplier) is sometimes used instead of TD (Time Dial). The relationship is:

$$TDM = \displaystyle \frac {TD}{7}$$
Curve type A B p
Moderately inverse 0.0515 0.114 0.02
Very inverse 19.61 .491 2
Extremely inverse 28.2 0.1217 2.0
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