Master Guide: Calculating IDMT Overcurrent and Earth Fault Settings (50/51).

In Previous days we have heard many times that a transformer at the post got fire, Transformer, Motors all have a huge costs, for using these efficiently we need reliability, for this reason we use protection Systems. The most common form is the Inverse Definite Minimum Time (IDMT) overcurrent and earth fault protection, designated by ANSI codes 51 (Time Overcurrent) and 50 (Instantaneous Overcurrent).

This article contains information about how to Calculate the Pick up ampere to the instantaneous tripping ampere.

1. Understanding the ANSI 50/51 Designations

Before going into calculations, we first need to know the basics of ANSI 50/51.

ANSI 50 (Instantaneous Overcurrent): This function operates without any intentional delays as soon as the current exceeds a specific threshold. It is usually set in much higher amperes than Inverse.
ANSI 51 (IDMT Overcurrent): It is called Inverse; the higher the ampere gets, the faster it trips. This allows the inrush current to settle down into the system, also holding the line so it doesn't flows all over the circuit to make a mess(Burning Wires, Cores, etc.)

2. The IDMT Relay Characteristics (IEC 60255)

The tripping time of an IDMT relay is governed by standardized mathematical formulas. According to IEC 60255, the standard operating time ( $t$ ) can be calculated as:

Where:

t: Operating time in seconds.
TMS: Time Multiplier Setting (also known as Time Dial).
I: Actual fault current.
Is: Pickup current (the setting).
$k$ and 𝛼: Constants based on the curve type selected.

Common Curve Constants:

Curve Type	k	α
Standard Inverse (SI)	0.14	0.02
Very Inverse (VI)	13.5	1.0
Extremely Inverse (EI)	80.0	2.0
Long Time Inverse (LTI)	120.0	1.0

3. Step-by-Step Calculation for Overcurrent (51)

Step 1: Determine the Full Load Current (FLC)

First, identify the maximum load current for a transformer:

I_{FLC} = \frac{kVA}{\sqrt{3} \times V_L}

I_{FLC} = \frac{kVA}{\sqrt{3} \times V_L}

I_{FLC} = \frac{kVA}{\sqrt{3} \times V_L}

I_{FLC} = \frac{kVA}{\sqrt{3} \times V_L}

I_{FLC} = \frac{kVA}{\sqrt{3} \times V_L}

I_{FLC} = \frac{kVA}{\sqrt{3} \times V_L}

I_{FLC} = \frac{kVA}{\sqrt{3} \times V_L}

I_{FLC} = \frac{kVA}{\sqrt{3} \times V_L}

I_{FLC} = \frac{kVA}{\sqrt{3} \times V_L}

I_{FLC} = \frac{kVA}{\sqrt{3} \times V_L}

I_{FLC} = \frac{kVA}{\sqrt{3} \times V_L}

I_{FLC} = \frac{kVA}{\sqrt{3} \times V_L}

Step 2: Set the Plug Setting (Pickup Current)

The pickup current must be higher than the FLC to avoid tripping at Full Load without reaching at the danger zone.

To avoid this, we will get the pickup current 110%-125% of FLC so that it doesn't trip while using the system at full load, also keeping the protection just before the danger zone.

Result: The relay will internally start the timer after it crosses it's set pickup current.

Step 3: Determine the Fault Current

You want to keep the tripping current & Time delay higher than the downstream breakers, so the the downstream breaker trips first and the main relay acts as a backup.

Step 4: Calculate the Time Multiplier Setting (TMS)

$t_{required}$ : The operating time you want (e.g., 0.5 seconds).
$I$ : The Fault Current (from Step 3).
$I_s$ : The Setting Current (or Pickup Current, $I_{pickup}$ ).
$\frac{I}{I_s}$ : This is the Plug Setting Multiplier (PSM) we discussed earlier.
$k$ and 𝛼: These are constants based on the type of curve you choose.

