IDMT Relay Curve Formula

Inverse Definite Minimum Time (IDMT) relays are used in protection systems to detect and respond to overcurrent conditions in electrical networks. The IDMT relay curve describes the relationship between the fault current magnitude and the time it takes for the relay to operate. The curve is typically characterized by its slope and the pickup current level.

The formula for the IDMT relay curve is generally given by:

​Where:

• $T$ is the time of operation for the relay.
• $K$ is a constant.
• $I$ is the fault current magnitude.
• Ip​ is the pickup current level of the relay.
• $n$ is the time multiplier exponent, which determines the slope of the curve.

The values of $K$ and $n$ depend on the specific type of IDMT relay curve you’re using. Different standards and relay manufacturers might have slightly different curves and coefficients. The time $T$ is the time it takes for the relay to operate once the fault current exceeds the pickup current level.

IDMT Relay Time Calculator with Graph

Fault Current (I):
Pickup Current (I_p):
Time Multiplier (n):
Calculate Time

Lets understand the Factors

1. T – Time of Operation for the Relay: In the context of an IDMT relay, “T” represents the time it takes for the relay to activate and respond to a fault condition in the electrical system. When a fault, such as a short circuit or overload, occurs in the system, the current flowing through the circuit can increase significantly. The IDMT relay is designed to detect this increase in current and trip (operate) the protective circuit breaker to isolate the faulty part of the system. The time “T” is the duration between the moment the fault current exceeds the pickup current level and the moment the relay actually trips the circuit breaker.
2. K – Constant: “K” is a constant value that is part of the formula. This constant is used to determine the relationship between fault current, pickup current, time multiplier, and the resulting operation time of the relay. The specific value of “K” depends on the relay’s design, its intended application, and the chosen units for current and time.
3. I – Fault Current Magnitude: “I” represents the magnitude of the fault current that flows through the electrical system when a fault occurs. Fault currents can arise from various situations such as short circuits, ground faults, or other abnormal conditions. The fault current is a critical parameter because it directly influences the relay’s operation time. As the fault current increases, the relay should respond more quickly to isolate the fault and prevent damage to the system.
4. Ip – Pickup Current Level of the Relay: “Ip” represents the pickup current level of the IDMT relay. This is the current magnitude at which the relay begins to monitor and respond to the system. When the actual current exceeds the pickup current level, the relay starts measuring the time it takes for the fault current to reach a certain threshold, based on the curve equation. The pickup current is set to a value that allows the relay to distinguish between normal operating conditions and fault conditions.
5. n – Time Multiplier Exponent: “n” is a parameter known as the time multiplier exponent. It’s a value that determines the slope of the IDMT relay curve. This exponent influences how quickly the operation time of the relay changes with varying fault current levels. Smaller values of “n” result in steeper curves where the relay operates more quickly for small increases in fault current, while larger values of “n” lead to flatter curves where the relay takes longer to operate.

In summary, the IDMT relay curve formula describes how the operating time of the relay depends on the relationship between fault current magnitude, pickup current level, and the time multiplier exponent. The constants “K” and “n” are used to fine-tune the curve’s behavior to suit the specific requirements of the protection scheme and the characteristics of the electrical system being monitored.

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