IDMT is an abbreviation for Inverse Definite Minimum Time. Essentially, an IDMT curve informs us how long a protective relay will wait before tripping when it discovers an overcurrent fault.

The “Inverse” portion is that the larger the fault current, the quicker the relay will trip. The “Definite Minimum Time” portion ensures that even when the fault current is extremely high, the relay waits for an infinitesimally small amount of time before tripping — it doesn’t simply trip right away.

This behavior is important as it provides both sensitivity and coordination in electrical systems. It enables downstream protection devices to clear fault locally prior to upstream devices activating, which enables us to hold system stability.

There are several kinds of IDMT curves depending on their rate of operation:

• – Standard Inverse (SI)
• – Very Inverse (VI)
• – Extremely Inverse (EI)

Each has its specific formula for finding the operating time.

How to Calculate IDMT Relay Operating Time

This is what you should do to calculate the operating time:

Find the Plug Setting Multiplier (PSM)

This is the fault current to set current ratio of the relay.

Use the Operating Time Formula:

Depending on the curve type, you can use different formulas to calculate the time. For a Standard Inverse curve (IEC 60255-151):

where:

• t = operating time in seconds
• TMS = Time Multiplier Setting

Other formulas you might need are:

• Very Inverse:



• Extremely Inverse:

Practical Example of an IDMT Calculation

Let’s work through an example.

Here’s what we’ve got:

• – Feeder Load Current: 384 A
• – Minimum Fault Current: 11,000 A
• – CT Ratio: 600/1
• – Relay Plug Setting: 2.5 A
• – Time Multiplier Setting (TMS): 0.1
• – Relay Characteristic: Standard Inverse

Step 1: Find PSM

The Plug Setting Multiplier (PSM) is the fault current divided by the product of the CT ratio and the relay plug setting:

Step 2: Calculate Operating Time

For a Standard Inverse characteristic, the operating time 𝑡 is given by:

Using the Standard Inverse formula:

Thus, the relay will trip in approximately 0.2745 seconds after the fault is detected.

Other Scenarios

What if we used a different curve type? Let’s see:

Very Inverse:

Extremely Inverse:

Thus, based on which curve you pick, the relay might trip even quicker!

One thing I have to stress is the importance of the Time Multiplier Setting (TMS). It’s not a random number you select. The TMS helps you to synchronize the action among several relays in the same network. By adjusting the TMS, you can make the nearest relay to the fault trip first, and if that fails, the next one will act — a principle we call backup protection.

You’ll find IDMT relays everywhere — in industrial switchboards, substations, even large commercial facilities. Whenever you need multiple levels of protection in concert, IDMT settings are your best choice. I for one like the way they offer us flexibility to adjust system response without over-complicating.

Before you put your calculated settings into the field, it’s actually very important to check them with software simulation tools or relay test kits. Every now and then real-world situations like CT saturation or cable impedance will have a slight effect on your theoretical values. Taking the extra time to check can save you a whole lot of trouble later on.