4. Calculating Earth Fault Settings (51N)

Earth fault protection (51N) operates on the residual current of the three phases. Because the residual current in a balanced system is near zero, earth fault settings can be much more sensitive than overcurrent settings.

Pickup Setting: Usually $20\% \text{ to } 40\%$ of the CT primary rating or the transformer's rated current.
Coordination: Earth fault relays must be graded with other earth fault relays downstream. If the system uses a Neutral Grounding Resistor (NGR), the pickup must be set lower than the NGR's rated current (typically $50\%$ of the NGR rating).

Once I remembered when we had visited a site at a rural viillage for examination of HT Regulator before the three panel VCB for the 2 transformers. there the main single panel before the AVR was tripping instantly after closing the VCB for the AVR feeder. later we discovered thst it had no NGR and the floating neutral was causing it to trip.

5. Coordination and Discrimination (The 0.3s Rule)

Selectivity is achieved through grading margins. When two relays are in series, the upstream relay must wait long enough for the downstream relay to clear the fault. The standard grading margin is typically 0.3 to 0.4 seconds.

This margin accounts for:

Circuit Breaker Interrupting Time: ~0.05s to 0.1s.
Relay Overshoot: ~0.05s.
CT Errors and Tolerances: ~0.1s.

Example: If a downstream breaker clears a fault in 0.1s (Instantaneous 50), the upstream IDMT relay should be timed to trip at $0.1s + 0.3s = 0.4s$ for that same fault magnitude.

6. Instantaneous Settings (50)

The instantaneous element is set to trip "instantaneously" for faults that far exceed the load current.

Setting Principle: Set the 50 element to $120\% \text{ to } 150\%$ of the maximum through-fault current seen by the downstream bus. This prevents the upstream breaker from tripping for a fault that the downstream breaker should handle (maintaining selectivity).

7. Practical Calculation Example

System Data:

Transformer: 2500 kVA, 11kV/433V.
CT Ratio: 200/5A.
Max Fault Current: 4000A.
Target: Grade with a downstream fuse that clears in 0.1s at 4000A.

1. Calculate FLC:

I_{FLC} = \frac{2500}{\sqrt{3} \times 11} \approx 131A

I_{FLC} = \frac{2500}{\sqrt{3} \times 11} \approx 131A

I_{FLC} = \frac{2500}{\sqrt{3} \times 11} \approx 131A

I_{FLC} = \frac{2500}{\sqrt{3} \times 11} \approx 131A

8. Common Pitfalls in IDMT Calculations

A. CT Saturation

During high-magnitude faults, CTs can saturate, leading to distorted secondary currents. This may cause the relay to "see" less current than exists, leading to delayed tripping. Ensure the CT accuracy class (e.g., 5P10 or 10P20) is sufficient for the calculated fault levels.

B. "Sympathetic" Tripping

In earth fault protection, healthy feeders might trip due to capacitive discharge during a fault on a parallel feeder. This is why transiently stable settings or directional relays (67N) are often required in cable-heavy networks.

C. Inrush Current

Transformers draw a high "magnetizing inrush" when energized typically $8\text{--}12 \times FLC$ . The IDMT curve (specifically the Extremely Inverse curve) is often chosen because its shape matches the inrush decay, preventing nuisance trips during energization.

9. Conclusion

Technical Comparison: IDMT (51) vs. Instantaneous (50) Overcurrent

Calculating IDMT 50/51 settings is a balance between sensitivity and stability. By using the IEC 60255 formulas, maintaining a strict 0.3s grading margin, and accounting for full load currents, engineers can design a protection system that maximizes uptime and minimizes equipment damage.

For modern digital relays, these calculations are often handled by software (like ETAP or SKM), but understanding the manual derivation remains a critical skill for any power systems engineer to validate results and troubleshoot coordination issues.

How to calculate IDMT Overcurrent and Earth Fault Settings (50/51)

Master Guide: Calculating IDMT Overcurrent and Earth Fault Settings (50/51).

1. Understanding the ANSI 50/51 Designations