IDMT Tripping Time Calculator, Formula, Calculation, Example

IDMT tripping time calculation:

Enter the TMS, Current setting and fault current, then press the calculate button to get the tripping time based on the relay characteristics setting.

Choose:	IEC Standard InverseIEC Very InverseIEC Extremely InverseIEC Long-Time InverseIEEE Moderately InverseIEEE Very InverseIEEE Extremely InverseUS CO-8 InverseUS CO-2 Inverse
Enter Relay Pickup Current		Amps
Fault Current:		Amps
TMS/TD Setting:
IDMT Timing Result:		Sec

IDMT Tripping Time Calculation:

Inverse Definite Minimum Time defines the tripping time of the relay according to its fault current. It consists of four classifications such as Standard inverse, Very inverse, extreme inverse, and longtime standard inverse.

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. Hence the formula can be written as,

T_(s) = TMS (k / ((I_(A)/Is_(A)) ^α – 1))

or

The curve constant k and α will be changed based on the type of curves. But IEC rule 60255 defines the values of k and α could be considered as below.

IEC 62055 Curve Constant
Curve Type	α	k
Standard inverse	0.02	0.14
Long time standard inverse	1	120
Very inverse	1	13.5
Extremely inverse	2	80

IEEE Standard:

Also, the IEEE section C37.112-1996 defines the IDMT timing in seconds by the below formula,

t_(s) = TD ((A / (I/Is)^p – 1) + B)

here TD = TMS/7

or

Here,

A, B, p are the curve constant and I = Actual current in Amps and Is = Setting current in Amps.

IEEE Tripping Curves Constant
Curve type	p	A	B
Inverse	0.02	0.0515	0.114
Very inverse	2	19.61	0.491
Extremely inverse	2	28.2	0.1217

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 will be

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

IDMT Calculation Example:

Let us calculate the IDMT tripping time of the relay which carries 3A, and it have pickup current of 1 A.  and the time dial is 1?

From Above,

Relay Pickup Current: 1 (A)

Fault Current: 3 (A)

Time Multiplier Setting: 1

Standard Inverse:

tripping Time: 6.302 (S)

Tip Curve: IEC 60255 Very Inverse

Tripping Time: 6.75 (S).

Tip Curve: IEC 60255 Extremely Inverse:

Tripping Time: 10 (S)

Tip Curve: IEC 60255 Long-Time Inverse:

Tripping Time: 60 (S)

Tip Curve: IEEE Moderately Inverse:

Tripping Time: 0.347 (S)

Tip Curve: IEEE Very Inverse:

Tripping Time: 0.42 (S)

Tip Curve: IEEE Extremely Inverse:

Tripping Time: 0.521 (S)

Tip Curve: US CO8 Inverse:

Tripping Time: 0.132 (S)

Tip Curve: US CO2 Inverse:

Tripping Time: 0.156 (S)