Glossary

Inverse Definite Minimum Time (IDMT) Curve

A family of time-current characteristic curves where the relay operating time is inversely proportional to fault current magnitude, with standard shapes including normal inverse, very inverse, and extremely inverse.

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PROTECTION COORDINATION

What is Inverse Definite Minimum Time (IDMT) Curve?

The foundational time-current characteristic defining how a protection relay's tripping speed varies inversely with fault current magnitude.

An Inverse Definite Minimum Time (IDMT) Curve is a time-current characteristic where the relay operating time is inversely proportional to the magnitude of the fault current; as current increases, the trip time decreases, eventually reaching a definite minimum time threshold. This behavior is defined by mathematical standards, primarily IEC 60255 and IEEE C37.112, which specify standard curve shapes such as Normal Inverse, Very Inverse, and Extremely Inverse to match the thermal damage characteristics of protected equipment.

The curve is shaped by two key settings: the pickup current (the threshold at which timing begins) and the Time Multiplier Setting (TMS) or time dial, which scales the entire curve vertically without changing its shape. The inverse characteristic enables selective coordination in radial distribution networks, ensuring the protective device closest to a fault trips fastest, while upstream devices provide backup protection with intentional time delays.

Time-Current Characteristic Fundamentals

Core Characteristics of IDMT Curves

The defining attributes that govern how an Inverse Definite Minimum Time relay translates measured fault current magnitude into a calculated operating time.

Inverse Time Principle

The core operating principle: operating time is inversely proportional to fault current magnitude. A higher fault current results in a faster trip. This natural characteristic provides automatic discrimination, as faults closer to the source (with higher current) are cleared more quickly than remote faults with lower magnitude, enhancing system stability.

Standard Curve Families

Defined by IEC 60255 and IEEE C37.112 standards, the primary curve shapes are:

Normal Inverse (NI): General purpose, moderate slope.
Very Inverse (VI): Steeper slope, coordinates well with fuse characteristics.
Extremely Inverse (EI): Very steep slope, ideal for transformer inrush and cold load pickup.
Long Time Inverse: Used for earth fault protection and motor starting.

Mathematical Formulation

The operating time t is calculated using the standard formula: t = TMS × (k / ((I/Is)^α - 1) + c) Where:

TMS (Time Multiplier Setting): A scalar that shifts the curve vertically.
I/Is: The multiple of the pickup current setting.
k, α, c: Constants that define the curve shape (e.g., for IEC NI: k=0.14, α=0.02, c=0).

Definite Minimum Time (DMT) Component

At very high multiples of pickup current, the inverse curve flattens into a definite minimum time. This prevents the relay from attempting to operate faster than its physical mechanism or interrupting current before a downstream device can clear the fault. It establishes a hard lower boundary for the operating time, ensuring coordination integrity.

Coordination Time Interval (CTI)

The intentional delay margin between upstream and downstream devices, typically 0.2 to 0.4 seconds. The IDMT curve shape is selected to ensure that for any given fault current, the upstream relay's operating time exceeds the downstream device's time by at least the CTI, accounting for breaker interrupting time, relay overshoot, and a safety margin.

Pickup Current and Plug Setting

The pickup current (Is) is the threshold above which the relay begins timing. It is set above normal load current but below the minimum expected fault current. The Plug Setting Multiplier (PSM) is the ratio of the actual fault current to the pickup setting. The relay only operates when PSM > 1, ensuring security against load fluctuations.

IDMT CURVE ESSENTIALS

Frequently Asked Questions

Clear, technically precise answers to the most common questions protection engineers ask about Inverse Definite Minimum Time curves and their application in modern power systems.

An Inverse Definite Minimum Time (IDMT) curve is a time-current characteristic used in protection relays where the relay's operating time is inversely proportional to the magnitude of the fault current. As the fault current increases, the tripping time decreases exponentially. The 'definite minimum time' component establishes a floor—a minimum operating time that the relay will not fall below, regardless of how high the fault current rises. This prevents nuisance tripping on transformer inrush currents and ensures coordination with downstream recloser controls and fuses. The curve is mathematically defined by the IEC 60255 and IEEE C37.112 standards, which specify the general equation: t = TMS × (k / ((I/Is)^α - 1) + c), where TMS is the Time Multiplier Setting, I/Is is the plug setting multiplier, and the constants k, α, and c define the curve shape.

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PROTECTION ENGINEERING

Related Terms

Core concepts that interact with IDMT curve selection and coordination in modern protection schemes.

Protection Coordination Study

An engineering analysis that selects pickup currents, time multiplier settings (TMS), and curve shapes to ensure the protective device closest to a fault trips first. The study plots IDMT curves on a log-log time-current coordination chart to verify that a downstream relay's curve lies entirely below and to the left of the upstream relay's curve, maintaining grading margins of 0.2-0.4 seconds between successive devices.

0.2-0.4s

Typical Grading Margin

Directional Overcurrent Protection

An overcurrent element that determines fault direction using a polarizing quantity (voltage or negative-sequence current). When combined with IDMT curves, directional elements enable selective coordination in meshed networks and parallel feeder configurations where fault current can flow in either direction. The relay only operates when both the current magnitude exceeds pickup and the fault direction is forward, preventing unnecessary tripping on reverse faults.

Adaptive Protection Scheme

A protection system that dynamically adjusts relay settings, coordination logic, or active protection groups in real time based on changes in grid topology, generation dispatch, or load conditions. When distributed generation connects or disconnects, the scheme may switch between normal inverse and very inverse IDMT curves to maintain proper coordination despite altered fault current levels. This is critical in networks with high inverter-based resource penetration.

Distributed Generation Fault Current

The fault current contribution from inverter-based resources (IBRs) like solar and battery storage, typically limited to 1.1-1.5 per unit of rated current. This low fault current creates challenges for conventional IDMT-based overcurrent protection because:

Fault current may fall below pickup thresholds
Coordination margins collapse when fault levels vary widely
Blinding occurs when DG infeed reduces utility fault current seen by the relay Solutions include voltage-controlled IDMT curves and differential protection.

1.1-1.5 pu

IBR Fault Current Limit

High-Impedance Fault Detection

The identification of faults where a conductor contacts a high-resistance surface (asphalt, sand, tree limbs), producing fault currents of 10-100A that conventional IDMT overcurrent protection cannot distinguish from normal load. Because the current magnitude never reaches pickup, the IDMT curve never initiates timing. Detection requires waveform analysis, harmonic signature recognition, or machine learning classifiers that identify the chaotic, non-linear current patterns characteristic of arcing high-impedance faults.

Recloser Control

An intelligent controller on a line recloser that executes multi-shot auto-reclosing sequences using IDMT or definite-time curves. The control coordinates with downstream sectionalizers and fuses through a fuse-saving or fuse-blowing strategy. In fuse-saving mode, the recloser uses a fast IDMT curve to trip before the fuse melts on temporary faults, then recloses after a dead time of 0.5-2 seconds. If the fault persists, it switches to a slower curve to let the fuse clear permanent faults.

0.5-2s

Recloser Dead Time

About the author

Prasad Kumkar

CEO & MD, Inference Systems

Prasad Kumkar is the CEO & MD of Inference Systems and writes about AI systems architecture, LLM infrastructure, model serving, evaluation, and production deployment. Over 5+ years, he has worked across computer vision models, L5 autonomous vehicle systems, and LLM research, with a focus on taking complex AI ideas into real-world engineering systems.

His work and writing cover AI systems, large language models, AI agents, multimodal systems, autonomous systems, inference optimization, RAG, evaluation, and production AI engineering.

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