IDMT Tripping Time Calculation, Formula, Example

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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.

Here the tripping sensitivity order will be

Extreme inverse > very Inverse > Standard Inverse > Long Time Standard Inverse.

Here, long time standard inverse consist of least sensitivity and the extreme inverse consist of higher sensitivity.

According to IEC 60255 IDMT Tripping Time t(s) is equal to the Time Setting Multiplier (TMS) times of the curve constant k divided by the power of curve constant α of ratio of actual current I(A) in Amps to Current setting Is(A) in amps minus 1.

IEC 60255 IDMT (TOC) Trip Curves

IDMT formula

Where:

  • Is is the current setting.

  • I is the actual current.

  • k and α are the curve type constants

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

IDMT (TOC) Trip Curves

Where:

  • Is is the current setting.

  • I is the actual current.

  • k and α are the curve type constants.

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

American standard IDMT relay tripping Calculation:

According to American standard the over current relay is classified based on the following,

  • Definite minimum- CO-6.

  • Moderately inverse – CO-7

  • Inverse, CO-8.

  • Very inverse – CO-9

  • Extremely inverse – CO-11

The formula for co-8 inverse curve will be

t(s) = TD (0.18 + (5.95 / (I/Is)2 – 1))

The formula for co-6 inverse curve will be

t(s) = TD (0.11858 + (0.16758 / (I/Is)0.02 – 1))

READ HERE  Complex Numbers (Definition, Formulas, Examples)

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