IDMT Overcurrent Relay Calculator: Operating Time, Plug Setting Multiplier and Grading

Find how long an inverse-time overcurrent relay takes to trip and grade the relay behind it.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose the IEC curve and enter the fault current, the CT primary and secondary rating, the plug setting (as a percent of the CT secondary) and the time multiplier setting.

The calculator turns the fault current into the current in the relay, finds the plug setting multiplier (PSM) and gives the operating time t = TMS x k / (PSM^alpha - 1).

To grade an upstream relay, enter its current setting and a grading margin. It gives the time the upstream relay must take and the time multiplier that does it.

Formulas used

  • t = \mathrm{TMS}\cdot\frac{k}{\mathrm{PSM}^{\alpha} - 1}
  • \mathrm{PSM} = \frac{I_f/\mathrm{CT\ ratio}}{I_s}
  • \mathrm{TMS}_2 = \frac{(t + m)(\mathrm{PSM}_2^{\alpha} - 1)}{k}

Worked example

With the default numbers in the calculator above:

  1. CT ratio and the fault current in the relay: 12.50 A in the relay (CT ratio 400/1)
  2. Relay current setting: 1.00 A secondary, which is 400.00 A primary
  3. Plug setting multiplier: 12.50
  4. Operating time (Standard inverse: k = 0.14, alpha = 0.02): 0.81 s
  5. Upstream relay: the time it must take (this relay's time plus the grading margin): 1.21 s
  6. Upstream relay: the time multiplier setting needed (same curve): TMS about 0.37. Round up to the next setting on the relay

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What do the curve constants mean?

Standard inverse is k 0.14 and alpha 0.02, very inverse 13.5 and 1, extremely inverse 80 and 2 and long-time inverse 120 and 1. A larger alpha makes the relay much faster at high current.

What is a grading margin?

The extra time given to the upstream relay so it does not operate before the downstream breaker has cleared the fault. 0.3 to 0.5 s is usual.

Where should the plug setting be?

Above the full-load current of the circuit, usually 1.05 to 1.3 times it, and well below the smallest fault current.

What is the plug setting multiplier?

The fault current as a multiple of the current setting. The relay only operates when it is above 1.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: IEC 60255-151, Measuring relays and protection equipment, functional requirements for over/under current protection; Network Protection and Automation Guide.

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